August 20 2021
I demonstrate that attempts to detect DIF using a logistic regression approach and estimated factor scores face strong bias when the two groups have latent traits measured with
I also show that attempting to get around the problem using Bayes estimates for factor scores seems to eliminate the excess type-I error problem.
It remains to be seen if the Bayes factor score estimate approach has any degree of statistical power.
. local nobs=10001 // total number of examinees
. clear
. set seed 3481
. simirt , nitems(30) ///
> pvalue( ///
> .050 .050 .050 .050 .050 ///
> .075 .075 .075 .075 .075 ///
> .100 .100 .100 .100 .100 ///
> .2 .2 .2 .2 .2 ///
> .4 .4 .4 .4 .4 ///
> .5 .5 .5 .5 .5 ) ///
> nobs(`nobs')
there are 30 items
true 2PL parameters sample statistics
input parameters ──────────────────────── 2PL
────────────────────────── slope slope loca- ───────────────────
item corr threshold Pvalue (D=1.7) (D=1.0) tion corr Pvalue slope(D=1.7) location
─────────────────────────────────────────────────────────────────────────────────────────────────
1 0.707 1.645 0.050 1.000 1.699 2.327 0.709 0.050 1.005 2.315
2 0.707 1.645 0.050 1.000 1.699 2.327 0.702 0.049 0.987 2.360
3 0.707 1.645 0.050 1.000 1.699 2.327 0.703 0.051 0.987 2.329
4 0.707 1.645 0.050 1.000 1.699 2.327 0.708 0.050 1.003 2.327
5 0.707 1.645 0.050 1.000 1.699 2.327 0.707 0.053 0.999 2.292
6 0.707 1.440 0.075 1.000 1.699 2.036 0.704 0.076 0.992 2.037
7 0.707 1.440 0.075 1.000 1.699 2.036 0.708 0.075 1.001 2.031
8 0.707 1.440 0.075 1.000 1.699 2.036 0.709 0.073 1.004 2.051
9 0.707 1.440 0.075 1.000 1.699 2.036 0.710 0.078 1.010 2.001
10 0.707 1.440 0.075 1.000 1.699 2.036 0.705 0.081 0.995 1.986
11 0.707 1.282 0.100 1.000 1.699 1.813 0.705 0.102 0.995 1.799
12 0.707 1.282 0.100 1.000 1.699 1.813 0.718 0.103 1.030 1.758
13 0.707 1.282 0.100 1.000 1.699 1.813 0.704 0.104 0.992 1.790
14 0.707 1.282 0.100 1.000 1.699 1.813 0.702 0.099 0.987 1.830
15 0.707 1.282 0.100 1.000 1.699 1.813 0.703 0.100 0.988 1.822
16 0.707 0.842 0.200 1.000 1.699 1.190 0.716 0.201 1.025 1.169
17 0.707 0.842 0.200 1.000 1.699 1.190 0.708 0.194 1.004 1.218
18 0.707 0.842 0.200 1.000 1.699 1.190 0.710 0.195 1.009 1.209
19 0.707 0.842 0.200 1.000 1.699 1.190 0.705 0.202 0.993 1.184
20 0.707 0.842 0.200 1.000 1.699 1.190 0.713 0.204 1.016 1.163
21 0.707 0.253 0.400 1.000 1.699 0.358 0.709 0.392 1.005 0.386
22 0.707 0.253 0.400 1.000 1.699 0.358 0.702 0.393 0.987 0.388
23 0.707 0.253 0.400 1.000 1.699 0.358 0.713 0.395 1.017 0.374
24 0.707 0.253 0.400 1.000 1.699 0.358 0.699 0.410 0.978 0.327
25 0.707 0.253 0.400 1.000 1.699 0.358 0.708 0.394 1.003 0.379
26 0.707 0.000 0.500 1.000 1.699 0.000 0.709 0.501 1.006 -0.003
27 0.707 0.000 0.500 1.000 1.699 0.000 0.703 0.496 0.989 0.013
28 0.707 0.000 0.500 1.000 1.699 0.000 0.705 0.502 0.995 -0.007
29 0.707 0.000 0.500 1.000 1.699 0.000 0.705 0.504 0.994 -0.013
30 0.707 0.000 0.500 1.000 1.699 0.000 0.714 0.498 1.021 0.009
─────────────────────────────────────────────────────────────────────────────────────────────────
All items scored 0/1. The Pvalue is the proportion item=1. Corr is the correlation of the latent
trait and the latent response variable underlying the item (i.e., the standardized factor
loading). 2PL refers to two parameter logistic item response theory models, which can be
parameterized with a scaling constant D that often assumed to be 1.0 or 1.7.
. keep u* q
. gen focal=_n>`c(N)'/2
. gen id=_n
. scoreit u* , gen(sumscore)
Applying the .4 rule: more than 40% of items must be non-missing to have a total score.
NB: 0 observations set to missing on sumscore due to missing on all items
Test scale = mean(unstandardized items)
Average interitem covariance: .0339592
Number of items in the scale: 30
Scale reliability coefficient: 0.9032
Item Means +/- 1 SD from mean on scale
Item High Low
────────────────────────────────────────
u1 0.24 0.00
u2 0.23 0.00
u3 0.23 0.00
u4 0.24 0.00
u5 0.24 0.00
u6 0.32 0.00
u7 0.35 0.00
u8 0.31 0.00
u9 0.36 0.00
u10 0.34 0.00
u11 0.42 0.00
u12 0.43 0.00
u13 0.43 0.00
u14 0.39 0.00
u15 0.39 0.00
u16 0.64 0.00
u17 0.62 0.00
u18 0.63 0.00
u19 0.65 0.00
u20 0.64 0.00
u21 0.86 0.00
u22 0.86 0.00
u23 0.88 0.00
u24 0.88 0.00
u25 0.87 0.00
u26 0.93 0.00
u27 0.93 0.00
u28 0.93 0.00
u29 0.94 0.00
u30 0.94 0.00
. table focal, c(min sumscore max sumscore med sumscore)
──────────┬────────────────────────────────────────────
focal │ min(sumscore) max(sumscore) med(sumscore)
──────────┼────────────────────────────────────────────
0 │ 0 30 5
1 │ 0 29 5
──────────┴────────────────────────────────────────────
. table focal, c(min q max q med q)
──────────┬───────────────────────────────────
focal │ min(q) max(q) med(q)
──────────┼───────────────────────────────────
0 │ -3.345039 3.336954 .0195344
1 │ -3.581353 3.495501 .0213594
──────────┴───────────────────────────────────
. tempfile f1
. save `f1' , replace
(note: file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000004 not found)
file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000004 saved
Note that I use WLSMV/theta because I want to switch to Bayes later on.
. runmplus u1-u30 , ///
> estimator(wlsmv) parameterization(theta) ///
> cat(all) model(f by u1-u30*; f@1;) ///
> output(svalues;) savelog(foo)
Mplus VERSION 8.6 (Mac)
MUTHEN & MUTHEN
Running input file '__000001.inp'...
Beginning Time: 13:11:27
Ending Time: 13:11:30
Elapsed Time: 00:00:03
Output saved in '__000001.out'.
THE MODEL ESTIMATION TERMINATED NORMALLY
Mplus VERSION 8.6 (Mac)
MUTHEN & MUTHEN
08/20/2021 1:11 PM
INPUT INSTRUCTIONS
TITLE:
Variable List -
u1 :
u2 :
u3 :
u4 :
u5 :
u6 :
u7 :
u8 :
u9 :
u10 :
u11 :
u12 :
u13 :
u14 :
u15 :
u16 :
u17 :
u18 :
u19 :
u20 :
u21 :
u22 :
u23 :
u24 :
u25 :
u26 :
u27 :
u28 :
u29 :
u30 :
DATA:
FILE = __000001.dat ;
VARIABLE:
NAMES =
u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11 u12 u13 u14 u15 u16 u17 u18
u19 u20 u21 u22 u23 u24 u25 u26 u27 u28 u29 u30 ;
MISSING ARE ALL (-9999) ;
CATEGORICAL =
all
;
ANALYSIS:
ESTIMATOR = wlsmv ;
PARAMETERIZATION = theta ;
OUTPUT:
svalues ;
MODEL:
f by u1-u30* ;
f@1 ;
INPUT READING TERMINATED NORMALLY
Variable List -
u1 :
u2 :
u3 :
u4 :
u5 :
u6 :
u7 :
u8 :
u9 :
u10 :
u11 :
u12 :
u13 :
u14 :
u15 :
u16 :
u17 :
u18 :
u19 :
u20 :
u21 :
u22 :
u23 :
u24 :
u25 :
u26 :
u27 :
u28 :
u29 :
u30 :
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 10001
Number of dependent variables 30
Number of independent variables 0
Number of continuous latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
U7 U8 U9 U10 U11 U12
U13 U14 U15 U16 U17 U18
U19 U20 U21 U22 U23 U24
U25 U26 U27 U28 U29 U30
Continuous latent variables
F
Estimator WLSMV
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Parameterization THETA
Link PROBIT
Input data file(s)
__000001.dat
Input data format FREE
SUMMARY OF DATA
Number of missing data patterns 1
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 1.000
U2 1.000 1.000
U3 1.000 1.000 1.000
U4 1.000 1.000 1.000 1.000
U5 1.000 1.000 1.000 1.000 1.000
U6 1.000 1.000 1.000 1.000 1.000
U7 1.000 1.000 1.000 1.000 1.000
U8 1.000 1.000 1.000 1.000 1.000
U9 1.000 1.000 1.000 1.000 1.000
U10 1.000 1.000 1.000 1.000 1.000
U11 1.000 1.000 1.000 1.000 1.000
U12 1.000 1.000 1.000 1.000 1.000
U13 1.000 1.000 1.000 1.000 1.000
U14 1.000 1.000 1.000 1.000 1.000
U15 1.000 1.000 1.000 1.000 1.000
U16 1.000 1.000 1.000 1.000 1.000
U17 1.000 1.000 1.000 1.000 1.000
U18 1.000 1.000 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 1.000
U7 1.000 1.000
U8 1.000 1.000 1.000
U9 1.000 1.000 1.000 1.000
U10 1.000 1.000 1.000 1.000 1.000
U11 1.000 1.000 1.000 1.000 1.000
U12 1.000 1.000 1.000 1.000 1.000
U13 1.000 1.000 1.000 1.000 1.000
U14 1.000 1.000 1.000 1.000 1.000
U15 1.000 1.000 1.000 1.000 1.000
U16 1.000 1.000 1.000 1.000 1.000
U17 1.000 1.000 1.000 1.000 1.000
U18 1.000 1.000 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
U11 1.000
U12 1.000 1.000
U13 1.000 1.000 1.000
U14 1.000 1.000 1.000 1.000
U15 1.000 1.000 1.000 1.000 1.000
U16 1.000 1.000 1.000 1.000 1.000
U17 1.000 1.000 1.000 1.000 1.000
U18 1.000 1.000 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
U16 1.000
U17 1.000 1.000
U18 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U21 U22 U23 U24 U25
________ ________ ________ ________ ________
U21 1.000
U22 1.000 1.000
U23 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U26 U27 U28 U29 U30
________ ________ ________ ________ ________
U26 1.000
U27 1.000 1.000
U28 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.950 9497.000
Category 2 0.050 504.000
U2
Category 1 0.951 9514.000
Category 2 0.049 487.000
U3
Category 1 0.949 9492.000
Category 2 0.051 509.000
U4
Category 1 0.950 9504.000
Category 2 0.050 497.000
U5
Category 1 0.947 9475.000
Category 2 0.053 526.000
U6
Category 1 0.924 9244.000
Category 2 0.076 757.000
U7
Category 1 0.925 9247.000
Category 2 0.075 754.000
U8
Category 1 0.927 9270.000
Category 2 0.073 731.000
U9
Category 1 0.922 9225.000
Category 2 0.078 776.000
U10
Category 1 0.919 9195.000
Category 2 0.081 806.000
U11
Category 1 0.898 8978.000
Category 2 0.102 1023.000
U12
Category 1 0.897 8966.000
Category 2 0.103 1035.000
U13
Category 1 0.896 8964.000
Category 2 0.104 1037.000
U14
Category 1 0.901 9008.000
Category 2 0.099 993.000
U15
Category 1 0.900 8999.000
Category 2 0.100 1002.000
U16
Category 1 0.799 7987.000
Category 2 0.201 2014.000
U17
Category 1 0.806 8060.000
Category 2 0.194 1941.000
U18
Category 1 0.805 8049.000
Category 2 0.195 1952.000
U19
Category 1 0.798 7980.000
Category 2 0.202 2021.000
U20
Category 1 0.796 7965.000
Category 2 0.204 2036.000
U21
Category 1 0.608 6078.000
Category 2 0.392 3923.000
U22
Category 1 0.607 6075.000
Category 2 0.393 3926.000
U23
Category 1 0.605 6052.000
Category 2 0.395 3949.000
U24
Category 1 0.590 5905.000
Category 2 0.410 4096.000
U25
Category 1 0.606 6060.000
Category 2 0.394 3941.000
U26
Category 1 0.499 4992.000
Category 2 0.501 5009.000
U27
Category 1 0.504 5038.000
Category 2 0.496 4963.000
U28
Category 1 0.498 4981.000
Category 2 0.502 5020.000
U29
Category 1 0.496 4963.000
Category 2 0.504 5038.000
U30
Category 1 0.502 5025.000
Category 2 0.498 4976.000
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 60
Chi-Square Test of Model Fit
Value 417.505*
Degrees of Freedom 405
P-Value 0.3234
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.002
90 Percent C.I. 0.000 0.004
Probability RMSEA <= .05 1.000
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 155989.957
Degrees of Freedom 435
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.016
Optimum Function Value for Weighted Least-Squares Estimator
Value 0.14370107D-01
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F BY
U1 1.014 0.042 24.271 0.000
U2 0.977 0.042 23.160 0.000
U3 0.965 0.041 23.529 0.000
U4 0.981 0.041 23.974 0.000
U5 0.909 0.036 25.021 0.000
U6 0.978 0.036 27.108 0.000
U7 1.076 0.040 26.980 0.000
U8 0.979 0.037 26.512 0.000
U9 1.063 0.039 27.584 0.000
U10 0.998 0.036 27.652 0.000
U11 1.017 0.034 30.032 0.000
U12 1.049 0.035 29.831 0.000
U13 1.025 0.034 30.042 0.000
U14 0.953 0.032 29.613 0.000
U15 0.955 0.032 29.478 0.000
U16 1.002 0.028 36.239 0.000
U17 0.982 0.027 36.147 0.000
U18 1.005 0.028 36.121 0.000
U19 1.031 0.028 36.332 0.000
U20 0.995 0.027 36.637 0.000
U21 0.983 0.024 40.952 0.000
U22 1.012 0.025 41.171 0.000
U23 1.037 0.025 41.654 0.000
U24 0.995 0.024 41.012 0.000
U25 0.990 0.024 41.094 0.000
U26 1.005 0.024 41.129 0.000
U27 1.006 0.024 41.463 0.000
U28 1.031 0.025 41.248 0.000
U29 1.014 0.024 41.746 0.000
U30 1.069 0.025 42.107 0.000
Thresholds
U1$1 2.337 0.052 45.223 0.000
U2$1 2.317 0.052 44.597 0.000
U3$1 2.274 0.050 45.522 0.000
U4$1 2.308 0.050 45.849 0.000
U5$1 2.190 0.044 50.280 0.000
U6$1 2.006 0.041 49.416 0.000
U7$1 2.111 0.046 46.190 0.000
U8$1 2.033 0.042 48.574 0.000
U9$1 2.074 0.044 47.395 0.000
U10$1 1.979 0.040 49.288 0.000
U11$1 1.810 0.036 50.554 0.000
U12$1 1.829 0.037 49.201 0.000
U13$1 1.805 0.036 50.176 0.000
U14$1 1.776 0.034 52.200 0.000
U15$1 1.770 0.034 51.873 0.000
U16$1 1.184 0.025 48.104 0.000
U17$1 1.209 0.025 49.314 0.000
U18$1 1.218 0.025 48.697 0.000
U19$1 1.199 0.025 47.643 0.000
U20$1 1.170 0.024 48.191 0.000
U21$1 0.384 0.018 20.972 0.000
U22$1 0.388 0.019 20.883 0.000
U23$1 0.384 0.019 20.429 0.000
U24$1 0.323 0.018 17.722 0.000
U25$1 0.378 0.018 20.623 0.000
U26$1 -0.003 0.018 -0.170 0.865
U27$1 0.013 0.018 0.750 0.453
U28$1 -0.007 0.018 -0.390 0.697
U29$1 -0.013 0.018 -0.750 0.453
U30$1 0.009 0.018 0.490 0.624
Variances
F 1.000 0.000 999.000 999.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.690E-01
(ratio of smallest to largest eigenvalue)
IRT PARAMETERIZATION
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Item Discriminations
F BY
U1 1.014 0.042 24.271 0.000
U2 0.977 0.042 23.160 0.000
U3 0.965 0.041 23.529 0.000
U4 0.981 0.041 23.974 0.000
U5 0.909 0.036 25.021 0.000
U6 0.978 0.036 27.108 0.000
U7 1.076 0.040 26.980 0.000
U8 0.979 0.037 26.512 0.000
U9 1.063 0.039 27.584 0.000
U10 0.998 0.036 27.652 0.000
U11 1.017 0.034 30.032 0.000
U12 1.049 0.035 29.831 0.000
U13 1.025 0.034 30.042 0.000
U14 0.953 0.032 29.613 0.000
U15 0.955 0.032 29.478 0.000
U16 1.002 0.028 36.239 0.000
U17 0.982 0.027 36.147 0.000
U18 1.005 0.028 36.121 0.000
U19 1.031 0.028 36.332 0.000
U20 0.995 0.027 36.637 0.000
U21 0.983 0.024 40.952 0.000
U22 1.012 0.025 41.171 0.000
U23 1.037 0.025 41.654 0.000
U24 0.995 0.024 41.012 0.000
U25 0.990 0.024 41.094 0.000
U26 1.005 0.024 41.129 0.000
U27 1.006 0.024 41.463 0.000
U28 1.031 0.025 41.248 0.000
U29 1.014 0.024 41.746 0.000
U30 1.069 0.025 42.107 0.000
Item Difficulties
U1$1 2.304 0.060 38.156 0.000
U2$1 2.373 0.066 36.137 0.000
U3$1 2.356 0.065 36.299 0.000
U4$1 2.353 0.064 37.037 0.000
U5$1 2.409 0.066 36.279 0.000
U6$1 2.052 0.051 40.501 0.000
U7$1 1.961 0.046 42.902 0.000
U8$1 2.078 0.052 40.013 0.000
U9$1 1.952 0.045 43.053 0.000
U10$1 1.984 0.048 41.509 0.000
U11$1 1.779 0.041 43.888 0.000
U12$1 1.744 0.039 44.584 0.000
U13$1 1.761 0.040 44.120 0.000
U14$1 1.864 0.044 42.013 0.000
U15$1 1.854 0.044 41.972 0.000
U16$1 1.182 0.027 43.449 0.000
U17$1 1.232 0.028 43.470 0.000
U18$1 1.212 0.028 43.834 0.000
U19$1 1.162 0.026 43.885 0.000
U20$1 1.175 0.027 43.366 0.000
U21$1 0.390 0.019 20.659 0.000
U22$1 0.383 0.019 20.659 0.000
U23$1 0.370 0.018 20.312 0.000
U24$1 0.324 0.018 17.579 0.000
U25$1 0.382 0.019 20.369 0.000
U26$1 -0.003 0.018 -0.170 0.865
U27$1 0.013 0.018 0.750 0.453
U28$1 -0.007 0.017 -0.390 0.697
U29$1 -0.013 0.018 -0.750 0.453
U30$1 0.008 0.017 0.490 0.624
Variances
F 1.000 0.000 0.000 1.000
MODEL COMMAND WITH FINAL ESTIMATES USED AS STARTING VALUES
f BY u1*1.01409;
f BY u2*0.97653;
f BY u3*0.96534;
f BY u4*0.98097;
f BY u5*0.90888;
f BY u6*0.97777;
f BY u7*1.07641;
f BY u8*0.97867;
f BY u9*1.06260;
f BY u10*0.99782;
f BY u11*1.01746;
f BY u12*1.04867;
f BY u13*1.02499;
f BY u14*0.95264;
f BY u15*0.95452;
f BY u16*1.00153;
f BY u17*0.98187;
f BY u18*1.00501;
f BY u19*1.03146;
f BY u20*0.99537;
f BY u21*0.98347;
f BY u22*1.01198;
f BY u23*1.03699;
f BY u24*0.99536;
f BY u25*0.99005;
f BY u26*1.00510;
f BY u27*1.00563;
f BY u28*1.03124;
f BY u29*1.01361;
f BY u30*1.06863;
[ u1$1*2.33686 ];
[ u2$1*2.31682 ];
[ u3$1*2.27431 ];
[ u4$1*2.30823 ];
[ u5$1*2.18950 ];
[ u6$1*2.00644 ];
[ u7$1*2.11101 ];
[ u8$1*2.03322 ];
[ u9$1*2.07416 ];
[ u10$1*1.97926 ];
[ u11$1*1.80978 ];
[ u12$1*1.82851 ];
[ u13$1*1.80543 ];
[ u14$1*1.77559 ];
[ u15$1*1.77015 ];
[ u16$1*1.18424 ];
[ u17$1*1.20945 ];
[ u18$1*1.21787 ];
[ u19$1*1.19854 ];
[ u20$1*1.16959 ];
[ u21$1*0.38352 ];
[ u22$1*0.38790 ];
[ u23$1*0.38417 ];
[ u24$1*0.32265 ];
[ u25$1*0.37819 ];
[ u26$1*-0.00302 ];
[ u27$1*0.01333 ];
[ u28$1*-0.00702 ];
[ u29$1*-0.01338 ];
[ u30$1*0.00899 ];
f@1;
Beginning Time: 13:11:27
Ending Time: 13:11:30
Elapsed Time: 00:00:03
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2021 Muthen & Muthen
. runmplus_read_svalues , out(foo.out)
svalues.txt saved
local macro passes consistency check
matrix svalues in return results
. mat svalues = r(Svalues)
The reference group has answers to all 30 items.
. use `f1' , clear
. keep if focal~=1
(5,001 observations deleted)
. forvalues i=1/30 {
2. local l`i' = svalues[`i',1]
3. local t=`i'+30
4. local t`i' = svalues[`t',1]
5. local model "`model' f by u`i'@`l`i'' ;"
6. local model "`model' [u`i'$1@`t`i''] ;"
7. }
. runmplus u1-u30 , cat(all) idvariable(id) ///
> estimator(wlsmv) parameterization(theta) ///
> model(`model' f@1;) ///
> savedata(save=fscores; file=ref.dat;) ///
> savelog(foo)
Mplus VERSION 8.6 (Mac)
MUTHEN & MUTHEN
Running input file '__000001.inp'...
Beginning Time: 13:11:31
Ending Time: 13:11:33
Elapsed Time: 00:00:02
Output saved in '__000001.out'.
THE MODEL ESTIMATION TERMINATED NORMALLY
Mplus VERSION 8.6 (Mac)
MUTHEN & MUTHEN
08/20/2021 1:11 PM
INPUT INSTRUCTIONS
TITLE:
Variable List -
u1 :
u2 :
u3 :
u4 :
u5 :
u6 :
u7 :
u8 :
u9 :
u10 :
u11 :
u12 :
u13 :
u14 :
u15 :
u16 :
u17 :
u18 :
u19 :
u20 :
u21 :
u22 :
u23 :
u24 :
u25 :
u26 :
u27 :
u28 :
u29 :
u30 :
id :
DATA:
FILE = __000001.dat ;
VARIABLE:
NAMES =
u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11 u12 u13 u14 u15 u16 u17 u18
u19 u20 u21 u22 u23 u24 u25 u26 u27 u28 u29 u30 id ;
MISSING ARE ALL (-9999) ;
CATEGORICAL =
all
;
IDVARIABLE = id ;
ANALYSIS:
ESTIMATOR = wlsmv ;
PARAMETERIZATION = theta ;
OUTPUT:
SAVEDATA:
save=fscores ;
file=ref.dat ;
MODEL:
f by u1@1.01409 ;
[u1$1@2.33686] ;
f by u2@.97653 ;
[u2$1@2.31682] ;
f by u3@.96534 ;
[u3$1@2.27431] ;
f by u4@.98097 ;
[u4$1@2.30823] ;
f by u5@.90888 ;
[u5$1@2.1895] ;
f by u6@.97777 ;
[u6$1@2.00644] ;
f by u7@1.07641 ;
[u7$1@2.11101] ;
f by u8@.97867 ;
[u8$1@2.03322] ;
f by u9@1.0626 ;
[u9$1@2.07416] ;
f by u10@.99782 ;
[u10$1@1.97926] ;
f by u11@1.01746 ;
[u11$1@1.80978] ;
f by u12@1.04867 ;
[u12$1@1.82851] ;
f by u13@1.02499 ;
[u13$1@1.80543] ;
f by u14@.95264 ;
[u14$1@1.77559] ;
f by u15@.95452 ;
[u15$1@1.77015] ;
f by u16@1.00153 ;
[u16$1@1.18424] ;
f by u17@.98187 ;
[u17$1@1.20945] ;
f by u18@1.00501 ;
[u18$1@1.21787] ;
f by u19@1.03146 ;
[u19$1@1.19854] ;
f by u20@.99537 ;
[u20$1@1.16959] ;
f by u21@.98347 ;
[u21$1@.38352] ;
f by u22@1.01198 ;
[u22$1@.3879] ;
f by u23@1.03699 ;
[u23$1@.38417] ;
f by u24@.99536 ;
[u24$1@.32265] ;
f by u25@.99005 ;
[u25$1@.37819] ;
f by u26@1.0051 ;
[u26$1@-.00302] ;
f by u27@1.00563 ;
[u27$1@.01333] ;
f by u28@1.03124 ;
[u28$1@-.00702] ;
f by u29@1.01361 ;
[u29$1@-.01338] ;
f by u30@1.06863 ;
[u30$1@.00899] ;
f@1 ;
INPUT READING TERMINATED NORMALLY
Variable List -
u1 :
u2 :
u3 :
u4 :
u5 :
u6 :
u7 :
u8 :
u9 :
u10 :
u11 :
u12 :
u13 :
u14 :
u15 :
u16 :
u17 :
u18 :
u19 :
u20 :
u21 :
u22 :
u23 :
u24 :
u25 :
u26 :
u27 :
u28 :
u29 :
u30 :
id :
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 5000
Number of dependent variables 30
Number of independent variables 0
Number of continuous latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
U7 U8 U9 U10 U11 U12
U13 U14 U15 U16 U17 U18
U19 U20 U21 U22 U23 U24
U25 U26 U27 U28 U29 U30
Continuous latent variables
F
Variables with special functions
ID variable ID
Estimator WLSMV
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Parameterization THETA
Link PROBIT
Input data file(s)
__000001.dat
Input data format FREE
SUMMARY OF DATA
Number of missing data patterns 1
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 1.000
U2 1.000 1.000
U3 1.000 1.000 1.000
U4 1.000 1.000 1.000 1.000
U5 1.000 1.000 1.000 1.000 1.000
U6 1.000 1.000 1.000 1.000 1.000
U7 1.000 1.000 1.000 1.000 1.000
U8 1.000 1.000 1.000 1.000 1.000
U9 1.000 1.000 1.000 1.000 1.000
U10 1.000 1.000 1.000 1.000 1.000
U11 1.000 1.000 1.000 1.000 1.000
U12 1.000 1.000 1.000 1.000 1.000
U13 1.000 1.000 1.000 1.000 1.000
U14 1.000 1.000 1.000 1.000 1.000
U15 1.000 1.000 1.000 1.000 1.000
U16 1.000 1.000 1.000 1.000 1.000
U17 1.000 1.000 1.000 1.000 1.000
U18 1.000 1.000 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 1.000
U7 1.000 1.000
U8 1.000 1.000 1.000
U9 1.000 1.000 1.000 1.000
U10 1.000 1.000 1.000 1.000 1.000
U11 1.000 1.000 1.000 1.000 1.000
U12 1.000 1.000 1.000 1.000 1.000
U13 1.000 1.000 1.000 1.000 1.000
U14 1.000 1.000 1.000 1.000 1.000
U15 1.000 1.000 1.000 1.000 1.000
U16 1.000 1.000 1.000 1.000 1.000
U17 1.000 1.000 1.000 1.000 1.000
U18 1.000 1.000 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
U11 1.000
U12 1.000 1.000
U13 1.000 1.000 1.000
U14 1.000 1.000 1.000 1.000
U15 1.000 1.000 1.000 1.000 1.000
U16 1.000 1.000 1.000 1.000 1.000
U17 1.000 1.000 1.000 1.000 1.000
U18 1.000 1.000 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
U16 1.000
U17 1.000 1.000
U18 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U21 U22 U23 U24 U25
________ ________ ________ ________ ________
U21 1.000
U22 1.000 1.000
U23 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U26 U27 U28 U29 U30
________ ________ ________ ________ ________
U26 1.000
U27 1.000 1.000
U28 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.950 4752.000
Category 2 0.050 248.000
U2
Category 1 0.955 4773.000
Category 2 0.045 227.000
U3
Category 1 0.949 4744.000
Category 2 0.051 256.000
U4
Category 1 0.949 4743.000
Category 2 0.051 257.000
U5
Category 1 0.949 4746.000
Category 2 0.051 254.000
U6
Category 1 0.929 4643.000
Category 2 0.071 357.000
U7
Category 1 0.928 4641.000
Category 2 0.072 359.000
U8
Category 1 0.930 4648.000
Category 2 0.070 352.000
U9
Category 1 0.926 4632.000
Category 2 0.074 368.000
U10
Category 1 0.922 4608.000
Category 2 0.078 392.000
U11
Category 1 0.894 4468.000
Category 2 0.106 532.000
U12
Category 1 0.896 4478.000
Category 2 0.104 522.000
U13
Category 1 0.899 4496.000
Category 2 0.101 504.000
U14
Category 1 0.899 4495.000
Category 2 0.101 505.000
U15
Category 1 0.900 4499.000
Category 2 0.100 501.000
U16
Category 1 0.793 3967.000
Category 2 0.207 1033.000
U17
Category 1 0.803 4017.000
Category 2 0.197 983.000
U18
Category 1 0.805 4023.000
Category 2 0.195 977.000
U19
Category 1 0.801 4004.000
Category 2 0.199 996.000
U20
Category 1 0.795 3973.000
Category 2 0.205 1027.000
U21
Category 1 0.602 3011.000
Category 2 0.398 1989.000
U22
Category 1 0.605 3024.000
Category 2 0.395 1976.000
U23
Category 1 0.610 3052.000
Category 2 0.390 1948.000
U24
Category 1 0.593 2965.000
Category 2 0.407 2035.000
U25
Category 1 0.608 3040.000
Category 2 0.392 1960.000
U26
Category 1 0.506 2531.000
Category 2 0.494 2469.000
U27
Category 1 0.503 2515.000
Category 2 0.497 2485.000
U28
Category 1 0.499 2494.000
Category 2 0.501 2506.000
U29
Category 1 0.503 2517.000
Category 2 0.497 2483.000
U30
Category 1 0.506 2531.000
Category 2 0.494 2469.000
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 0
Chi-Square Test of Model Fit
Value 424.486*
Degrees of Freedom 465
P-Value 0.9110
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
90 Percent C.I. 0.000 0.002
Probability RMSEA <= .05 1.000
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 79339.170
Degrees of Freedom 435
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.025
Optimum Function Value for Weighted Least-Squares Estimator
Value 0.37896276D-01
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F BY
U1 1.014 0.000 999.000 999.000
U2 0.977 0.000 999.000 999.000
U3 0.965 0.000 999.000 999.000
U4 0.981 0.000 999.000 999.000
U5 0.909 0.000 999.000 999.000
U6 0.978 0.000 999.000 999.000
U7 1.076 0.000 999.000 999.000
U8 0.979 0.000 999.000 999.000
U9 1.063 0.000 999.000 999.000
U10 0.998 0.000 999.000 999.000
U11 1.017 0.000 999.000 999.000
U12 1.049 0.000 999.000 999.000
U13 1.025 0.000 999.000 999.000
U14 0.953 0.000 999.000 999.000
U15 0.955 0.000 999.000 999.000
U16 1.002 0.000 999.000 999.000
U17 0.982 0.000 999.000 999.000
U18 1.005 0.000 999.000 999.000
U19 1.031 0.000 999.000 999.000
U20 0.995 0.000 999.000 999.000
U21 0.983 0.000 999.000 999.000
U22 1.012 0.000 999.000 999.000
U23 1.037 0.000 999.000 999.000
U24 0.995 0.000 999.000 999.000
U25 0.990 0.000 999.000 999.000
U26 1.005 0.000 999.000 999.000
U27 1.006 0.000 999.000 999.000
U28 1.031 0.000 999.000 999.000
U29 1.014 0.000 999.000 999.000
U30 1.069 0.000 999.000 999.000
Thresholds
U1$1 2.337 0.000 999.000 999.000
U2$1 2.317 0.000 999.000 999.000
U3$1 2.274 0.000 999.000 999.000
U4$1 2.308 0.000 999.000 999.000
U5$1 2.190 0.000 999.000 999.000
U6$1 2.006 0.000 999.000 999.000
U7$1 2.111 0.000 999.000 999.000
U8$1 2.033 0.000 999.000 999.000
U9$1 2.074 0.000 999.000 999.000
U10$1 1.979 0.000 999.000 999.000
U11$1 1.810 0.000 999.000 999.000
U12$1 1.829 0.000 999.000 999.000
U13$1 1.805 0.000 999.000 999.000
U14$1 1.776 0.000 999.000 999.000
U15$1 1.770 0.000 999.000 999.000
U16$1 1.184 0.000 999.000 999.000
U17$1 1.209 0.000 999.000 999.000
U18$1 1.218 0.000 999.000 999.000
U19$1 1.199 0.000 999.000 999.000
U20$1 1.170 0.000 999.000 999.000
U21$1 0.384 0.000 999.000 999.000
U22$1 0.388 0.000 999.000 999.000
U23$1 0.384 0.000 999.000 999.000
U24$1 0.323 0.000 999.000 999.000
U25$1 0.378 0.000 999.000 999.000
U26$1 -0.003 0.000 999.000 999.000
U27$1 0.013 0.000 999.000 999.000
U28$1 -0.007 0.000 999.000 999.000
U29$1 -0.013 0.000 999.000 999.000
U30$1 0.009 0.000 999.000 999.000
Variances
F 1.000 0.000 999.000 999.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.000E+00
(ratio of smallest to largest eigenvalue)
IRT PARAMETERIZATION
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Item Discriminations
F BY
U1 1.014 0.000 0.000 1.000
U2 0.977 0.000 0.000 1.000
U3 0.965 0.000 0.000 1.000
U4 0.981 0.000 0.000 1.000
U5 0.909 0.000 0.000 1.000
U6 0.978 0.000 0.000 1.000
U7 1.076 0.000 0.000 1.000
U8 0.979 0.000 0.000 1.000
U9 1.063 0.000 0.000 1.000
U10 0.998 0.000 0.000 1.000
U11 1.017 0.000 0.000 1.000
U12 1.049 0.000 0.000 1.000
U13 1.025 0.000 0.000 1.000
U14 0.953 0.000 0.000 1.000
U15 0.955 0.000 0.000 1.000
U16 1.002 0.000 0.000 1.000
U17 0.982 0.000 0.000 1.000
U18 1.005 0.000 0.000 1.000
U19 1.031 0.000 0.000 1.000
U20 0.995 0.000 0.000 1.000
U21 0.983 0.000 0.000 1.000
U22 1.012 0.000 0.000 1.000
U23 1.037 0.000 0.000 1.000
U24 0.995 0.000 0.000 1.000
U25 0.990 0.000 0.000 1.000
U26 1.005 0.000 0.000 1.000
U27 1.006 0.000 0.000 1.000
U28 1.031 0.000 0.000 1.000
U29 1.014 0.000 0.000 1.000
U30 1.069 0.000 0.000 1.000
Item Difficulties
U1$1 2.304 0.000 0.000 1.000
U2$1 2.373 0.000 0.000 1.000
U3$1 2.356 0.000 0.000 1.000
U4$1 2.353 0.000 0.000 1.000
U5$1 2.409 0.000 0.000 1.000
U6$1 2.052 0.000 0.000 1.000
U7$1 1.961 0.000 0.000 1.000
U8$1 2.078 0.000 0.000 1.000
U9$1 1.952 0.000 0.000 1.000
U10$1 1.984 0.000 0.000 1.000
U11$1 1.779 0.000 0.000 1.000
U12$1 1.744 0.000 0.000 1.000
U13$1 1.761 0.000 0.000 1.000
U14$1 1.864 0.000 0.000 1.000
U15$1 1.854 0.000 0.000 1.000
U16$1 1.182 0.000 0.000 1.000
U17$1 1.232 0.000 0.000 1.000
U18$1 1.212 0.000 0.000 1.000
U19$1 1.162 0.000 0.000 1.000
U20$1 1.175 0.000 0.000 1.000
U21$1 0.390 0.000 0.000 1.000
U22$1 0.383 0.000 0.000 1.000
U23$1 0.370 0.000 0.000 1.000
U24$1 0.324 0.000 0.000 1.000
U25$1 0.382 0.000 0.000 1.000
U26$1 -0.003 0.000 0.000 1.000
U27$1 0.013 0.000 0.000 1.000
U28$1 -0.007 0.000 0.000 1.000
U29$1 -0.013 0.000 0.000 1.000
U30$1 0.008 0.000 0.000 1.000
Variances
F 1.000 0.000 0.000 1.000
SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES
SAMPLE STATISTICS
Means
F F_SE
________ ________
0.024 0.336
Covariances
F F_SE
________ ________
F 0.819
F_SE -0.071 0.008
Correlations
F F_SE
________ ________
F 1.000
F_SE -0.863 1.000
SAVEDATA INFORMATION
Save file
ref.dat
Order and format of variables
U1 F10.3
U2 F10.3
U3 F10.3
U4 F10.3
U5 F10.3
U6 F10.3
U7 F10.3
U8 F10.3
U9 F10.3
U10 F10.3
U11 F10.3
U12 F10.3
U13 F10.3
U14 F10.3
U15 F10.3
U16 F10.3
U17 F10.3
U18 F10.3
U19 F10.3
U20 F10.3
U21 F10.3
U22 F10.3
U23 F10.3
U24 F10.3
U25 F10.3
U26 F10.3
U27 F10.3
U28 F10.3
U29 F10.3
U30 F10.3
F F10.3
F_SE F10.3
ID I5
Save file format
32F10.3 I5
Save file record length 10000
Save missing symbol *
Beginning Time: 13:11:31
Ending Time: 13:11:33
Elapsed Time: 00:00:02
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2021 Muthen & Muthen
. clear
. runmplus_load_savedata , out(foo.out)
. rename f f_est
. rename f_se f_est_se
. tempfile reference
. save `reference' , replace
(note: file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000005 not found)
file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000005 saved
The focal group only answers questions 1-10.
. local model ""
. use `f1' , clear
. keep if focal==1
(5,000 observations deleted)
. forvalues i=1/10 {
2. local l`i' = svalues[`i',1]
3. local t=`i'+30
4. local t`i' = svalues[`t',1]
5. local model "`model' f by u`i'@`l`i'' ;"
6. local model "`model' [u`i'$1@`t`i''] ;"
7. }
. runmplus u1-u10 , cat(all) idvariable(id) ///
> estimator(wlsmv) parameterization(theta) ///
> model(`model' f@1;) ///
> savedata(save=fscores; file=foc.dat;) ///
> savelog(goo)
Mplus VERSION 8.6 (Mac)
MUTHEN & MUTHEN
Running input file '__000001.inp'...
Beginning Time: 13:11:34
Ending Time: 13:11:35
Elapsed Time: 00:00:01
Output saved in '__000001.out'.
THE MODEL ESTIMATION TERMINATED NORMALLY
Mplus VERSION 8.6 (Mac)
MUTHEN & MUTHEN
08/20/2021 1:11 PM
INPUT INSTRUCTIONS
TITLE:
Variable List -
u1 :
u2 :
u3 :
u4 :
u5 :
u6 :
u7 :
u8 :
u9 :
u10 :
id :
DATA:
FILE = __000001.dat ;
VARIABLE:
NAMES =
u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 id ;
MISSING ARE ALL (-9999) ;
CATEGORICAL =
all
;
IDVARIABLE = id ;
ANALYSIS:
ESTIMATOR = wlsmv ;
PARAMETERIZATION = theta ;
OUTPUT:
SAVEDATA:
save=fscores ;
file=foc.dat ;
MODEL:
f by u1@1.01409 ;
[u1$1@2.33686] ;
f by u2@.97653 ;
[u2$1@2.31682] ;
f by u3@.96534 ;
[u3$1@2.27431] ;
f by u4@.98097 ;
[u4$1@2.30823] ;
f by u5@.90888 ;
[u5$1@2.1895] ;
f by u6@.97777 ;
[u6$1@2.00644] ;
f by u7@1.07641 ;
[u7$1@2.11101] ;
f by u8@.97867 ;
[u8$1@2.03322] ;
f by u9@1.0626 ;
[u9$1@2.07416] ;
f by u10@.99782 ;
[u10$1@1.97926] ;
f@1 ;
INPUT READING TERMINATED NORMALLY
Variable List -
u1 :
u2 :
u3 :
u4 :
u5 :
u6 :
u7 :
u8 :
u9 :
u10 :
id :
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 5001
Number of dependent variables 10
Number of independent variables 0
Number of continuous latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
U7 U8 U9 U10
Continuous latent variables
F
Variables with special functions
ID variable ID
Estimator WLSMV
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Parameterization THETA
Link PROBIT
Input data file(s)
__000001.dat
Input data format FREE
SUMMARY OF DATA
Number of missing data patterns 1
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 1.000
U2 1.000 1.000
U3 1.000 1.000 1.000
U4 1.000 1.000 1.000 1.000
U5 1.000 1.000 1.000 1.000 1.000
U6 1.000 1.000 1.000 1.000 1.000
U7 1.000 1.000 1.000 1.000 1.000
U8 1.000 1.000 1.000 1.000 1.000
U9 1.000 1.000 1.000 1.000 1.000
U10 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 1.000
U7 1.000 1.000
U8 1.000 1.000 1.000
U9 1.000 1.000 1.000 1.000
U10 1.000 1.000 1.000 1.000 1.000
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.949 4745.000
Category 2 0.051 256.000
U2
Category 1 0.948 4741.000
Category 2 0.052 260.000
U3
Category 1 0.949 4748.000
Category 2 0.051 253.000
U4
Category 1 0.952 4761.000
Category 2 0.048 240.000
U5
Category 1 0.946 4729.000
Category 2 0.054 272.000
U6
Category 1 0.920 4601.000
Category 2 0.080 400.000
U7
Category 1 0.921 4606.000
Category 2 0.079 395.000
U8
Category 1 0.924 4622.000
Category 2 0.076 379.000
U9
Category 1 0.918 4593.000
Category 2 0.082 408.000
U10
Category 1 0.917 4587.000
Category 2 0.083 414.000
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 0
Chi-Square Test of Model Fit
Value 47.798*
Degrees of Freedom 55
P-Value 0.7437
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
90 Percent C.I. 0.000 0.007
Probability RMSEA <= .05 1.000
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 6319.812
Degrees of Freedom 45
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.027
Optimum Function Value for Weighted Least-Squares Estimator
Value 0.45244242D-02
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F BY
U1 1.014 0.000 999.000 999.000
U2 0.977 0.000 999.000 999.000
U3 0.965 0.000 999.000 999.000
U4 0.981 0.000 999.000 999.000
U5 0.909 0.000 999.000 999.000
U6 0.978 0.000 999.000 999.000
U7 1.076 0.000 999.000 999.000
U8 0.979 0.000 999.000 999.000
U9 1.063 0.000 999.000 999.000
U10 0.998 0.000 999.000 999.000
Thresholds
U1$1 2.337 0.000 999.000 999.000
U2$1 2.317 0.000 999.000 999.000
U3$1 2.274 0.000 999.000 999.000
U4$1 2.308 0.000 999.000 999.000
U5$1 2.190 0.000 999.000 999.000
U6$1 2.006 0.000 999.000 999.000
U7$1 2.111 0.000 999.000 999.000
U8$1 2.033 0.000 999.000 999.000
U9$1 2.074 0.000 999.000 999.000
U10$1 1.979 0.000 999.000 999.000
Variances
F 1.000 0.000 999.000 999.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.000E+00
(ratio of smallest to largest eigenvalue)
IRT PARAMETERIZATION
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Item Discriminations
F BY
U1 1.014 0.000 0.000 1.000
U2 0.977 0.000 0.000 1.000
U3 0.965 0.000 0.000 1.000
U4 0.981 0.000 0.000 1.000
U5 0.909 0.000 0.000 1.000
U6 0.978 0.000 0.000 1.000
U7 1.076 0.000 0.000 1.000
U8 0.979 0.000 0.000 1.000
U9 1.063 0.000 0.000 1.000
U10 0.998 0.000 0.000 1.000
Item Difficulties
U1$1 2.304 0.000 0.000 1.000
U2$1 2.373 0.000 0.000 1.000
U3$1 2.356 0.000 0.000 1.000
U4$1 2.353 0.000 0.000 1.000
U5$1 2.409 0.000 0.000 1.000
U6$1 2.052 0.000 0.000 1.000
U7$1 1.961 0.000 0.000 1.000
U8$1 2.078 0.000 0.000 1.000
U9$1 1.952 0.000 0.000 1.000
U10$1 1.984 0.000 0.000 1.000
Variances
F 1.000 0.000 0.000 1.000
SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES
SAMPLE STATISTICS
Means
F F_SE
________ ________
0.154 0.697
Covariances
F F_SE
________ ________
F 0.419
F_SE -0.100 0.026
Correlations
F F_SE
________ ________
F 1.000
F_SE -0.966 1.000
SAVEDATA INFORMATION
Save file
foc.dat
Order and format of variables
U1 F10.3
U2 F10.3
U3 F10.3
U4 F10.3
U5 F10.3
U6 F10.3
U7 F10.3
U8 F10.3
U9 F10.3
U10 F10.3
F F10.3
F_SE F10.3
ID I6
Save file format
12F10.3 I6
Save file record length 10000
Save missing symbol *
Beginning Time: 13:11:34
Ending Time: 13:11:35
Elapsed Time: 00:00:01
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2021 Muthen & Muthen
. clear
. runmplus_load_savedata , out(goo.out)
. rename f f_est
. rename f_se f_est_se
. tempfile focal
. save `focal' , replace
(note: file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000006 not found)
file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000006 saved
Match files back together
. use `focal'
. append using `reference'
. merge 1:1 id using `f1' , nogen
(note: variable u1 was byte, now float to accommodate using data's values)
(note: variable u2 was byte, now float to accommodate using data's values)
(note: variable u3 was byte, now float to accommodate using data's values)
(note: variable u4 was byte, now float to accommodate using data's values)
(note: variable u5 was byte, now float to accommodate using data's values)
(note: variable u6 was byte, now float to accommodate using data's values)
(note: variable u7 was byte, now float to accommodate using data's values)
(note: variable u8 was byte, now float to accommodate using data's values)
(note: variable u9 was byte, now float to accommodate using data's values)
(note: variable u10 was byte, now float to accommodate using data's values)
(note: variable u11 was byte, now float to accommodate using data's values)
(note: variable u12 was byte, now float to accommodate using data's values)
(note: variable u13 was byte, now float to accommodate using data's values)
(note: variable u14 was byte, now float to accommodate using data's values)
(note: variable u15 was byte, now float to accommodate using data's values)
(note: variable u16 was byte, now float to accommodate using data's values)
(note: variable u17 was byte, now float to accommodate using data's values)
(note: variable u18 was byte, now float to accommodate using data's values)
(note: variable u19 was byte, now float to accommodate using data's values)
(note: variable u20 was byte, now float to accommodate using data's values)
(note: variable u21 was byte, now float to accommodate using data's values)
(note: variable u22 was byte, now float to accommodate using data's values)
(note: variable u23 was byte, now float to accommodate using data's values)
(note: variable u24 was byte, now float to accommodate using data's values)
(note: variable u25 was byte, now float to accommodate using data's values)
(note: variable u26 was byte, now float to accommodate using data's values)
(note: variable u27 was byte, now float to accommodate using data's values)
(note: variable u28 was byte, now float to accommodate using data's values)
(note: variable u29 was byte, now float to accommodate using data's values)
(note: variable u30 was byte, now float to accommodate using data's values)
(note: variable id was int, now float to accommodate using data's values)
Result # of obs.
─────────────────────────────────────────
not matched 0
matched 10,001
─────────────────────────────────────────
. su
Variable │ Obs Mean Std. Dev. Min Max
─────────────┼─────────────────────────────────────────────────────────
u1 │ 10,001 .050395 .2187695 0 1
u2 │ 10,001 .0486951 .2152407 0 1
u3 │ 10,001 .0508949 .2197941 0 1
u4 │ 10,001 .049695 .217325 0 1
u5 │ 10,001 .0525947 .2232342 0 1
─────────────┼─────────────────────────────────────────────────────────
u6 │ 10,001 .0756924 .2645186 0 1
u7 │ 10,001 .0753925 .2640368 0 1
u8 │ 10,001 .0730927 .2603016 0 1
u9 │ 10,001 .0775922 .2675422 0 1
u10 │ 10,001 .0805919 .272221 0 1
─────────────┼─────────────────────────────────────────────────────────
f_est │ 10,001 .0889216 .7894857 -1.373 3.324
f_est_se │ 10,001 .5163873 .2227443 .233 .801
id │ 10,001 5001 2887.184 1 10001
u11 │ 5,000 .1064 .3083797 0 1
u12 │ 5,000 .1044 .3058093 0 1
─────────────┼─────────────────────────────────────────────────────────
u13 │ 5,000 .1008 .3010938 0 1
u14 │ 5,000 .101 .3013589 0 1
u15 │ 5,000 .1002 .3002965 0 1
u16 │ 5,000 .2066 .4049064 0 1
u17 │ 5,000 .1966 .397467 0 1
─────────────┼─────────────────────────────────────────────────────────
u18 │ 5,000 .1954 .396548 0 1
u19 │ 5,000 .1992 .3994387 0 1
u20 │ 5,000 .2054 .404034 0 1
u21 │ 5,000 .3978 .4894927 0 1
u22 │ 5,000 .3952 .4889425 0 1
─────────────┼─────────────────────────────────────────────────────────
u23 │ 5,000 .3896 .4877083 0 1
u24 │ 5,000 .407 .491324 0 1
u25 │ 5,000 .392 .4882455 0 1
u26 │ 5,000 .4938 .5000116 0 1
u27 │ 5,000 .497 .500041 0 1
─────────────┼─────────────────────────────────────────────────────────
u28 │ 5,000 .5012 .5000486 0 1
u29 │ 5,000 .4966 .5000384 0 1
u30 │ 5,000 .4938 .5000116 0 1
q │ 10,001 .0129183 .9931195 -3.581353 3.495501
focal │ 10,001 .50005 .500025 0 1
─────────────┼─────────────────────────────────────────────────────────
sumscore │ 10,001 6.623538 5.817109 0 30
Pyramid plot of factor score estimate by group
(file /Users/rnj/Dropbox/Work/Syntax/pyramid.png written in PNG format)
See how the type-I error rate is reasonably close to the nominal 5% level. A type-I error is concluding that an item has DIF when it does not have DIF (we know they all do not have DIF because that is how we generated them). Let’s say any finding of a significant effect of i.focal or focal#c.q is a type-I error.
. forvalues i=1/10 {
2. logit u`i' i.focal##c.q
3. }
Iteration 0: log likelihood = -1996.9651
Iteration 1: log likelihood = -1605.5008
Iteration 2: log likelihood = -1355.9574
Iteration 3: log likelihood = -1345.3758
Iteration 4: log likelihood = -1345.33
Iteration 5: log likelihood = -1345.33
Logistic regression Number of obs = 10,001
LR chi2(3) = 1303.27
Prob > chi2 = 0.0000
Log likelihood = -1345.33 Pseudo R2 = 0.3263
─────────────┬────────────────────────────────────────────────────────────────
u1 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.0541798 .2109964 -0.26 0.797 -.4677252 .3593656
q │ 2.041188 .1043095 19.57 0.000 1.836745 2.245631
│
focal#c.q │
1 │ .0612937 .1472744 0.42 0.677 -.2273588 .3499462
│
_cons │ -4.475801 .1481821 -30.20 0.000 -4.766232 -4.185369
─────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -1946.7453
Iteration 1: log likelihood = -1583.1608
Iteration 2: log likelihood = -1350.4161
Iteration 3: log likelihood = -1341.2978
Iteration 4: log likelihood = -1341.2495
Iteration 5: log likelihood = -1341.2495
Logistic regression Number of obs = 10,001
LR chi2(3) = 1210.99
Prob > chi2 = 0.0000
Log likelihood = -1341.2495 Pseudo R2 = 0.3110
─────────────┬────────────────────────────────────────────────────────────────
u2 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
1.focal │ .403318 .2094668 1.93 0.054 -.0072293 .8138653
q │ 2.098197 .109934 19.09 0.000 1.882731 2.313664
│
focal#c.q │
1 │ -.1949534 .1458075 -1.34 0.181 -.4807308 .0908241
│
_cons │ -4.667082 .1597794 -29.21 0.000 -4.980244 -4.35392
─────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2011.6198
Iteration 1: log likelihood = -1637.1294
Iteration 2: log likelihood = -1422.7188
Iteration 3: log likelihood = -1415.6532
Iteration 4: log likelihood = -1415.6175
Iteration 5: log likelihood = -1415.6175
Logistic regression Number of obs = 10,001
LR chi2(3) = 1192.00
Prob > chi2 = 0.0000
Log likelihood = -1415.6175 Pseudo R2 = 0.2963
─────────────┬────────────────────────────────────────────────────────────────
u3 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
1.focal │ .1930252 .1955539 0.99 0.324 -.1902533 .5763037
q │ 2.015173 .1021407 19.73 0.000 1.814981 2.215365
│
focal#c.q │
1 │ -.188861 .1387559 -1.36 0.173 -.4608175 .0830956
│
_cons │ -4.400949 .1438351 -30.60 0.000 -4.682861 -4.119037
─────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -1976.3606
Iteration 1: log likelihood = -1603.2029
Iteration 2: log likelihood = -1372.5586
Iteration 3: log likelihood = -1364.0271
Iteration 4: log likelihood = -1363.99
Iteration 5: log likelihood = -1363.99
Logistic regression Number of obs = 10,001
LR chi2(3) = 1224.74
Prob > chi2 = 0.0000
Log likelihood = -1363.99 Pseudo R2 = 0.3098
─────────────┬────────────────────────────────────────────────────────────────
u4 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
1.focal │ .0328805 .2044798 0.16 0.872 -.3678925 .4336535
q │ 2.047888 .1033271 19.82 0.000 1.845371 2.250405
│
focal#c.q │
1 │ -.1178829 .1434274 -0.82 0.411 -.3989955 .1632297
│
_cons │ -4.435502 .1457816 -30.43 0.000 -4.721229 -4.149776
─────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2061.0617
Iteration 1: log likelihood = -1683.1117
Iteration 2: log likelihood = -1482.4644
Iteration 3: log likelihood = -1476.5498
Iteration 4: log likelihood = -1476.512
Iteration 5: log likelihood = -1476.512
Logistic regression Number of obs = 10,001
LR chi2(3) = 1169.10
Prob > chi2 = 0.0000
Log likelihood = -1476.512 Pseudo R2 = 0.2836
─────────────┬────────────────────────────────────────────────────────────────
u5 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
1.focal │ .2780871 .1865839 1.49 0.136 -.0876106 .6437848
q │ 1.94329 .0995694 19.52 0.000 1.748138 2.138443
│
focal#c.q │
1 │ -.1744182 .133971 -1.30 0.193 -.4369966 .0881602
│
_cons │ -4.324749 .139563 -30.99 0.000 -4.598287 -4.051211
─────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2681.4743
Iteration 1: log likelihood = -2110.5374
Iteration 2: log likelihood = -1886.0808
Iteration 3: log likelihood = -1879.1908
Iteration 4: log likelihood = -1879.1587
Iteration 5: log likelihood = -1879.1587
Logistic regression Number of obs = 10,001
LR chi2(3) = 1604.63
Prob > chi2 = 0.0000
Log likelihood = -1879.1587 Pseudo R2 = 0.2992
─────────────┬────────────────────────────────────────────────────────────────
u6 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
1.focal │ .2377681 .1556885 1.53 0.127 -.0673757 .542912
q │ 1.94666 .0889273 21.89 0.000 1.772366 2.120955
│
focal#c.q │
1 │ -.084265 .120796 -0.70 0.485 -.3210207 .1524908
│
_cons │ -3.861973 .1156741 -33.39 0.000 -4.08869 -3.635256
─────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2673.9607
Iteration 1: log likelihood = -2074.9823
Iteration 2: log likelihood = -1821.6572
Iteration 3: log likelihood = -1812.1294
Iteration 4: log likelihood = -1812.093
Iteration 5: log likelihood = -1812.093
Logistic regression Number of obs = 10,001
LR chi2(3) = 1723.74
Prob > chi2 = 0.0000
Log likelihood = -1812.093 Pseudo R2 = 0.3223
─────────────┬────────────────────────────────────────────────────────────────
u7 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.1332035 .1640321 -0.81 0.417 -.4547004 .1882934
q │ 1.902192 .0872081 21.81 0.000 1.731267 2.073116
│
focal#c.q │
1 │ .235329 .1264615 1.86 0.063 -.0125309 .4831889
│
_cons │ -3.805852 .1129382 -33.70 0.000 -4.027207 -3.584497
─────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2615.9245
Iteration 1: log likelihood = -2067.475
Iteration 2: log likelihood = -1848.0155
Iteration 3: log likelihood = -1841.4272
Iteration 4: log likelihood = -1841.3952
Iteration 5: log likelihood = -1841.3952
Logistic regression Number of obs = 10,001
LR chi2(3) = 1549.06
Prob > chi2 = 0.0000
Log likelihood = -1841.3952 Pseudo R2 = 0.2961
─────────────┬────────────────────────────────────────────────────────────────
u8 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
1.focal │ .23617 .1579182 1.50 0.135 -.073344 .5456841
q │ 1.960847 .0898478 21.82 0.000 1.784748 2.136945
│
focal#c.q │
1 │ -.1357641 .121616 -1.12 0.264 -.374127 .1025989
│
_cons │ -3.897458 .1173793 -33.20 0.000 -4.127518 -3.667399
─────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2728.7632
Iteration 1: log likelihood = -2111.5809
Iteration 2: log likelihood = -1858.3102
Iteration 3: log likelihood = -1849.061
Iteration 4: log likelihood = -1849.0264
Iteration 5: log likelihood = -1849.0264
Logistic regression Number of obs = 10,001
LR chi2(3) = 1759.47
Prob > chi2 = 0.0000
Log likelihood = -1849.0264 Pseudo R2 = 0.3224
─────────────┬────────────────────────────────────────────────────────────────
u9 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.01748 .1612107 -0.11 0.914 -.3334472 .2984871
q │ 1.947741 .088081 22.11 0.000 1.775105 2.120377
│
focal#c.q │
1 │ .142265 .1251908 1.14 0.256 -.1031045 .3876344
│
_cons │ -3.82012 .1137469 -33.58 0.000 -4.04306 -3.59718
─────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2802.4074
Iteration 1: log likelihood = -2186.6497
Iteration 2: log likelihood = -1957.2862
Iteration 3: log likelihood = -1950.4299
Iteration 4: log likelihood = -1950.3994
Iteration 5: log likelihood = -1950.3994
Logistic regression Number of obs = 10,001
LR chi2(3) = 1704.02
Prob > chi2 = 0.0000
Log likelihood = -1950.3994 Pseudo R2 = 0.3040
─────────────┬────────────────────────────────────────────────────────────────
u10 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
1.focal │ .0136848 .1509607 0.09 0.928 -.2821927 .3095622
q │ 1.89887 .0846118 22.44 0.000 1.733034 2.064706
│
focal#c.q │
1 │ .0495596 .1190077 0.42 0.677 -.1836912 .2828104
│
_cons │ -3.678189 .1072464 -34.30 0.000 -3.888388 -3.46799
─────────────┴────────────────────────────────────────────────────────────────
. forvalues i=1/10 {
2. logit u`i' i.focal##c.f_est
3. }
Iteration 0: log likelihood = -1996.9651
Iteration 1: log likelihood = -1444.0276
Iteration 2: log likelihood = -1249.4473
Iteration 3: log likelihood = -1238.375
Iteration 4: log likelihood = -1238.3403
Iteration 5: log likelihood = -1238.3403
Logistic regression Number of obs = 10,001
LR chi2(3) = 1517.25
Prob > chi2 = 0.0000
Log likelihood = -1238.3403 Pseudo R2 = 0.3799
──────────────┬────────────────────────────────────────────────────────────────
u1 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
──────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.4609363 .2309965 -2.00 0.046 -.9136811 -.0081915
f_est │ 2.159441 .1090277 19.81 0.000 1.94575 2.373131
│
focal#c.f_est │
1 │ .5488406 .1662254 3.30 0.001 .2230448 .8746364
│
_cons │ -4.529971 .1520203 -29.80 0.000 -4.827925 -4.232017
──────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -1946.7453
Iteration 1: log likelihood = -1423.1899
Iteration 2: log likelihood = -1239.7219
Iteration 3: log likelihood = -1226.424
Iteration 4: log likelihood = -1226.338
Iteration 5: log likelihood = -1226.3379
Logistic regression Number of obs = 10,001
LR chi2(3) = 1440.81
Prob > chi2 = 0.0000
Log likelihood = -1226.3379 Pseudo R2 = 0.3701
──────────────┬────────────────────────────────────────────────────────────────
u2 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
──────────────┼────────────────────────────────────────────────────────────────
1.focal │ .0987777 .2287411 0.43 0.666 -.3495467 .5471021
f_est │ 2.273433 .1175636 19.34 0.000 2.043013 2.503854
│
focal#c.f_est │
1 │ .2101677 .1634829 1.29 0.199 -.1102529 .5305884
│
_cons │ -4.793589 .1684611 -28.46 0.000 -5.123767 -4.463412
──────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2011.6198
Iteration 1: log likelihood = -1967.4926
Iteration 2: log likelihood = -1347.4157
Iteration 3: log likelihood = -1278.2212
Iteration 4: log likelihood = -1274.8067
Iteration 5: log likelihood = -1274.8009
Iteration 6: log likelihood = -1274.8009
Logistic regression Number of obs = 10,001
LR chi2(3) = 1473.64
Prob > chi2 = 0.0000
Log likelihood = -1274.8009 Pseudo R2 = 0.3663
──────────────┬────────────────────────────────────────────────────────────────
u3 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
──────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.0842917 .220735 -0.38 0.703 -.5169243 .3483409
f_est │ 2.266778 .1123715 20.17 0.000 2.046534 2.487022
│
focal#c.f_est │
1 │ .187769 .1596139 1.18 0.239 -.1250685 .5006064
│
_cons │ -4.617136 .1570002 -29.41 0.000 -4.924851 -4.309421
──────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -1976.3606
Iteration 1: log likelihood = -1935.8175
Iteration 2: log likelihood = -1329.1271
Iteration 3: log likelihood = -1269.8037
Iteration 4: log likelihood = -1267.2189
Iteration 5: log likelihood = -1267.2133
Iteration 6: log likelihood = -1267.2133
Logistic regression Number of obs = 10,001
LR chi2(3) = 1418.29
Prob > chi2 = 0.0000
Log likelihood = -1267.2133 Pseudo R2 = 0.3588
──────────────┬────────────────────────────────────────────────────────────────
u4 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
──────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.2849609 .220362 -1.29 0.196 -.7168625 .1469408
f_est │ 2.180674 .108545 20.09 0.000 1.96793 2.393419
│
focal#c.f_est │
1 │ .2834307 .1588539 1.78 0.074 -.0279172 .5947787
│
_cons │ -4.506576 .1505061 -29.94 0.000 -4.801563 -4.211589
──────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2061.0617
Iteration 1: log likelihood = -2008.4219
Iteration 2: log likelihood = -1434.7079
Iteration 3: log likelihood = -1371.8632
Iteration 4: log likelihood = -1369.3595
Iteration 5: log likelihood = -1369.3527
Iteration 6: log likelihood = -1369.3527
Logistic regression Number of obs = 10,001
LR chi2(3) = 1383.42
Prob > chi2 = 0.0000
Log likelihood = -1369.3527 Pseudo R2 = 0.3356
──────────────┬────────────────────────────────────────────────────────────────
u5 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
──────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.0038278 .2001354 -0.02 0.985 -.3960859 .3884304
f_est │ 2.088623 .1051992 19.85 0.000 1.882436 2.294809
│
focal#c.f_est │
1 │ .2117394 .1477552 1.43 0.152 -.0778555 .5013342
│
_cons │ -4.412121 .1450765 -30.41 0.000 -4.696466 -4.127776
──────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2681.4743
Iteration 1: log likelihood = -2302.8295
Iteration 2: log likelihood = -1763.2541
Iteration 3: log likelihood = -1694.9643
Iteration 4: log likelihood = -1693.3586
Iteration 5: log likelihood = -1693.3546
Iteration 6: log likelihood = -1693.3546
Logistic regression Number of obs = 10,001
LR chi2(3) = 1976.24
Prob > chi2 = 0.0000
Log likelihood = -1693.3546 Pseudo R2 = 0.3685
──────────────┬────────────────────────────────────────────────────────────────
u6 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
──────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.2994474 .1720579 -1.74 0.082 -.6366747 .0377799
f_est │ 2.037892 .0916184 22.24 0.000 1.858323 2.217461
│
focal#c.f_est │
1 │ .609999 .1388094 4.39 0.000 .3379376 .8820603
│
_cons │ -3.881219 .116727 -33.25 0.000 -4.109999 -3.652438
──────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2673.9607
Iteration 1: log likelihood = -2268.9386
Iteration 2: log likelihood = -1681.1379
Iteration 3: log likelihood = -1594.2697
Iteration 4: log likelihood = -1591.1527
Iteration 5: log likelihood = -1591.1494
Iteration 6: log likelihood = -1591.1494
Logistic regression Number of obs = 10,001
LR chi2(3) = 2165.62
Prob > chi2 = 0.0000
Log likelihood = -1591.1494 Pseudo R2 = 0.4049
──────────────┬────────────────────────────────────────────────────────────────
u7 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
──────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.4616133 .1906904 -2.42 0.015 -.8353596 -.087867
f_est │ 2.187211 .0969439 22.56 0.000 1.997205 2.377218
│
focal#c.f_est │
1 │ .7378798 .1523001 4.84 0.000 .4393771 1.036383
│
_cons │ -4.035244 .124554 -32.40 0.000 -4.279365 -3.791123
──────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2615.9245
Iteration 1: log likelihood = -2255.965
Iteration 2: log likelihood = -1712.5828
Iteration 3: log likelihood = -1653.05
Iteration 4: log likelihood = -1651.7968
Iteration 5: log likelihood = -1651.7927
Iteration 6: log likelihood = -1651.7927
Logistic regression Number of obs = 10,001
LR chi2(3) = 1928.26
Prob > chi2 = 0.0000
Log likelihood = -1651.7927 Pseudo R2 = 0.3686
──────────────┬────────────────────────────────────────────────────────────────
u8 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
──────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.0590926 .1763326 -0.34 0.738 -.4046982 .2865129
f_est │ 2.191298 .0977474 22.42 0.000 1.999717 2.38288
│
focal#c.f_est │
1 │ .317793 .1401422 2.27 0.023 .0431194 .5924667
│
_cons │ -4.068907 .1262405 -32.23 0.000 -4.316334 -3.82148
──────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2728.7632
Iteration 1: log likelihood = -2290.5504
Iteration 2: log likelihood = -1723.5771
Iteration 3: log likelihood = -1647.4923
Iteration 4: log likelihood = -1645.4327
Iteration 5: log likelihood = -1645.4292
Iteration 6: log likelihood = -1645.4292
Logistic regression Number of obs = 10,001
LR chi2(3) = 2166.67
Prob > chi2 = 0.0000
Log likelihood = -1645.4292 Pseudo R2 = 0.3970
──────────────┬────────────────────────────────────────────────────────────────
u9 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
──────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.2297291 .1820959 -1.26 0.207 -.5866305 .1271723
f_est │ 2.233943 .0979127 22.82 0.000 2.042037 2.425848
│
focal#c.f_est │
1 │ .5423606 .1466388 3.70 0.000 .2549539 .8297674
│
_cons │ -4.049666 .1253515 -32.31 0.000 -4.295351 -3.803982
──────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2802.4074
Iteration 1: log likelihood = -2335.8654
Iteration 2: log likelihood = -1822.9185
Iteration 3: log likelihood = -1771.462
Iteration 4: log likelihood = -1770.5868
Iteration 5: log likelihood = -1770.5843
Iteration 6: log likelihood = -1770.5843
Logistic regression Number of obs = 10,001
LR chi2(3) = 2063.65
Prob > chi2 = 0.0000
Log likelihood = -1770.5843 Pseudo R2 = 0.3682
──────────────┬────────────────────────────────────────────────────────────────
u10 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
──────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.2905401 .1655492 -1.76 0.079 -.6150105 .0339304
f_est │ 2.080355 .0902621 23.05 0.000 1.903445 2.257266
│
focal#c.f_est │
1 │ .5283475 .1357359 3.89 0.000 .26231 .7943851
│
_cons │ -3.790544 .1126596 -33.65 0.000 -4.011353 -3.569735
──────────────┴────────────────────────────────────────────────────────────────
6 of 10 items have DIF.
save working file
. tempfile f2 . save `f2' , replace (note: file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000007 not found) file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000007 saved
. local model ""
. use `f1' , clear
. keep if focal==1
(5,000 observations deleted)
. forvalues i=1/10 {
2. local l`i' = svalues[`i',1]
3. local t=`i'+30
4. local t`i' = svalues[`t',1]
5. local model "`model' f by u`i'@`l`i'' ;"
6. local model "`model' [u`i'$1@`t`i''] ;"
7. }
. runmplus u1-u10 , cat(all) idvariable(id) ///
> estimator(bayes) ///
> model(`model' f@1;) ///
> savedata(save=fscores(1 1); file=foc_bayes.dat;) ///
> savelog(hoo)
Mplus VERSION 8.6 (Mac)
MUTHEN & MUTHEN
Running input file '__000001.inp'...
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
POTENTIAL PARAMETER WITH TOTAL
ITERATION SCALE REDUCTION HIGHEST PSR TIME TIME
100 1.000 0 1.09 1.1
DUE TO SAVE=FSCORES REQUEST IN THE SAVEDATA COMMAND, FACTOR SCORES
(PLAUSIBLE VALUES) ARE OBTAINED BY MULTIPLE IMPUTATIONS. THE
NUMBER OF IMPUTATIONS CAN BE CHANGED WITH THE SAVE=FSCORES REQUEST.
GENERATING IMPUTATION 1
WRITING FACTOR SCORES (PLAUSIBLE VALUES) TO SAVEDATA AND/OR PLOT FILE
Beginning Time: 13:11:40
Ending Time: 13:11:41
Elapsed Time: 00:00:01
Output saved in '__000001.out'.
Mplus VERSION 8.6 (Mac)
MUTHEN & MUTHEN
08/20/2021 1:11 PM
INPUT INSTRUCTIONS
TITLE:
Variable List -
u1 :
u2 :
u3 :
u4 :
u5 :
u6 :
u7 :
u8 :
u9 :
u10 :
id :
DATA:
FILE = __000001.dat ;
VARIABLE:
NAMES =
u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 id ;
MISSING ARE ALL (-9999) ;
CATEGORICAL =
all
;
IDVARIABLE = id ;
ANALYSIS:
ESTIMATOR = bayes ;
OUTPUT:
SAVEDATA:
save=fscores(1 1) ;
file=foc_bayes.dat ;
MODEL:
f by u1@1.01409 ;
[u1$1@2.33686] ;
f by u2@.97653 ;
[u2$1@2.31682] ;
f by u3@.96534 ;
[u3$1@2.27431] ;
f by u4@.98097 ;
[u4$1@2.30823] ;
f by u5@.90888 ;
[u5$1@2.1895] ;
f by u6@.97777 ;
[u6$1@2.00644] ;
f by u7@1.07641 ;
[u7$1@2.11101] ;
f by u8@.97867 ;
[u8$1@2.03322] ;
f by u9@1.0626 ;
[u9$1@2.07416] ;
f by u10@.99782 ;
[u10$1@1.97926] ;
f@1 ;
INPUT READING TERMINATED NORMALLY
Variable List -
u1 :
u2 :
u3 :
u4 :
u5 :
u6 :
u7 :
u8 :
u9 :
u10 :
id :
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 5001
Number of dependent variables 10
Number of independent variables 0
Number of continuous latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
U7 U8 U9 U10
Continuous latent variables
F
Variables with special functions
ID variable ID
Estimator BAYES
Specifications for Bayesian Estimation
Point estimate MEDIAN
Number of Markov chain Monte Carlo (MCMC) chains 2
Random seed for the first chain 0
Starting value information UNPERTURBED
Algorithm used for Markov chain Monte Carlo GIBBS(PX1)
Convergence criterion 0.500D-01
Maximum number of iterations 50000
K-th iteration used for thinning 1
Link PROBIT
Specifications for Bayes Factor Score Estimation
Number of imputed data sets 1
Iteration intervals for thinning 1
Input data file(s)
__000001.dat
Input data format FREE
SUMMARY OF DATA
SUMMARY OF MISSING DATA PATTERNS
Number of missing data patterns 1
MISSING DATA PATTERNS (x = not missing)
1
U1 x
U2 x
U3 x
U4 x
U5 x
U6 x
U7 x
U8 x
U9 x
U10 x
MISSING DATA PATTERN FREQUENCIES
Pattern Frequency
1 5001
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 1.000
U2 1.000 1.000
U3 1.000 1.000 1.000
U4 1.000 1.000 1.000 1.000
U5 1.000 1.000 1.000 1.000 1.000
U6 1.000 1.000 1.000 1.000 1.000
U7 1.000 1.000 1.000 1.000 1.000
U8 1.000 1.000 1.000 1.000 1.000
U9 1.000 1.000 1.000 1.000 1.000
U10 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 1.000
U7 1.000 1.000
U8 1.000 1.000 1.000
U9 1.000 1.000 1.000 1.000
U10 1.000 1.000 1.000 1.000 1.000
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.949 4745.000
Category 2 0.051 256.000
U2
Category 1 0.948 4741.000
Category 2 0.052 260.000
U3
Category 1 0.949 4748.000
Category 2 0.051 253.000
U4
Category 1 0.952 4761.000
Category 2 0.048 240.000
U5
Category 1 0.946 4729.000
Category 2 0.054 272.000
U6
Category 1 0.920 4601.000
Category 2 0.080 400.000
U7
Category 1 0.921 4606.000
Category 2 0.079 395.000
U8
Category 1 0.924 4622.000
Category 2 0.076 379.000
U9
Category 1 0.918 4593.000
Category 2 0.082 408.000
U10
Category 1 0.917 4587.000
Category 2 0.083 414.000
THE MODEL ESTIMATION TERMINATED NORMALLY
USE THE FBITERATIONS OPTION TO INCREASE THE NUMBER OF ITERATIONS BY A FACTOR
OF AT LEAST TWO TO CHECK CONVERGENCE AND THAT THE PSR VALUE DOES NOT INCREASE.
MODEL FIT INFORMATION
Number of Free Parameters 0
Bayesian Posterior Predictive Checking using Chi-Square
95% Confidence Interval for the Difference Between
the Observed and the Replicated Chi-Square Values
-31.736 14.981
Posterior Predictive P-Value 0.667
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
F BY
U1 1.014 0.000 0.000 1.014 1.014
U2 0.977 0.000 0.000 0.977 0.977
U3 0.965 0.000 0.000 0.965 0.965
U4 0.981 0.000 0.000 0.981 0.981
U5 0.909 0.000 0.000 0.909 0.909
U6 0.978 0.000 0.000 0.978 0.978
U7 1.076 0.000 0.000 1.076 1.076
U8 0.979 0.000 0.000 0.979 0.979
U9 1.063 0.000 0.000 1.063 1.063
U10 0.998 0.000 0.000 0.998 0.998
Thresholds
U1$1 2.337 0.000 0.000 2.337 2.337
U2$1 2.317 0.000 0.000 2.317 2.317
U3$1 2.274 0.000 0.000 2.274 2.274
U4$1 2.308 0.000 0.000 2.308 2.308
U5$1 2.190 0.000 0.000 2.190 2.190
U6$1 2.006 0.000 0.000 2.006 2.006
U7$1 2.111 0.000 0.000 2.111 2.111
U8$1 2.033 0.000 0.000 2.033 2.033
U9$1 2.074 0.000 0.000 2.074 2.074
U10$1 1.979 0.000 0.000 1.979 1.979
Variances
F 1.000 0.000 0.000 1.000 1.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
0 0 0 0 0
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
0 0 0 0 0
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0 0 0 0 0
NU
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
F
________
U1 0
U2 0
U3 0
U4 0
U5 0
U6 0
U7 0
U8 0
U9 0
U10 0
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
U5 0 0 0 0 0
U6 0 0 0 0 0
U7 0 0 0 0 0
U8 0 0 0 0 0
U9 0 0 0 0 0
U10 0 0 0 0 0
THETA
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 0
U7 0 0
U8 0 0 0
U9 0 0 0 0
U10 0 0 0 0 0
ALPHA
F
________
0
BETA
F
________
F 0
PSI
F
________
F 0
STARTING VALUES
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
2.337 2.317 2.274 2.308 2.190
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
2.006 2.111 2.033 2.074 1.979
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F
________
U1 1.014
U2 0.977
U3 0.965
U4 0.981
U5 0.909
U6 0.978
U7 1.076
U8 0.979
U9 1.063
U10 0.998
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
U5 0.000 0.000 0.000 0.000 1.000
U6 0.000 0.000 0.000 0.000 0.000
U7 0.000 0.000 0.000 0.000 0.000
U8 0.000 0.000 0.000 0.000 0.000
U9 0.000 0.000 0.000 0.000 0.000
U10 0.000 0.000 0.000 0.000 0.000
THETA
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 1.000
U7 0.000 1.000
U8 0.000 0.000 1.000
U9 0.000 0.000 0.000 1.000
U10 0.000 0.000 0.000 0.000 1.000
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 1.000
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
SUMMARIES OF PLAUSIBLE VALUES (N = NUMBER OF OBSERVATIONS * NUMBER OF IMPUTATIONS)
SAMPLE STATISTICS
Means
F
________
-0.011
Covariances
F
________
F 1.054
Correlations
F
________
F 1.000
SUMMARY OF PLAUSIBLE STANDARD DEVIATION (N = NUMBER OF OBSERVATIONS)
SAMPLE STATISTICS
Means
F_SD
________
0.000
Covariances
F_SD
________
F_SD 0.000
Correlations
F_SD
________
F_SD 1.000
SAVEDATA INFORMATION
Save file
foc_bayes.dat
Order and format of variables
U1 F10.3
U2 F10.3
U3 F10.3
U4 F10.3
U5 F10.3
U6 F10.3
U7 F10.3
U8 F10.3
U9 F10.3
U10 F10.3
F Mean F10.3
F Median F10.3
F Standard Deviation F10.3
F 2.5% Value F10.3
F 97.5% Value F10.3
ID I6
Save file format
15F10.3 I6
Save file record length 10000
Save missing symbol *
Beginning Time: 13:11:40
Ending Time: 13:11:41
Elapsed Time: 00:00:01
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2021 Muthen & Muthen
. clear
. runmplus_load_savedata , out(hoo.out)
. rename f_mean f_est_bayes
. keep id f_est_bayes
. tempfile focal_bayes
. save `focal_bayes' , replace
(note: file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000008 not found)
file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000008 saved
Reference group
. local model ""
. use `f1' , clear
. keep if focal~=1
(5,001 observations deleted)
. forvalues i=1/30 {
2. local l`i' = svalues[`i',1]
3. local t=`i'+30
4. local t`i' = svalues[`t',1]
5. local model "`model' f by u`i'@`l`i'' ;"
6. local model "`model' [u`i'$1@`t`i''] ;"
7. }
. runmplus u1-u30 , cat(all) idvariable(id) ///
> estimator(bayes) ///
> model(`model' f@1;) ///
> savedata(save=fscores(1 1); file=ref_bayes.dat;) ///
> savelog(ioo)
Mplus VERSION 8.6 (Mac)
MUTHEN & MUTHEN
Running input file '__000001.inp'...
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
POTENTIAL PARAMETER WITH TOTAL
ITERATION SCALE REDUCTION HIGHEST PSR TIME TIME
100 1.000 0 3.20 3.2
DUE TO SAVE=FSCORES REQUEST IN THE SAVEDATA COMMAND, FACTOR SCORES
(PLAUSIBLE VALUES) ARE OBTAINED BY MULTIPLE IMPUTATIONS. THE
NUMBER OF IMPUTATIONS CAN BE CHANGED WITH THE SAVE=FSCORES REQUEST.
GENERATING IMPUTATION 1
WRITING FACTOR SCORES (PLAUSIBLE VALUES) TO SAVEDATA AND/OR PLOT FILE
Beginning Time: 13:11:42
Ending Time: 13:11:46
Elapsed Time: 00:00:04
Output saved in '__000001.out'.
Mplus VERSION 8.6 (Mac)
MUTHEN & MUTHEN
08/20/2021 1:11 PM
INPUT INSTRUCTIONS
TITLE:
Variable List -
u1 :
u2 :
u3 :
u4 :
u5 :
u6 :
u7 :
u8 :
u9 :
u10 :
u11 :
u12 :
u13 :
u14 :
u15 :
u16 :
u17 :
u18 :
u19 :
u20 :
u21 :
u22 :
u23 :
u24 :
u25 :
u26 :
u27 :
u28 :
u29 :
u30 :
id :
DATA:
FILE = __000001.dat ;
VARIABLE:
NAMES =
u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11 u12 u13 u14 u15 u16 u17 u18
u19 u20 u21 u22 u23 u24 u25 u26 u27 u28 u29 u30 id ;
MISSING ARE ALL (-9999) ;
CATEGORICAL =
all
;
IDVARIABLE = id ;
ANALYSIS:
ESTIMATOR = bayes ;
OUTPUT:
SAVEDATA:
save=fscores(1 1) ;
file=ref_bayes.dat ;
MODEL:
f by u1@1.01409 ;
[u1$1@2.33686] ;
f by u2@.97653 ;
[u2$1@2.31682] ;
f by u3@.96534 ;
[u3$1@2.27431] ;
f by u4@.98097 ;
[u4$1@2.30823] ;
f by u5@.90888 ;
[u5$1@2.1895] ;
f by u6@.97777 ;
[u6$1@2.00644] ;
f by u7@1.07641 ;
[u7$1@2.11101] ;
f by u8@.97867 ;
[u8$1@2.03322] ;
f by u9@1.0626 ;
[u9$1@2.07416] ;
f by u10@.99782 ;
[u10$1@1.97926] ;
f by u11@1.01746 ;
[u11$1@1.80978] ;
f by u12@1.04867 ;
[u12$1@1.82851] ;
f by u13@1.02499 ;
[u13$1@1.80543] ;
f by u14@.95264 ;
[u14$1@1.77559] ;
f by u15@.95452 ;
[u15$1@1.77015] ;
f by u16@1.00153 ;
[u16$1@1.18424] ;
f by u17@.98187 ;
[u17$1@1.20945] ;
f by u18@1.00501 ;
[u18$1@1.21787] ;
f by u19@1.03146 ;
[u19$1@1.19854] ;
f by u20@.99537 ;
[u20$1@1.16959] ;
f by u21@.98347 ;
[u21$1@.38352] ;
f by u22@1.01198 ;
[u22$1@.3879] ;
f by u23@1.03699 ;
[u23$1@.38417] ;
f by u24@.99536 ;
[u24$1@.32265] ;
f by u25@.99005 ;
[u25$1@.37819] ;
f by u26@1.0051 ;
[u26$1@-.00302] ;
f by u27@1.00563 ;
[u27$1@.01333] ;
f by u28@1.03124 ;
[u28$1@-.00702] ;
f by u29@1.01361 ;
[u29$1@-.01338] ;
f by u30@1.06863 ;
[u30$1@.00899] ;
f@1 ;
INPUT READING TERMINATED NORMALLY
Variable List -
u1 :
u2 :
u3 :
u4 :
u5 :
u6 :
u7 :
u8 :
u9 :
u10 :
u11 :
u12 :
u13 :
u14 :
u15 :
u16 :
u17 :
u18 :
u19 :
u20 :
u21 :
u22 :
u23 :
u24 :
u25 :
u26 :
u27 :
u28 :
u29 :
u30 :
id :
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 5000
Number of dependent variables 30
Number of independent variables 0
Number of continuous latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
U7 U8 U9 U10 U11 U12
U13 U14 U15 U16 U17 U18
U19 U20 U21 U22 U23 U24
U25 U26 U27 U28 U29 U30
Continuous latent variables
F
Variables with special functions
ID variable ID
Estimator BAYES
Specifications for Bayesian Estimation
Point estimate MEDIAN
Number of Markov chain Monte Carlo (MCMC) chains 2
Random seed for the first chain 0
Starting value information UNPERTURBED
Algorithm used for Markov chain Monte Carlo GIBBS(PX1)
Convergence criterion 0.500D-01
Maximum number of iterations 50000
K-th iteration used for thinning 1
Link PROBIT
Specifications for Bayes Factor Score Estimation
Number of imputed data sets 1
Iteration intervals for thinning 1
Input data file(s)
__000001.dat
Input data format FREE
SUMMARY OF DATA
SUMMARY OF MISSING DATA PATTERNS
Number of missing data patterns 1
MISSING DATA PATTERNS (x = not missing)
1
U1 x
U2 x
U3 x
U4 x
U5 x
U6 x
U7 x
U8 x
U9 x
U10 x
U11 x
U12 x
U13 x
U14 x
U15 x
U16 x
U17 x
U18 x
U19 x
U20 x
U21 x
U22 x
U23 x
U24 x
U25 x
U26 x
U27 x
U28 x
U29 x
U30 x
MISSING DATA PATTERN FREQUENCIES
Pattern Frequency
1 5000
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 1.000
U2 1.000 1.000
U3 1.000 1.000 1.000
U4 1.000 1.000 1.000 1.000
U5 1.000 1.000 1.000 1.000 1.000
U6 1.000 1.000 1.000 1.000 1.000
U7 1.000 1.000 1.000 1.000 1.000
U8 1.000 1.000 1.000 1.000 1.000
U9 1.000 1.000 1.000 1.000 1.000
U10 1.000 1.000 1.000 1.000 1.000
U11 1.000 1.000 1.000 1.000 1.000
U12 1.000 1.000 1.000 1.000 1.000
U13 1.000 1.000 1.000 1.000 1.000
U14 1.000 1.000 1.000 1.000 1.000
U15 1.000 1.000 1.000 1.000 1.000
U16 1.000 1.000 1.000 1.000 1.000
U17 1.000 1.000 1.000 1.000 1.000
U18 1.000 1.000 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 1.000
U7 1.000 1.000
U8 1.000 1.000 1.000
U9 1.000 1.000 1.000 1.000
U10 1.000 1.000 1.000 1.000 1.000
U11 1.000 1.000 1.000 1.000 1.000
U12 1.000 1.000 1.000 1.000 1.000
U13 1.000 1.000 1.000 1.000 1.000
U14 1.000 1.000 1.000 1.000 1.000
U15 1.000 1.000 1.000 1.000 1.000
U16 1.000 1.000 1.000 1.000 1.000
U17 1.000 1.000 1.000 1.000 1.000
U18 1.000 1.000 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
U11 1.000
U12 1.000 1.000
U13 1.000 1.000 1.000
U14 1.000 1.000 1.000 1.000
U15 1.000 1.000 1.000 1.000 1.000
U16 1.000 1.000 1.000 1.000 1.000
U17 1.000 1.000 1.000 1.000 1.000
U18 1.000 1.000 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
U16 1.000
U17 1.000 1.000
U18 1.000 1.000 1.000
U19 1.000 1.000 1.000 1.000
U20 1.000 1.000 1.000 1.000 1.000
U21 1.000 1.000 1.000 1.000 1.000
U22 1.000 1.000 1.000 1.000 1.000
U23 1.000 1.000 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U21 U22 U23 U24 U25
________ ________ ________ ________ ________
U21 1.000
U22 1.000 1.000
U23 1.000 1.000 1.000
U24 1.000 1.000 1.000 1.000
U25 1.000 1.000 1.000 1.000 1.000
U26 1.000 1.000 1.000 1.000 1.000
U27 1.000 1.000 1.000 1.000 1.000
U28 1.000 1.000 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
U26 U27 U28 U29 U30
________ ________ ________ ________ ________
U26 1.000
U27 1.000 1.000
U28 1.000 1.000 1.000
U29 1.000 1.000 1.000 1.000
U30 1.000 1.000 1.000 1.000 1.000
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.950 4752.000
Category 2 0.050 248.000
U2
Category 1 0.955 4773.000
Category 2 0.045 227.000
U3
Category 1 0.949 4744.000
Category 2 0.051 256.000
U4
Category 1 0.949 4743.000
Category 2 0.051 257.000
U5
Category 1 0.949 4746.000
Category 2 0.051 254.000
U6
Category 1 0.929 4643.000
Category 2 0.071 357.000
U7
Category 1 0.928 4641.000
Category 2 0.072 359.000
U8
Category 1 0.930 4648.000
Category 2 0.070 352.000
U9
Category 1 0.926 4632.000
Category 2 0.074 368.000
U10
Category 1 0.922 4608.000
Category 2 0.078 392.000
U11
Category 1 0.894 4468.000
Category 2 0.106 532.000
U12
Category 1 0.896 4478.000
Category 2 0.104 522.000
U13
Category 1 0.899 4496.000
Category 2 0.101 504.000
U14
Category 1 0.899 4495.000
Category 2 0.101 505.000
U15
Category 1 0.900 4499.000
Category 2 0.100 501.000
U16
Category 1 0.793 3967.000
Category 2 0.207 1033.000
U17
Category 1 0.803 4017.000
Category 2 0.197 983.000
U18
Category 1 0.805 4023.000
Category 2 0.195 977.000
U19
Category 1 0.801 4004.000
Category 2 0.199 996.000
U20
Category 1 0.795 3973.000
Category 2 0.205 1027.000
U21
Category 1 0.602 3011.000
Category 2 0.398 1989.000
U22
Category 1 0.605 3024.000
Category 2 0.395 1976.000
U23
Category 1 0.610 3052.000
Category 2 0.390 1948.000
U24
Category 1 0.593 2965.000
Category 2 0.407 2035.000
U25
Category 1 0.608 3040.000
Category 2 0.392 1960.000
U26
Category 1 0.506 2531.000
Category 2 0.494 2469.000
U27
Category 1 0.503 2515.000
Category 2 0.497 2485.000
U28
Category 1 0.499 2494.000
Category 2 0.501 2506.000
U29
Category 1 0.503 2517.000
Category 2 0.497 2483.000
U30
Category 1 0.506 2531.000
Category 2 0.494 2469.000
THE MODEL ESTIMATION TERMINATED NORMALLY
USE THE FBITERATIONS OPTION TO INCREASE THE NUMBER OF ITERATIONS BY A FACTOR
OF AT LEAST TWO TO CHECK CONVERGENCE AND THAT THE PSR VALUE DOES NOT INCREASE.
MODEL FIT INFORMATION
Number of Free Parameters 0
Bayesian Posterior Predictive Checking using Chi-Square
95% Confidence Interval for the Difference Between
the Observed and the Replicated Chi-Square Values
-71.585 94.774
Posterior Predictive P-Value 0.417
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
F BY
U1 1.014 0.000 0.000 1.014 1.014
U2 0.977 0.000 0.000 0.977 0.977
U3 0.965 0.000 0.000 0.965 0.965
U4 0.981 0.000 0.000 0.981 0.981
U5 0.909 0.000 0.000 0.909 0.909
U6 0.978 0.000 0.000 0.978 0.978
U7 1.076 0.000 0.000 1.076 1.076
U8 0.979 0.000 0.000 0.979 0.979
U9 1.063 0.000 0.000 1.063 1.063
U10 0.998 0.000 0.000 0.998 0.998
U11 1.017 0.000 0.000 1.017 1.017
U12 1.049 0.000 0.000 1.049 1.049
U13 1.025 0.000 0.000 1.025 1.025
U14 0.953 0.000 0.000 0.953 0.953
U15 0.955 0.000 0.000 0.955 0.955
U16 1.002 0.000 0.000 1.002 1.002
U17 0.982 0.000 0.000 0.982 0.982
U18 1.005 0.000 0.000 1.005 1.005
U19 1.031 0.000 0.000 1.031 1.031
U20 0.995 0.000 0.000 0.995 0.995
U21 0.983 0.000 0.000 0.983 0.983
U22 1.012 0.000 0.000 1.012 1.012
U23 1.037 0.000 0.000 1.037 1.037
U24 0.995 0.000 0.000 0.995 0.995
U25 0.990 0.000 0.000 0.990 0.990
U26 1.005 0.000 0.000 1.005 1.005
U27 1.006 0.000 0.000 1.006 1.006
U28 1.031 0.000 0.000 1.031 1.031
U29 1.014 0.000 0.000 1.014 1.014
U30 1.069 0.000 0.000 1.069 1.069
Thresholds
U1$1 2.337 0.000 0.000 2.337 2.337
U2$1 2.317 0.000 0.000 2.317 2.317
U3$1 2.274 0.000 0.000 2.274 2.274
U4$1 2.308 0.000 0.000 2.308 2.308
U5$1 2.190 0.000 0.000 2.190 2.190
U6$1 2.006 0.000 0.000 2.006 2.006
U7$1 2.111 0.000 0.000 2.111 2.111
U8$1 2.033 0.000 0.000 2.033 2.033
U9$1 2.074 0.000 0.000 2.074 2.074
U10$1 1.979 0.000 0.000 1.979 1.979
U11$1 1.810 0.000 0.000 1.810 1.810
U12$1 1.829 0.000 0.000 1.829 1.829
U13$1 1.805 0.000 0.000 1.805 1.805
U14$1 1.776 0.000 0.000 1.776 1.776
U15$1 1.770 0.000 0.000 1.770 1.770
U16$1 1.184 0.000 0.000 1.184 1.184
U17$1 1.209 0.000 0.000 1.209 1.209
U18$1 1.218 0.000 0.000 1.218 1.218
U19$1 1.199 0.000 0.000 1.199 1.199
U20$1 1.170 0.000 0.000 1.170 1.170
U21$1 0.384 0.000 0.000 0.384 0.384
U22$1 0.388 0.000 0.000 0.388 0.388
U23$1 0.384 0.000 0.000 0.384 0.384
U24$1 0.323 0.000 0.000 0.323 0.323
U25$1 0.378 0.000 0.000 0.378 0.378
U26$1 -0.003 0.000 0.000 -0.003 -0.003
U27$1 0.013 0.000 0.000 0.013 0.013
U28$1 -0.007 0.000 0.000 -0.007 -0.007
U29$1 -0.013 0.000 0.000 -0.013 -0.013
U30$1 0.009 0.000 0.000 0.009 0.009
Variances
F 1.000 0.000 0.000 1.000 1.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
0 0 0 0 0
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
0 0 0 0 0
TAU
U11$1 U12$1 U13$1 U14$1 U15$1
________ ________ ________ ________ ________
0 0 0 0 0
TAU
U16$1 U17$1 U18$1 U19$1 U20$1
________ ________ ________ ________ ________
0 0 0 0 0
TAU
U21$1 U22$1 U23$1 U24$1 U25$1
________ ________ ________ ________ ________
0 0 0 0 0
TAU
U26$1 U27$1 U28$1 U29$1 U30$1
________ ________ ________ ________ ________
0 0 0 0 0
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0 0 0 0 0
NU
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0 0 0 0 0
NU
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
0 0 0 0 0
NU
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
0 0 0 0 0
NU
U21 U22 U23 U24 U25
________ ________ ________ ________ ________
0 0 0 0 0
NU
U26 U27 U28 U29 U30
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
F
________
U1 0
U2 0
U3 0
U4 0
U5 0
U6 0
U7 0
U8 0
U9 0
U10 0
U11 0
U12 0
U13 0
U14 0
U15 0
U16 0
U17 0
U18 0
U19 0
U20 0
U21 0
U22 0
U23 0
U24 0
U25 0
U26 0
U27 0
U28 0
U29 0
U30 0
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
U5 0 0 0 0 0
U6 0 0 0 0 0
U7 0 0 0 0 0
U8 0 0 0 0 0
U9 0 0 0 0 0
U10 0 0 0 0 0
U11 0 0 0 0 0
U12 0 0 0 0 0
U13 0 0 0 0 0
U14 0 0 0 0 0
U15 0 0 0 0 0
U16 0 0 0 0 0
U17 0 0 0 0 0
U18 0 0 0 0 0
U19 0 0 0 0 0
U20 0 0 0 0 0
U21 0 0 0 0 0
U22 0 0 0 0 0
U23 0 0 0 0 0
U24 0 0 0 0 0
U25 0 0 0 0 0
U26 0 0 0 0 0
U27 0 0 0 0 0
U28 0 0 0 0 0
U29 0 0 0 0 0
U30 0 0 0 0 0
THETA
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 0
U7 0 0
U8 0 0 0
U9 0 0 0 0
U10 0 0 0 0 0
U11 0 0 0 0 0
U12 0 0 0 0 0
U13 0 0 0 0 0
U14 0 0 0 0 0
U15 0 0 0 0 0
U16 0 0 0 0 0
U17 0 0 0 0 0
U18 0 0 0 0 0
U19 0 0 0 0 0
U20 0 0 0 0 0
U21 0 0 0 0 0
U22 0 0 0 0 0
U23 0 0 0 0 0
U24 0 0 0 0 0
U25 0 0 0 0 0
U26 0 0 0 0 0
U27 0 0 0 0 0
U28 0 0 0 0 0
U29 0 0 0 0 0
U30 0 0 0 0 0
THETA
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
U11 0
U12 0 0
U13 0 0 0
U14 0 0 0 0
U15 0 0 0 0 0
U16 0 0 0 0 0
U17 0 0 0 0 0
U18 0 0 0 0 0
U19 0 0 0 0 0
U20 0 0 0 0 0
U21 0 0 0 0 0
U22 0 0 0 0 0
U23 0 0 0 0 0
U24 0 0 0 0 0
U25 0 0 0 0 0
U26 0 0 0 0 0
U27 0 0 0 0 0
U28 0 0 0 0 0
U29 0 0 0 0 0
U30 0 0 0 0 0
THETA
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
U16 0
U17 0 0
U18 0 0 0
U19 0 0 0 0
U20 0 0 0 0 0
U21 0 0 0 0 0
U22 0 0 0 0 0
U23 0 0 0 0 0
U24 0 0 0 0 0
U25 0 0 0 0 0
U26 0 0 0 0 0
U27 0 0 0 0 0
U28 0 0 0 0 0
U29 0 0 0 0 0
U30 0 0 0 0 0
THETA
U21 U22 U23 U24 U25
________ ________ ________ ________ ________
U21 0
U22 0 0
U23 0 0 0
U24 0 0 0 0
U25 0 0 0 0 0
U26 0 0 0 0 0
U27 0 0 0 0 0
U28 0 0 0 0 0
U29 0 0 0 0 0
U30 0 0 0 0 0
THETA
U26 U27 U28 U29 U30
________ ________ ________ ________ ________
U26 0
U27 0 0
U28 0 0 0
U29 0 0 0 0
U30 0 0 0 0 0
ALPHA
F
________
0
BETA
F
________
F 0
PSI
F
________
F 0
STARTING VALUES
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
2.337 2.317 2.274 2.308 2.190
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
2.006 2.111 2.033 2.074 1.979
TAU
U11$1 U12$1 U13$1 U14$1 U15$1
________ ________ ________ ________ ________
1.810 1.829 1.805 1.776 1.770
TAU
U16$1 U17$1 U18$1 U19$1 U20$1
________ ________ ________ ________ ________
1.184 1.209 1.218 1.199 1.170
TAU
U21$1 U22$1 U23$1 U24$1 U25$1
________ ________ ________ ________ ________
0.384 0.388 0.384 0.323 0.378
TAU
U26$1 U27$1 U28$1 U29$1 U30$1
________ ________ ________ ________ ________
-0.003 0.013 -0.007 -0.013 0.009
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U21 U22 U23 U24 U25
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U26 U27 U28 U29 U30
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F
________
U1 1.014
U2 0.977
U3 0.965
U4 0.981
U5 0.909
U6 0.978
U7 1.076
U8 0.979
U9 1.063
U10 0.998
U11 1.017
U12 1.049
U13 1.025
U14 0.953
U15 0.955
U16 1.002
U17 0.982
U18 1.005
U19 1.031
U20 0.995
U21 0.983
U22 1.012
U23 1.037
U24 0.995
U25 0.990
U26 1.005
U27 1.006
U28 1.031
U29 1.014
U30 1.069
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
U5 0.000 0.000 0.000 0.000 1.000
U6 0.000 0.000 0.000 0.000 0.000
U7 0.000 0.000 0.000 0.000 0.000
U8 0.000 0.000 0.000 0.000 0.000
U9 0.000 0.000 0.000 0.000 0.000
U10 0.000 0.000 0.000 0.000 0.000
U11 0.000 0.000 0.000 0.000 0.000
U12 0.000 0.000 0.000 0.000 0.000
U13 0.000 0.000 0.000 0.000 0.000
U14 0.000 0.000 0.000 0.000 0.000
U15 0.000 0.000 0.000 0.000 0.000
U16 0.000 0.000 0.000 0.000 0.000
U17 0.000 0.000 0.000 0.000 0.000
U18 0.000 0.000 0.000 0.000 0.000
U19 0.000 0.000 0.000 0.000 0.000
U20 0.000 0.000 0.000 0.000 0.000
U21 0.000 0.000 0.000 0.000 0.000
U22 0.000 0.000 0.000 0.000 0.000
U23 0.000 0.000 0.000 0.000 0.000
U24 0.000 0.000 0.000 0.000 0.000
U25 0.000 0.000 0.000 0.000 0.000
U26 0.000 0.000 0.000 0.000 0.000
U27 0.000 0.000 0.000 0.000 0.000
U28 0.000 0.000 0.000 0.000 0.000
U29 0.000 0.000 0.000 0.000 0.000
U30 0.000 0.000 0.000 0.000 0.000
THETA
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 1.000
U7 0.000 1.000
U8 0.000 0.000 1.000
U9 0.000 0.000 0.000 1.000
U10 0.000 0.000 0.000 0.000 1.000
U11 0.000 0.000 0.000 0.000 0.000
U12 0.000 0.000 0.000 0.000 0.000
U13 0.000 0.000 0.000 0.000 0.000
U14 0.000 0.000 0.000 0.000 0.000
U15 0.000 0.000 0.000 0.000 0.000
U16 0.000 0.000 0.000 0.000 0.000
U17 0.000 0.000 0.000 0.000 0.000
U18 0.000 0.000 0.000 0.000 0.000
U19 0.000 0.000 0.000 0.000 0.000
U20 0.000 0.000 0.000 0.000 0.000
U21 0.000 0.000 0.000 0.000 0.000
U22 0.000 0.000 0.000 0.000 0.000
U23 0.000 0.000 0.000 0.000 0.000
U24 0.000 0.000 0.000 0.000 0.000
U25 0.000 0.000 0.000 0.000 0.000
U26 0.000 0.000 0.000 0.000 0.000
U27 0.000 0.000 0.000 0.000 0.000
U28 0.000 0.000 0.000 0.000 0.000
U29 0.000 0.000 0.000 0.000 0.000
U30 0.000 0.000 0.000 0.000 0.000
THETA
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
U11 1.000
U12 0.000 1.000
U13 0.000 0.000 1.000
U14 0.000 0.000 0.000 1.000
U15 0.000 0.000 0.000 0.000 1.000
U16 0.000 0.000 0.000 0.000 0.000
U17 0.000 0.000 0.000 0.000 0.000
U18 0.000 0.000 0.000 0.000 0.000
U19 0.000 0.000 0.000 0.000 0.000
U20 0.000 0.000 0.000 0.000 0.000
U21 0.000 0.000 0.000 0.000 0.000
U22 0.000 0.000 0.000 0.000 0.000
U23 0.000 0.000 0.000 0.000 0.000
U24 0.000 0.000 0.000 0.000 0.000
U25 0.000 0.000 0.000 0.000 0.000
U26 0.000 0.000 0.000 0.000 0.000
U27 0.000 0.000 0.000 0.000 0.000
U28 0.000 0.000 0.000 0.000 0.000
U29 0.000 0.000 0.000 0.000 0.000
U30 0.000 0.000 0.000 0.000 0.000
THETA
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
U16 1.000
U17 0.000 1.000
U18 0.000 0.000 1.000
U19 0.000 0.000 0.000 1.000
U20 0.000 0.000 0.000 0.000 1.000
U21 0.000 0.000 0.000 0.000 0.000
U22 0.000 0.000 0.000 0.000 0.000
U23 0.000 0.000 0.000 0.000 0.000
U24 0.000 0.000 0.000 0.000 0.000
U25 0.000 0.000 0.000 0.000 0.000
U26 0.000 0.000 0.000 0.000 0.000
U27 0.000 0.000 0.000 0.000 0.000
U28 0.000 0.000 0.000 0.000 0.000
U29 0.000 0.000 0.000 0.000 0.000
U30 0.000 0.000 0.000 0.000 0.000
THETA
U21 U22 U23 U24 U25
________ ________ ________ ________ ________
U21 1.000
U22 0.000 1.000
U23 0.000 0.000 1.000
U24 0.000 0.000 0.000 1.000
U25 0.000 0.000 0.000 0.000 1.000
U26 0.000 0.000 0.000 0.000 0.000
U27 0.000 0.000 0.000 0.000 0.000
U28 0.000 0.000 0.000 0.000 0.000
U29 0.000 0.000 0.000 0.000 0.000
U30 0.000 0.000 0.000 0.000 0.000
THETA
U26 U27 U28 U29 U30
________ ________ ________ ________ ________
U26 1.000
U27 0.000 1.000
U28 0.000 0.000 1.000
U29 0.000 0.000 0.000 1.000
U30 0.000 0.000 0.000 0.000 1.000
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 1.000
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
SUMMARIES OF PLAUSIBLE VALUES (N = NUMBER OF OBSERVATIONS * NUMBER OF IMPUTATIONS)
SAMPLE STATISTICS
Means
F
________
-0.017
Covariances
F
________
F 1.024
Correlations
F
________
F 1.000
SUMMARY OF PLAUSIBLE STANDARD DEVIATION (N = NUMBER OF OBSERVATIONS)
SAMPLE STATISTICS
Means
F_SD
________
0.000
Covariances
F_SD
________
F_SD 0.000
Correlations
F_SD
________
F_SD 1.000
SAVEDATA INFORMATION
Save file
ref_bayes.dat
Order and format of variables
U1 F10.3
U2 F10.3
U3 F10.3
U4 F10.3
U5 F10.3
U6 F10.3
U7 F10.3
U8 F10.3
U9 F10.3
U10 F10.3
U11 F10.3
U12 F10.3
U13 F10.3
U14 F10.3
U15 F10.3
U16 F10.3
U17 F10.3
U18 F10.3
U19 F10.3
U20 F10.3
U21 F10.3
U22 F10.3
U23 F10.3
U24 F10.3
U25 F10.3
U26 F10.3
U27 F10.3
U28 F10.3
U29 F10.3
U30 F10.3
F Mean F10.3
F Median F10.3
F Standard Deviation F10.3
F 2.5% Value F10.3
F 97.5% Value F10.3
ID I5
Save file format
35F10.3 I5
Save file record length 10000
Save missing symbol *
Beginning Time: 13:11:42
Ending Time: 13:11:46
Elapsed Time: 00:00:04
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2021 Muthen & Muthen
. clear
. runmplus_load_savedata , out(ioo.out)
. rename f_mean f_est_bayes
. keep id f_est_bayes
. tempfile reference_bayes
. save `reference_bayes' , replace
(note: file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000009 not found)
file /var/folders/lq/w3m6z0dj41ngkbbc0204xb7m0000gp/T//S_03002.000009 saved
Merge files
. use `focal_bayes' , clear
. append using `reference_bayes'
. merge 1:1 id using `f2' , nogen
(note: variable id was int, now float to accommodate using data's values)
Result # of obs.
─────────────────────────────────────────
not matched 0
matched 10,001
─────────────────────────────────────────
Pyramid plot of Bayes factor score estimates, by group
(file /Users/rnj/Dropbox/Work/Syntax/pyramid_bayes.png written in PNG format)
DIF testing with regression approach
. forvalues i=1/10 {
2. logit u`i' i.focal##c.f_est_bayes
3. }
Iteration 0: log likelihood = -1996.9651
Iteration 1: log likelihood = -1618.5238
Iteration 2: log likelihood = -1385.8062
Iteration 3: log likelihood = -1376.8779
Iteration 4: log likelihood = -1376.8367
Iteration 5: log likelihood = -1376.8367
Logistic regression Number of obs = 10,001
LR chi2(3) = 1240.26
Prob > chi2 = 0.0000
Log likelihood = -1376.8367 Pseudo R2 = 0.3105
────────────────────┬────────────────────────────────────────────────────────────────
u1 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
────────────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.0880271 .2023997 -0.43 0.664 -.4847234 .3086691
f_est_bayes │ 1.918393 .0990831 19.36 0.000 1.724194 2.112592
│
focal#c.f_est_bayes │
1 │ .0645699 .1404867 0.46 0.646 -.2107789 .3399188
│
_cons │ -4.324077 .1413382 -30.59 0.000 -4.601095 -4.04706
────────────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -1946.7453
Iteration 1: log likelihood = -1588.4771
Iteration 2: log likelihood = -1356.071
Iteration 3: log likelihood = -1347.0241
Iteration 4: log likelihood = -1346.9788
Iteration 5: log likelihood = -1346.9788
Logistic regression Number of obs = 10,001
LR chi2(3) = 1199.53
Prob > chi2 = 0.0000
Log likelihood = -1346.9788 Pseudo R2 = 0.3081
────────────────────┬────────────────────────────────────────────────────────────────
u2 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
────────────────────┼────────────────────────────────────────────────────────────────
1.focal │ .2445174 .2063609 1.18 0.236 -.1599425 .6489774
f_est_bayes │ 1.98933 .1052249 18.91 0.000 1.783093 2.195567
│
focal#c.f_est_bayes │
1 │ -.0923086 .1422146 -0.65 0.516 -.3710442 .186427
│
_cons │ -4.52888 .1537272 -29.46 0.000 -4.83018 -4.227581
────────────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2011.6198
Iteration 1: log likelihood = -1628.2482
Iteration 2: log likelihood = -1396.5351
Iteration 3: log likelihood = -1387.6987
Iteration 4: log likelihood = -1387.6569
Iteration 5: log likelihood = -1387.6569
Logistic regression Number of obs = 10,001
LR chi2(3) = 1247.93
Prob > chi2 = 0.0000
Log likelihood = -1387.6569 Pseudo R2 = 0.3102
────────────────────┬────────────────────────────────────────────────────────────────
u3 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
────────────────────┼────────────────────────────────────────────────────────────────
1.focal │ .1010664 .2011999 0.50 0.615 -.2932782 .495411
f_est_bayes │ 2.017137 .101751 19.82 0.000 1.817708 2.216565
│
focal#c.f_est_bayes │
1 │ -.1353194 .1398696 -0.97 0.333 -.4094587 .1388199
│
_cons │ -4.403405 .1457512 -30.21 0.000 -4.689072 -4.117738
────────────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -1976.3606
Iteration 1: log likelihood = -1611.9891
Iteration 2: log likelihood = -1392.8889
Iteration 3: log likelihood = -1385.2905
Iteration 4: log likelihood = -1385.2512
Iteration 5: log likelihood = -1385.2512
Logistic regression Number of obs = 10,001
LR chi2(3) = 1182.22
Prob > chi2 = 0.0000
Log likelihood = -1385.2512 Pseudo R2 = 0.2991
────────────────────┬────────────────────────────────────────────────────────────────
u4 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
────────────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.0003828 .1983158 -0.00 0.998 -.3890746 .3883089
f_est_bayes │ 1.95136 .0990443 19.70 0.000 1.757237 2.145483
│
focal#c.f_est_bayes │
1 │ -.1139427 .1379302 -0.83 0.409 -.3842809 .1563955
│
_cons │ -4.317148 .1408297 -30.66 0.000 -4.593169 -4.041127
────────────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2061.0617
Iteration 1: log likelihood = -1684.9126
Iteration 2: log likelihood = -1482.0622
Iteration 3: log likelihood = -1475.962
Iteration 4: log likelihood = -1475.9244
Iteration 5: log likelihood = -1475.9244
Logistic regression Number of obs = 10,001
LR chi2(3) = 1170.27
Prob > chi2 = 0.0000
Log likelihood = -1475.9244 Pseudo R2 = 0.2839
────────────────────┬────────────────────────────────────────────────────────────────
u5 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
────────────────────┼────────────────────────────────────────────────────────────────
1.focal │ .16324 .1852528 0.88 0.378 -.1998488 .5263288
f_est_bayes │ 1.867065 .0962936 19.39 0.000 1.678333 2.055797
│
focal#c.f_est_bayes │
1 │ -.1008039 .1313737 -0.77 0.443 -.3582915 .1566838
│
_cons │ -4.230571 .1359761 -31.11 0.000 -4.497079 -3.964063
────────────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2681.4743
Iteration 1: log likelihood = -2123.0032
Iteration 2: log likelihood = -1905.2671
Iteration 3: log likelihood = -1898.816
Iteration 4: log likelihood = -1898.7924
Iteration 5: log likelihood = -1898.7924
Logistic regression Number of obs = 10,001
LR chi2(3) = 1565.36
Prob > chi2 = 0.0000
Log likelihood = -1898.7924 Pseudo R2 = 0.2919
────────────────────┬────────────────────────────────────────────────────────────────
u6 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
────────────────────┼────────────────────────────────────────────────────────────────
1.focal │ .1617065 .1512602 1.07 0.285 -.1347579 .458171
f_est_bayes │ 1.839442 .084289 21.82 0.000 1.674239 2.004646
│
focal#c.f_est_bayes │
1 │ -.0372411 .1160421 -0.32 0.748 -.2646795 .1901974
│
_cons │ -3.741616 .1107006 -33.80 0.000 -3.958585 -3.524647
────────────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2673.9607
Iteration 1: log likelihood = -2072.4919
Iteration 2: log likelihood = -1814.1819
Iteration 3: log likelihood = -1804.1159
Iteration 4: log likelihood = -1804.0777
Iteration 5: log likelihood = -1804.0777
Logistic regression Number of obs = 10,001
LR chi2(3) = 1739.77
Prob > chi2 = 0.0000
Log likelihood = -1804.0777 Pseudo R2 = 0.3253
────────────────────┬────────────────────────────────────────────────────────────────
u7 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
────────────────────┼────────────────────────────────────────────────────────────────
1.focal │ .0018105 .1640085 0.01 0.991 -.3196402 .3232611
f_est_bayes │ 1.945328 .0877178 22.18 0.000 1.773404 2.117252
│
focal#c.f_est_bayes │
1 │ .0875813 .124389 0.70 0.481 -.1562168 .3313793
│
_cons │ -3.850159 .1160671 -33.17 0.000 -4.077646 -3.622671
────────────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2615.9245
Iteration 1: log likelihood = -2052.747
Iteration 2: log likelihood = -1816.2245
Iteration 3: log likelihood = -1808.0281
Iteration 4: log likelihood = -1807.9863
Iteration 5: log likelihood = -1807.9863
Logistic regression Number of obs = 10,001
LR chi2(3) = 1615.88
Prob > chi2 = 0.0000
Log likelihood = -1807.9863 Pseudo R2 = 0.3089
────────────────────┬────────────────────────────────────────────────────────────────
u8 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
────────────────────┼────────────────────────────────────────────────────────────────
1.focal │ .2425535 .1613619 1.50 0.133 -.0737101 .5588171
f_est_bayes │ 1.991921 .0899627 22.14 0.000 1.815597 2.168245
│
focal#c.f_est_bayes │
1 │ -.1603309 .1218368 -1.32 0.188 -.3991266 .0784648
│
_cons │ -3.93049 .1200288 -32.75 0.000 -4.165743 -3.695238
────────────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2728.7632
Iteration 1: log likelihood = -2092.9326
Iteration 2: log likelihood = -1820.0639
Iteration 3: log likelihood = -1808.4247
Iteration 4: log likelihood = -1808.3851
Iteration 5: log likelihood = -1808.3851
Logistic regression Number of obs = 10,001
LR chi2(3) = 1840.76
Prob > chi2 = 0.0000
Log likelihood = -1808.3851 Pseudo R2 = 0.3373
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u9 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
────────────────────┼────────────────────────────────────────────────────────────────
1.focal │ .1863548 .1663344 1.12 0.263 -.1396547 .5123643
f_est_bayes │ 2.084298 .0919163 22.68 0.000 1.904146 2.264451
│
focal#c.f_est_bayes │
1 │ -.0653359 .1264097 -0.52 0.605 -.3130944 .1824226
│
_cons │ -3.970444 .1221161 -32.51 0.000 -4.209787 -3.7311
────────────────────┴────────────────────────────────────────────────────────────────
Iteration 0: log likelihood = -2802.4074
Iteration 1: log likelihood = -2177.9652
Iteration 2: log likelihood = -1937.4252
Iteration 3: log likelihood = -1929.4049
Iteration 4: log likelihood = -1929.3664
Iteration 5: log likelihood = -1929.3664
Logistic regression Number of obs = 10,001
LR chi2(3) = 1746.08
Prob > chi2 = 0.0000
Log likelihood = -1929.3664 Pseudo R2 = 0.3115
────────────────────┬────────────────────────────────────────────────────────────────
u10 │ Coef. Std. Err. z P>|z| [95% Conf. Interval]
────────────────────┼────────────────────────────────────────────────────────────────
1.focal │ -.0948999 .1522199 -0.62 0.533 -.3932455 .2034456
f_est_bayes │ 1.850282 .0819606 22.58 0.000 1.689642 2.010921
│
focal#c.f_est_bayes │
1 │ .1275024 .1180057 1.08 0.280 -.1037844 .3587893
│
_cons │ -3.622359 .105405 -34.37 0.000 -3.828949 -3.415769
────────────────────┴────────────────────────────────────────────────────────────────
The answer is yes, the excess type-I error problem goes away with Bayes factor score estimates.
It is unknown if there is any power to detect DIF if it really existed with the Bayes factor score estimate approach, so this is only half the important answer.
fin