Chapter 9 Multilevel Models
9.1 Syntax - R
9.1.1 A complex multilevel model example
## IDCNTRY IDSCHOOL IDCLASS IDSTUD ITSEX HOUWGT TOTWGT SENWGT WGTADJ1
## 1 840 1 101 10101 1 2.376047 670.8743 0.093354 1.357143
## 2 840 1 101 10102 0 2.376047 670.8743 0.093354 1.357143
## 3 840 1 101 10103 0 2.376047 670.8743 0.093354 1.357143
## 4 840 1 101 10104 0 2.376047 670.8743 0.093354 1.357143
## 5 840 1 101 10105 0 2.376047 670.8743 0.093354 1.357143
## 6 840 1 101 10107 0 2.376047 670.8743 0.093354 1.357143
## WGTADJ2 WGTADJ3 WGTFAC1 WGTFAC2 WGTFAC3 ASRREA01 ASRLIT01 ASRINF01 ASRIIE01
## 1 1 1.047619 235.9295 2 1 623.0440 616.2586 684.2183 611.2626
## 2 1 1.047619 235.9295 2 1 567.8146 531.5564 537.5982 551.6583
## 3 1 1.047619 235.9295 2 1 526.2780 541.2821 508.9297 512.5652
## 4 1 1.047619 235.9295 2 1 462.7912 510.8852 486.9025 467.2205
## 5 1 1.047619 235.9295 2 1 466.4158 447.5467 494.9719 517.2582
## 6 1 1.047619 235.9295 2 1 614.8899 615.3620 605.4589 512.6821
## ASRRSI01 ASBGSBS ASBGSLR ASBGSMR ASBGSCR ASBGERL ASDG05S ASBG03N ASNG03B
## 1 601.7178 13.28372 9.88980 8.78118 12.25876 10.51137 2 2 2
## 2 546.1009 8.29063 10.61953 12.36856 10.12500 8.64503 2 1 1
## 3 510.4456 9.56564 9.31239 8.78118 8.37394 9.45792 2 1 1
## 4 470.2884 NA 8.74575 8.31489 8.67056 7.39451 1 1 NA
## 5 516.4948 13.15502 6.89835 6.78134 8.98289 8.64503 2 3 2
## 6 490.1887 8.55138 11.09533 12.36856 11.29688 10.51137 2 2 2
## ASNG04A ASNG04B ASNG04C ASNG09A ASNG09B ASNG09C ASNG09D ASNG10 MSRACE2
## 1 1 1 1 2 1 2 2 2 5
## 2 1 1 1 1 2 1 1 1 2
## 3 1 2 1 1 2 1 2 5 3
## 4 1 1 1 2 2 1 2 2 3
## 5 1 1 1 1 2 2 2 4 3
## 6 2 2 1 1 2 2 2 2 2## IDCNTRY IDSCHOOL IDCLASS IDSTUD ITSEX HOUWGT TOTWGT SENWGT
## 0 0 0 0 0 0 0 0
## WGTADJ1 WGTADJ2 WGTADJ3 WGTFAC1 WGTFAC2 WGTFAC3 ASRREA01 ASRLIT01
## 0 0 0 0 0 0 0 0
## ASRINF01 ASRIIE01 ASRRSI01 ASBGSBS ASBGSLR ASBGSMR ASBGSCR ASBGERL
## 0 0 0 299 104 345 323 303
## ASDG05S ASBG03N ASNG03B ASNG04A ASNG04B ASNG04C ASNG09A ASNG09B
## 237 240 7412 398 426 216 170 270
## ASNG09C ASNG09D ASNG10 MSRACE2
## 372 318 303 268complex.2level.dat$read <- complex.2level.dat$ASRREA01/50 #rescale variable for reading achievement
complex.2level.model <- '
level: 1
read ~ b1*ASBGSBS + b2*ASBGSLR + b3*ASBGSMR + b4*ASBGSCR + b5*ASBGERL
read ~~ read
ASBGSBS ~~ ASBGSBS
ASBGSLR ~~ ASBGSLR
ASBGSMR ~~ ASBGSMR
ASBGSCR ~~ ASBGSCR
ASBGERL ~~ ASBGERL
ASBGSBS ~~ ASBGSLR + ASBGSMR + ASBGSCR + ASBGERL
ASBGSLR ~~ ASBGSMR + ASBGSCR + ASBGERL
ASBGSMR ~~ ASBGSCR + ASBGERL
ASBGSCR ~~ ASBGERL
level: 2
read ~ bb1*ASBGSBS + bb2*ASBGSLR + bb3*ASBGSMR + bb4*ASBGSCR + bb5*ASBGERL
read ~~ read
ASBGSBS ~~ ASBGSBS
ASBGSLR ~~ ASBGSLR
ASBGSMR ~~ ASBGSMR
ASBGSCR ~~ ASBGSCR
ASBGERL ~~ ASBGERL
ASBGSBS ~~ ASBGSLR + ASBGSMR + ASBGSCR + ASBGERL
ASBGSLR ~~ ASBGSMR + ASBGSCR + ASBGERL
ASBGSMR ~~ ASBGSCR + ASBGERL
ASBGSCR ~~ ASBGERL
effect1 := bb1-b1
effect2 := bb2-b2
effect3 := bb3-b3
effect4 := bb4-b4
effect5 := bb5-b5'
complex.2level.fit <- sem(model = complex.2level.model, data = complex.2level.dat, cluster = "IDCLASS")
summary(complex.2level.fit, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE) ## lavaan 0.6-8 ended normally after 128 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 48
##
## Used Total
## Number of observations 12057 12726
## Number of clusters [IDCLASS] 618
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 13993.766
## Degrees of freedom 30
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -142454.898
## Loglikelihood unrestricted model (H1) -142454.899
##
## Akaike (AIC) 285005.797
## Bayesian (BIC) 285360.872
## Sample-size adjusted Bayesian (BIC) 285208.334
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value RMSEA <= 0.05 NA
##
## Standardized Root Mean Square Residual (corr metric):
##
## SRMR (within covariance matrix) 0.000
## SRMR (between covariance matrix) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
##
## Level 1 [within]:
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## read ~
## ASBGSBS (b1) 0.051 0.005 9.666 0.000 0.051 0.083
## ASBGSLR (b2) 0.100 0.006 15.918 0.000 0.100 0.171
## ASBGSMR (b3) -0.096 0.007 -14.576 0.000 -0.096 -0.151
## ASBGSCR (b4) 0.236 0.006 41.372 0.000 0.236 0.379
## ASBGERL (b5) -0.003 0.007 -0.439 0.660 -0.003 -0.004
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ASBGSBS ~~
## ASBGSLR 0.176 0.041 4.324 0.000 0.176 0.040
## ASBGSMR 0.134 0.037 3.578 0.000 0.134 0.033
## ASBGSCR 0.431 0.039 11.179 0.000 0.431 0.105
## ASBGERL 0.722 0.037 19.662 0.000 0.722 0.187
## ASBGSLR ~~
## ASBGSMR 2.272 0.045 50.448 0.000 2.272 0.535
## ASBGSCR 1.652 0.044 37.956 0.000 1.652 0.380
## ASBGERL 1.925 0.042 45.469 0.000 1.925 0.470
## ASBGSMR ~~
## ASBGSCR 1.124 0.039 28.948 0.000 1.124 0.281
## ASBGERL 1.739 0.039 44.850 0.000 1.739 0.462
## ASBGSCR ~~
## ASBGERL 1.072 0.037 28.640 0.000 1.072 0.278
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .read 0.000 0.000 0.000
## ASBGSBS 0.000 0.000 0.000
## ASBGSLR 0.000 0.000 0.000
## ASBGSMR 0.000 0.000 0.000
## ASBGSCR 0.000 0.000 0.000
## ASBGERL 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .read 1.271 0.017 75.620 0.000 1.271 0.802
## ASBGSBS 4.108 0.054 75.648 0.000 4.108 1.000
## ASBGSLR 4.626 0.061 75.671 0.000 4.626 1.000
## ASBGSMR 3.904 0.052 75.666 0.000 3.904 1.000
## ASBGSCR 4.090 0.054 75.588 0.000 4.090 1.000
## ASBGERL 3.631 0.048 75.591 0.000 3.631 1.000
##
## R-Square:
## Estimate
## read 0.198
##
##
## Level 2 [IDCLASS]:
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## read ~
## ASBGSBS (bb1) 0.080 0.135 0.593 0.553 0.080 0.050
## ASBGSLR (bb2) 0.959 0.171 5.619 0.000 0.959 0.752
## ASBGSMR (bb3) -1.086 0.212 -5.121 0.000 -1.086 -0.658
## ASBGSCR (bb4) 0.508 0.146 3.473 0.001 0.508 0.297
## ASBGERL (bb5) -0.023 0.144 -0.163 0.871 -0.023 -0.018
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ASBGSBS ~~
## ASBGSLR 0.138 0.021 6.605 0.000 0.138 0.525
## ASBGSMR 0.034 0.017 1.989 0.047 0.034 0.165
## ASBGSCR 0.067 0.017 3.902 0.000 0.067 0.342
## ASBGERL 0.116 0.020 5.866 0.000 0.116 0.460
## ASBGSLR ~~
## ASBGSMR 0.170 0.023 7.484 0.000 0.170 0.660
## ASBGSCR 0.128 0.021 5.992 0.000 0.128 0.517
## ASBGERL 0.236 0.026 9.183 0.000 0.236 0.742
## ASBGSMR ~~
## ASBGSCR 0.021 0.017 1.258 0.208 0.021 0.109
## ASBGERL 0.172 0.021 8.111 0.000 0.172 0.697
## ASBGSCR ~~
## ASBGERL 0.100 0.019 5.168 0.000 0.100 0.421
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .read 6.707 2.055 3.264 0.001 6.707 9.112
## ASBGSBS 10.169 0.026 387.428 0.000 10.169 22.252
## ASBGSLR 9.725 0.031 317.934 0.000 9.725 16.861
## ASBGSMR 9.774 0.026 381.719 0.000 9.774 21.914
## ASBGSCR 10.177 0.025 399.648 0.000 10.177 23.636
## ASBGERL 10.058 0.028 353.999 0.000 10.058 18.217
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .read 0.188 0.026 7.218 0.000 0.188 0.346
## ASBGSBS 0.209 0.024 8.540 0.000 0.209 1.000
## ASBGSLR 0.333 0.033 10.112 0.000 0.333 1.000
## ASBGSMR 0.199 0.023 8.628 0.000 0.199 1.000
## ASBGSCR 0.185 0.023 7.983 0.000 0.185 1.000
## ASBGERL 0.305 0.029 10.614 0.000 0.305 1.000
##
## R-Square:
## Estimate
## read 0.654
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## effect1 0.029 0.135 0.211 0.833 0.029 -0.033
## effect2 0.859 0.171 5.020 0.000 0.859 0.581
## effect3 -0.990 0.213 -4.656 0.000 -0.990 -0.507
## effect4 0.272 0.147 1.851 0.064 0.272 -0.082
## effect5 -0.020 0.144 -0.142 0.887 -0.020 -0.0139.2 Syntax - Mplus
9.2.1 A complex multilevel model example
TITLE:
DATA: FILE IS "data\P4_STUDENT11US_reduceddatasetPV1.dat";
FORMAT IS F3 F4 F6 F8 F1 F9 F12 4F9 F12 F9 F6 5F10 5F13 12F1;
VARIABLE: NAMES ARE IDCNTRY IDSCHOOL IDCLASS IDSTUD ITSEX
HOUWGT TOTWGT SENWGT WGTADJ1 WGTADJ2 WGTADJ3 WGTFAC1 WGTFAC2 WGTFAC3
ASRREA ASRLIT ASRINF ASRIIE ASRRSI
ASBGSBS ASBGSLR ASBGSMR ASBGSCR ASBGERL ASDG05S ASBG03N ASNG03B
ASNG04A ASNG04B ASNG04C ASNG09A ASNG09B ASNG09C ASNG09D ASNG10 MSRACE2;
MISSING = BLANK;
USEVARIABLES ARE ASBGSBS ASBGSLR ASBGSMR ASBGSCR ASBGERL
read wt1 wt2;
AUXILIARY ARE IDCNTRY IDSTUD ITSEX;
CLUSTER = IDSCHOOL IDCLASS;
WEIGHT IS wt1;
WTSCALE IS CLUSTER;
BWEIGHT IS wt2;
BWTSCALE IS SAMPLE;
DEFINE:
read=ASRREA/50;
wt1 = WGTADJ3*WGTFAC3;
wt2 = WGTADJ1*WGTFAC1*WGTADJ2*WGTFAC2;
ANALYSIS: TYPE = COMPLEX TWOLEVEL;
OUTPUT: SAMPSTAT STANDARDIZED MODINDICES;
MODEL: %WITHIN%
read on ASBGSBS (b1)
ASBGSLR (b2)
ASBGSMR (b3)
ASBGSCR (b4)
ASBGERL (b5);
read (var1);
ASBGSBS (var2);
ASBGSLR (var3);
ASBGSMR (var4);
ASBGSCR (var5);
ASBGERL (var6);
ASBGSBS with ASBGSLR (cov1);
ASBGSBS with ASBGSMR (cov2);
ASBGSBS with ASBGSCR (cov3);
ASBGSBS with ASBGERL (cov4);
ASBGSLR with ASBGSMR (cov5);
ASBGSLR with ASBGSCR (cov6);
ASBGSLR with ASBGERL (cov7);
ASBGSMR with ASBGSCR (cov8);
ASBGSMR with ASBGERL (cov9);
ASBGSCR with ASBGERL (cov10);
%BETWEEN%
read on ASBGSBS (bb1)
ASBGSLR (bb2)
ASBGSMR (bb3)
ASBGSCR (bb4)
ASBGERL (bb5);
read (vvar1);
ASBGSBS (vvar2);
ASBGSLR (vvar3);
ASBGSMR (vvar4);
ASBGSCR (vvar5);
ASBGERL (vvar6);
ASBGSBS with ASBGSLR (ccov1);
ASBGSBS with ASBGSMR (ccov2);
ASBGSBS with ASBGSCR (ccov3);
ASBGSBS with ASBGERL (ccov4);
ASBGSLR with ASBGSMR (ccov5);
ASBGSLR with ASBGSCR (ccov6);
ASBGSLR with ASBGERL (ccov7);
ASBGSMR with ASBGSCR (ccov8);
ASBGSMR with ASBGERL (ccov9);
ASBGSCR with ASBGERL (ccov10);
MODEL CONSTRAINT:
NEW(effect1);
NEW(effect2);
NEW(effect3);
NEW(effect4);
NEW(effect5);
effect1=bb1-b1;
effect2=bb2-b2;
effect3=bb3-b3;
effect4=bb4-b4;
effect5=bb5-b5;
MODEL TEST:
effect1=0;
effect2=0;
effect3=0;
effect4=0;
effect5=0;## Mplus VERSION 8.4
## MUTHEN & MUTHEN
## 06/10/2021 12:20 PM
##
## INPUT INSTRUCTIONS
##
## TITLE:
## DATA: FILE IS "data\P4_STUDENT11US_reduceddatasetPV1.dat";
## FORMAT IS F3 F4 F6 F8 F1 F9 F12 4F9 F12 F9 F6 5F10 5F13 12F1;
## VARIABLE: NAMES ARE IDCNTRY IDSCHOOL IDCLASS IDSTUD ITSEX
## HOUWGT TOTWGT SENWGT WGTADJ1 WGTADJ2 WGTADJ3 WGTFAC1 WGTFAC2 WGTFAC3
## ASRREA ASRLIT ASRINF ASRIIE ASRRSI
## ASBGSBS ASBGSLR ASBGSMR ASBGSCR ASBGERL ASDG05S ASBG03N ASNG03B
## ASNG04A ASNG04B ASNG04C ASNG09A ASNG09B ASNG09C ASNG09D ASNG10 MSRACE2;
## MISSING = BLANK;
## USEVARIABLES ARE ASBGSBS ASBGSLR ASBGSMR ASBGSCR ASBGERL
## read wt1 wt2;
## AUXILIARY ARE IDCNTRY IDSTUD ITSEX;
## CLUSTER = IDSCHOOL IDCLASS;
## WEIGHT IS wt1;
## WTSCALE IS CLUSTER;
## BWEIGHT IS wt2;
## BWTSCALE IS SAMPLE;
## DEFINE:
## read=ASRREA/50;
## wt1 = WGTADJ3*WGTFAC3;
## wt2 = WGTADJ1*WGTFAC1*WGTADJ2*WGTFAC2;
## ANALYSIS: TYPE = COMPLEX TWOLEVEL;
## OUTPUT: SAMPSTAT STANDARDIZED MODINDICES;
## MODEL: %WITHIN%
## read on ASBGSBS (b1)
## ASBGSLR (b2)
## ASBGSMR (b3)
## ASBGSCR (b4)
## ASBGERL (b5);
## read (var1);
## ASBGSBS (var2);
## ASBGSLR (var3);
## ASBGSMR (var4);
## ASBGSCR (var5);
## ASBGERL (var6);
## ASBGSBS with ASBGSLR (cov1);
## ASBGSBS with ASBGSMR (cov2);
## ASBGSBS with ASBGSCR (cov3);
## ASBGSBS with ASBGERL (cov4);
## ASBGSLR with ASBGSMR (cov5);
## ASBGSLR with ASBGSCR (cov6);
## ASBGSLR with ASBGERL (cov7);
## ASBGSMR with ASBGSCR (cov8);
## ASBGSMR with ASBGERL (cov9);
## ASBGSCR with ASBGERL (cov10);
## %BETWEEN%
## read on ASBGSBS (bb1)
## ASBGSLR (bb2)
## ASBGSMR (bb3)
## ASBGSCR (bb4)
## ASBGERL (bb5);
## read (vvar1);
## ASBGSBS (vvar2);
## ASBGSLR (vvar3);
## ASBGSMR (vvar4);
## ASBGSCR (vvar5);
## ASBGERL (vvar6);
## ASBGSBS with ASBGSLR (ccov1);
## ASBGSBS with ASBGSMR (ccov2);
## ASBGSBS with ASBGSCR (ccov3);
## ASBGSBS with ASBGERL (ccov4);
## ASBGSLR with ASBGSMR (ccov5);
## ASBGSLR with ASBGSCR (ccov6);
## ASBGSLR with ASBGERL (ccov7);
## ASBGSMR with ASBGSCR (ccov8);
## ASBGSMR with ASBGERL (ccov9);
## ASBGSCR with ASBGERL (ccov10);
## MODEL CONSTRAINT:
## NEW(effect1);
## NEW(effect2);
## NEW(effect3);
## NEW(effect4);
## NEW(effect5);
## effect1=bb1-b1;
## effect2=bb2-b2;
## effect3=bb3-b3;
## effect4=bb4-b4;
## effect5=bb5-b5;
## MODEL TEST:
## effect1=0;
## effect2=0;
## effect3=0;
## effect4=0;
## effect5=0;
##
##
##
## *** WARNING in OUTPUT command
## MODINDICES option is not available in conjunction with nonlinear constraints
## through the use of MODEL CONSTRAINT. Request for MODINDICES is ignored.
## 1 ERROR(S) FOUND IN THE INPUT INSTRUCTIONS
## 1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
##
##
##
##
## SUMMARY OF ANALYSIS
##
## Number of groups 1
## Number of observations 12726
##
## Number of dependent variables 1
## Number of independent variables 5
## Number of continuous latent variables 0
##
## Observed dependent variables
##
## Continuous
## READ
##
## Observed independent variables
## ASBGSBS ASBGSLR ASBGSMR ASBGSCR ASBGERL
##
## Observed auxiliary variables
## IDCNTRY IDSTUD ITSEX
##
## Variables with special functions
##
## Cluster variables IDSCHOOL IDCLASS
## Weight variable (cluster-size scaling)
## WT1
## Between weight variable (sample-size scaling)
## WT2
##
## Estimator MLR
## Information matrix OBSERVED
## Maximum number of iterations 100
## Convergence criterion 0.100D-05
## Maximum number of EM iterations 500
## Convergence criteria for the EM algorithm
## Loglikelihood change 0.100D-02
## Relative loglikelihood change 0.100D-05
## Derivative 0.100D-03
## Minimum variance 0.100D-03
## Maximum number of steepest descent iterations 20
## Maximum number of iterations for H1 2000
## Convergence criterion for H1 0.100D-03
## Optimization algorithm EMA
##
## Input data file(s)
## data\P4_STUDENT11US_reduceddatasetPV1.dat
## Input data format
## (F3 F4 F6 F8 F1 F9 F12 4F9 F12 F9 F6 5F10 5F13 12F1)
##
##
## SUMMARY OF DATA
##
## Number of missing data patterns 25
## Number of IDSCHOOL clusters 370
## Number of IDCLASS clusters 618
##
##
## COVARIANCE COVERAGE OF DATA
##
## Minimum covariance coverage value 0.100
##
##
## PROPORTION OF DATA PRESENT
##
##
## Covariance Coverage
## READ ASBGSBS ASBGSLR ASBGSMR ASBGSCR
## ________ ________ ________ ________ ________
## READ 1.000
## ASBGSBS 0.977 0.977
## ASBGSLR 0.992 0.976 0.992
## ASBGSMR 0.973 0.962 0.972 0.973
## ASBGSCR 0.975 0.964 0.974 0.965 0.975
## ASBGERL 0.976 0.966 0.976 0.964 0.967
##
##
## Covariance Coverage
## ASBGERL
## ________
## ASBGERL 0.976
##
##
## SAMPLE STATISTICS
##
## NOTE: The sample statistics for within and between refer to the
## maximum-likelihood estimated within and between covariance
## matrices, respectively.
##
##
## ESTIMATED SAMPLE STATISTICS FOR WITHIN
##
##
## Means
## READ ASBGSBS ASBGSLR ASBGSMR ASBGSCR
## ________ ________ ________ ________ ________
## 0.000 0.000 0.000 0.000 0.000
##
##
## Means
## ASBGERL
## ________
## 0.000
##
##
## Covariances
## READ ASBGSBS ASBGSLR ASBGSMR ASBGSCR
## ________ ________ ________ ________ ________
## READ 1.604
## ASBGSBS 0.330 4.106
## ASBGSLR 0.645 0.166 4.701
## ASBGSMR 0.116 0.134 2.289 3.888
## ASBGSCR 1.026 0.445 1.606 1.111 4.023
## ASBGERL 0.305 0.718 1.913 1.730 1.038
##
##
## Covariances
## ASBGERL
## ________
## ASBGERL 3.594
##
##
## Correlations
## READ ASBGSBS ASBGSLR ASBGSMR ASBGSCR
## ________ ________ ________ ________ ________
## READ 1.000
## ASBGSBS 0.128 1.000
## ASBGSLR 0.235 0.038 1.000
## ASBGSMR 0.047 0.034 0.535 1.000
## ASBGSCR 0.404 0.110 0.369 0.281 1.000
## ASBGERL 0.127 0.187 0.465 0.463 0.273
##
##
## Correlations
## ASBGERL
## ________
## ASBGERL 1.000
##
##
## ESTIMATED SAMPLE STATISTICS FOR BETWEEN
##
##
## Means
## READ ASBGSBS ASBGSLR ASBGSMR ASBGSCR
## ________ ________ ________ ________ ________
## 11.134 10.164 9.716 9.737 10.153
##
##
## Means
## ASBGERL
## ________
## 10.046
##
##
## Covariances
## READ ASBGSBS ASBGSLR ASBGSMR ASBGSCR
## ________ ________ ________ ________ ________
## READ 0.566
## ASBGSBS 0.159 0.232
## ASBGSLR 0.218 0.157 0.333
## ASBGSMR -0.044 0.039 0.169 0.201
## ASBGSCR 0.212 0.061 0.133 0.024 0.193
## ASBGERL 0.104 0.108 0.220 0.155 0.103
##
##
## Covariances
## ASBGERL
## ________
## ASBGERL 0.288
##
##
## Correlations
## READ ASBGSBS ASBGSLR ASBGSMR ASBGSCR
## ________ ________ ________ ________ ________
## READ 1.000
## ASBGSBS 0.440 1.000
## ASBGSLR 0.502 0.565 1.000
## ASBGSMR -0.131 0.181 0.652 1.000
## ASBGSCR 0.640 0.290 0.524 0.120 1.000
## ASBGERL 0.258 0.417 0.712 0.646 0.438
##
##
## Correlations
## ASBGERL
## ________
## ASBGERL 1.000
##
##
## MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -147892.013
##
##
## UNIVARIATE SAMPLE STATISTICS
##
##
## UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
##
## Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
## Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
##
## READ 11.140 -0.224 5.493 0.01% 9.914 10.835 11.203
## 12726.000 2.149 0.008 16.347 0.01% 11.564 12.371
## ASBGSBS 10.173 -0.168 3.759 1.25% 8.551 9.403 10.147
## 12427.000 4.331 -0.074 13.284 19.94% 10.668 13.013
## ASBGSLR 9.725 0.152 2.546 0.90% 8.123 9.055 9.591
## 12622.000 5.028 0.896 14.956 5.88% 9.947 11.095
## ASBGSMR 9.739 -0.219 2.453 0.53% 7.935 8.781 9.402
## 12381.000 4.094 -0.313 12.369 28.99% 10.350 12.369
## ASBGSCR 10.169 0.538 1.979 0.03% 8.374 9.320 9.697
## 12403.000 4.200 -0.039 14.359 11.51% 10.641 11.297
## ASBGERL 10.050 0.368 2.071 0.07% 8.298 9.458 9.945
## 12423.000 3.878 0.315 14.323 8.77% 10.511 11.210
##
##
## THE MODEL ESTIMATION TERMINATED NORMALLY
##
##
##
## MODEL FIT INFORMATION
##
## Number of Free Parameters 48
##
## Loglikelihood
##
## H0 Value -147892.012
## H0 Scaling Correction Factor 1.5963
## for MLR
## H1 Value -147892.013
## H1 Scaling Correction Factor 1.5963
## for MLR
##
## Information Criteria
##
## Akaike (AIC) 295880.025
## Bayesian (BIC) 296237.692
## Sample-Size Adjusted BIC 296085.153
## (n* = (n + 2) / 24)
##
## Chi-Square Test of Model Fit
##
## Value 0.000*
## Degrees of Freedom 0
## P-Value 1.0000
## Scaling Correction Factor 1.0000
## for MLR
##
## * 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
##
## CFI/TLI
##
## CFI 1.000
## TLI 1.000
##
## Chi-Square Test of Model Fit for the Baseline Model
##
## Value 9153.483
## Degrees of Freedom 30
## P-Value 0.0000
##
## SRMR (Standardized Root Mean Square Residual)
##
## Value for Within 0.000
## Value for Between 0.000
##
## Wald Test of Parameter Constraints
##
## Value 102.281
## Degrees of Freedom 5
## P-Value 0.0000
##
##
##
## MODEL RESULTS
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Within Level
##
## READ ON
## ASBGSBS 0.054 0.006 8.313 0.000
## ASBGSLR 0.104 0.007 14.140 0.000
## ASBGSMR -0.100 0.008 -12.776 0.000
## ASBGSCR 0.236 0.006 38.895 0.000
## ASBGERL -0.001 0.008 -0.164 0.870
##
## ASBGSBS WITH
## ASBGSLR 0.166 0.049 3.396 0.001
## ASBGSMR 0.134 0.046 2.942 0.003
## ASBGSCR 0.445 0.041 10.862 0.000
## ASBGERL 0.718 0.044 16.426 0.000
##
## ASBGSLR WITH
## ASBGSMR 2.289 0.066 34.561 0.000
## ASBGSCR 1.606 0.058 27.751 0.000
## ASBGERL 1.913 0.062 31.003 0.000
##
## ASBGSMR WITH
## ASBGSCR 1.111 0.052 21.320 0.000
## ASBGERL 1.730 0.053 32.824 0.000
##
## ASBGSCR WITH
## ASBGERL 1.038 0.049 21.171 0.000
##
## Variances
## ASBGSBS 4.106 0.064 64.092 0.000
## ASBGSLR 4.701 0.105 44.710 0.000
## ASBGSMR 3.888 0.065 59.959 0.000
## ASBGSCR 4.023 0.072 55.682 0.000
## ASBGERL 3.594 0.065 55.493 0.000
##
## Residual Variances
## READ 1.289 0.022 57.418 0.000
##
## Between Level
##
## READ ON
## ASBGSBS 0.077 0.165 0.468 0.640
## ASBGSLR 0.962 0.227 4.240 0.000
## ASBGSMR -1.107 0.240 -4.618 0.000
## ASBGSCR 0.545 0.173 3.159 0.002
## ASBGERL -0.001 0.155 -0.008 0.994
##
## ASBGSBS WITH
## ASBGSLR 0.157 0.021 7.378 0.000
## ASBGSMR 0.039 0.019 2.051 0.040
## ASBGSCR 0.061 0.021 2.919 0.004
## ASBGERL 0.108 0.023 4.627 0.000
##
## ASBGSLR WITH
## ASBGSMR 0.169 0.026 6.444 0.000
## ASBGSCR 0.133 0.026 5.181 0.000
## ASBGERL 0.220 0.025 8.721 0.000
##
## ASBGSMR WITH
## ASBGSCR 0.024 0.021 1.124 0.261
## ASBGERL 0.155 0.021 7.310 0.000
##
## ASBGSCR WITH
## ASBGERL 0.103 0.020 5.131 0.000
##
## Means
## ASBGSBS 10.164 0.035 292.331 0.000
## ASBGSLR 9.716 0.037 263.533 0.000
## ASBGSMR 9.737 0.031 312.511 0.000
## ASBGSCR 10.153 0.032 322.181 0.000
## ASBGERL 10.046 0.032 315.028 0.000
##
## Intercepts
## READ 6.259 2.438 2.568 0.010
##
## Variances
## ASBGSBS 0.232 0.030 7.650 0.000
## ASBGSLR 0.333 0.033 10.048 0.000
## ASBGSMR 0.201 0.027 7.502 0.000
## ASBGSCR 0.193 0.029 6.741 0.000
## ASBGERL 0.288 0.033 8.871 0.000
##
## Residual Variances
## READ 0.180 0.031 5.903 0.000
##
## New/Additional Parameters
## EFFECT1 0.023 0.166 0.139 0.889
## EFFECT2 0.858 0.228 3.768 0.000
## EFFECT3 -1.007 0.240 -4.194 0.000
## EFFECT4 0.309 0.173 1.792 0.073
## EFFECT5 0.000 0.156 0.001 0.999
##
##
## STANDARDIZED MODEL RESULTS
##
##
## STDYX Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Within Level
##
## READ ON
## ASBGSBS 0.086 0.010 8.277 0.000
## ASBGSLR 0.178 0.013 14.000 0.000
## ASBGSMR -0.155 0.012 -13.031 0.000
## ASBGSCR 0.373 0.009 41.817 0.000
## ASBGERL -0.002 0.012 -0.164 0.870
##
## ASBGSBS WITH
## ASBGSLR 0.038 0.011 3.392 0.001
## ASBGSMR 0.034 0.011 2.936 0.003
## ASBGSCR 0.110 0.010 10.763 0.000
## ASBGERL 0.187 0.011 17.031 0.000
##
## ASBGSLR WITH
## ASBGSMR 0.535 0.009 60.873 0.000
## ASBGSCR 0.369 0.012 31.613 0.000
## ASBGERL 0.465 0.010 46.207 0.000
##
## ASBGSMR WITH
## ASBGSCR 0.281 0.012 24.054 0.000
## ASBGERL 0.463 0.010 46.828 0.000
##
## ASBGSCR WITH
## ASBGERL 0.273 0.012 23.633 0.000
##
## Variances
## ASBGSBS 1.000 0.000 999.000 999.000
## ASBGSLR 1.000 0.000 999.000 999.000
## ASBGSMR 1.000 0.000 999.000 999.000
## ASBGSCR 1.000 0.000 999.000 999.000
## ASBGERL 1.000 0.000 999.000 999.000
##
## Residual Variances
## READ 0.804 0.007 110.332 0.000
##
## Between Level
##
## READ ON
## ASBGSBS 0.049 0.105 0.470 0.638
## ASBGSLR 0.738 0.177 4.179 0.000
## ASBGSMR -0.659 0.142 -4.625 0.000
## ASBGSCR 0.318 0.096 3.303 0.001
## ASBGERL -0.001 0.111 -0.008 0.994
##
## ASBGSBS WITH
## ASBGSLR 0.566 0.064 8.903 0.000
## ASBGSMR 0.180 0.085 2.111 0.035
## ASBGSCR 0.290 0.096 3.019 0.003
## ASBGERL 0.417 0.081 5.152 0.000
##
## ASBGSLR WITH
## ASBGSMR 0.653 0.054 12.076 0.000
## ASBGSCR 0.524 0.080 6.561 0.000
## ASBGERL 0.712 0.044 16.315 0.000
##
## ASBGSMR WITH
## ASBGSCR 0.120 0.105 1.146 0.252
## ASBGERL 0.646 0.055 11.854 0.000
##
## ASBGSCR WITH
## ASBGERL 0.438 0.064 6.803 0.000
##
## Means
## ASBGSBS 21.107 1.390 15.187 0.000
## ASBGSLR 16.840 0.844 19.960 0.000
## ASBGSMR 21.742 1.468 14.806 0.000
## ASBGSCR 23.107 1.711 13.507 0.000
## ASBGERL 18.710 1.058 17.689 0.000
##
## Intercepts
## READ 8.319 3.312 2.512 0.012
##
## Variances
## ASBGSBS 1.000 0.000 999.000 999.000
## ASBGSLR 1.000 0.000 999.000 999.000
## ASBGSMR 1.000 0.000 999.000 999.000
## ASBGSCR 1.000 0.000 999.000 999.000
## ASBGERL 1.000 0.000 999.000 999.000
##
## Residual Variances
## READ 0.319 0.055 5.828 0.000
##
##
## STDY Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Within Level
##
## READ ON
## ASBGSBS 0.086 0.010 8.277 0.000
## ASBGSLR 0.178 0.013 14.000 0.000
## ASBGSMR -0.155 0.012 -13.031 0.000
## ASBGSCR 0.373 0.009 41.817 0.000
## ASBGERL -0.002 0.012 -0.164 0.870
##
## ASBGSBS WITH
## ASBGSLR 0.038 0.011 3.392 0.001
## ASBGSMR 0.034 0.011 2.936 0.003
## ASBGSCR 0.110 0.010 10.763 0.000
## ASBGERL 0.187 0.011 17.031 0.000
##
## ASBGSLR WITH
## ASBGSMR 0.535 0.009 60.873 0.000
## ASBGSCR 0.369 0.012 31.613 0.000
## ASBGERL 0.465 0.010 46.207 0.000
##
## ASBGSMR WITH
## ASBGSCR 0.281 0.012 24.054 0.000
## ASBGERL 0.463 0.010 46.828 0.000
##
## ASBGSCR WITH
## ASBGERL 0.273 0.012 23.633 0.000
##
## Variances
## ASBGSBS 1.000 0.000 999.000 999.000
## ASBGSLR 1.000 0.000 999.000 999.000
## ASBGSMR 1.000 0.000 999.000 999.000
## ASBGSCR 1.000 0.000 999.000 999.000
## ASBGERL 1.000 0.000 999.000 999.000
##
## Residual Variances
## READ 0.804 0.007 110.332 0.000
##
## Between Level
##
## READ ON
## ASBGSBS 0.049 0.105 0.470 0.638
## ASBGSLR 0.738 0.177 4.179 0.000
## ASBGSMR -0.659 0.142 -4.625 0.000
## ASBGSCR 0.318 0.096 3.303 0.001
## ASBGERL -0.001 0.111 -0.008 0.994
##
## ASBGSBS WITH
## ASBGSLR 0.566 0.064 8.903 0.000
## ASBGSMR 0.180 0.085 2.111 0.035
## ASBGSCR 0.290 0.096 3.019 0.003
## ASBGERL 0.417 0.081 5.152 0.000
##
## ASBGSLR WITH
## ASBGSMR 0.653 0.054 12.076 0.000
## ASBGSCR 0.524 0.080 6.561 0.000
## ASBGERL 0.712 0.044 16.315 0.000
##
## ASBGSMR WITH
## ASBGSCR 0.120 0.105 1.146 0.252
## ASBGERL 0.646 0.055 11.854 0.000
##
## ASBGSCR WITH
## ASBGERL 0.438 0.064 6.803 0.000
##
## Means
## ASBGSBS 21.107 1.390 15.187 0.000
## ASBGSLR 16.840 0.844 19.960 0.000
## ASBGSMR 21.742 1.468 14.806 0.000
## ASBGSCR 23.107 1.711 13.507 0.000
## ASBGERL 18.710 1.058 17.689 0.000
##
## Intercepts
## READ 8.319 3.312 2.512 0.012
##
## Variances
## ASBGSBS 1.000 0.000 999.000 999.000
## ASBGSLR 1.000 0.000 999.000 999.000
## ASBGSMR 1.000 0.000 999.000 999.000
## ASBGSCR 1.000 0.000 999.000 999.000
## ASBGERL 1.000 0.000 999.000 999.000
##
## Residual Variances
## READ 0.319 0.055 5.828 0.000
##
##
## STD Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Within Level
##
## READ ON
## ASBGSBS 0.054 0.006 8.313 0.000
## ASBGSLR 0.104 0.007 14.140 0.000
## ASBGSMR -0.100 0.008 -12.776 0.000
## ASBGSCR 0.236 0.006 38.895 0.000
## ASBGERL -0.001 0.008 -0.164 0.870
##
## ASBGSBS WITH
## ASBGSLR 0.166 0.049 3.396 0.001
## ASBGSMR 0.134 0.046 2.942 0.003
## ASBGSCR 0.445 0.041 10.862 0.000
## ASBGERL 0.718 0.044 16.426 0.000
##
## ASBGSLR WITH
## ASBGSMR 2.289 0.066 34.561 0.000
## ASBGSCR 1.606 0.058 27.751 0.000
## ASBGERL 1.913 0.062 31.003 0.000
##
## ASBGSMR WITH
## ASBGSCR 1.111 0.052 21.320 0.000
## ASBGERL 1.730 0.053 32.824 0.000
##
## ASBGSCR WITH
## ASBGERL 1.038 0.049 21.171 0.000
##
## Variances
## ASBGSBS 4.106 0.064 64.092 0.000
## ASBGSLR 4.701 0.105 44.710 0.000
## ASBGSMR 3.888 0.065 59.959 0.000
## ASBGSCR 4.023 0.072 55.682 0.000
## ASBGERL 3.594 0.065 55.493 0.000
##
## Residual Variances
## READ 1.289 0.022 57.418 0.000
##
## Between Level
##
## READ ON
## ASBGSBS 0.077 0.165 0.468 0.640
## ASBGSLR 0.962 0.227 4.240 0.000
## ASBGSMR -1.107 0.240 -4.618 0.000
## ASBGSCR 0.545 0.173 3.159 0.002
## ASBGERL -0.001 0.155 -0.008 0.994
##
## ASBGSBS WITH
## ASBGSLR 0.157 0.021 7.378 0.000
## ASBGSMR 0.039 0.019 2.051 0.040
## ASBGSCR 0.061 0.021 2.919 0.004
## ASBGERL 0.108 0.023 4.627 0.000
##
## ASBGSLR WITH
## ASBGSMR 0.169 0.026 6.444 0.000
## ASBGSCR 0.133 0.026 5.181 0.000
## ASBGERL 0.220 0.025 8.721 0.000
##
## ASBGSMR WITH
## ASBGSCR 0.024 0.021 1.124 0.261
## ASBGERL 0.155 0.021 7.310 0.000
##
## ASBGSCR WITH
## ASBGERL 0.103 0.020 5.131 0.000
##
## Means
## ASBGSBS 10.164 0.035 292.331 0.000
## ASBGSLR 9.716 0.037 263.533 0.000
## ASBGSMR 9.737 0.031 312.511 0.000
## ASBGSCR 10.153 0.032 322.181 0.000
## ASBGERL 10.046 0.032 315.028 0.000
##
## Intercepts
## READ 6.259 2.438 2.568 0.010
##
## Variances
## ASBGSBS 0.232 0.030 7.650 0.000
## ASBGSLR 0.333 0.033 10.048 0.000
## ASBGSMR 0.201 0.027 7.502 0.000
## ASBGSCR 0.193 0.029 6.741 0.000
## ASBGERL 0.288 0.033 8.871 0.000
##
## Residual Variances
## READ 0.180 0.031 5.903 0.000
##
##
## R-SQUARE
##
## Within Level
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## READ 0.196 0.007 26.920 0.000
##
## Between Level
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## READ 0.681 0.055 12.464 0.000
##
##
## QUALITY OF NUMERICAL RESULTS
##
## Condition Number for the Information Matrix 0.326E-08
## (ratio of smallest to largest eigenvalue)
##
##
## Beginning Time: 12:20:36
## Ending Time: 12:20:38
## 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) 1998-2019 Muthen & Muthen9.2.2 An example of multilevel modeling – model 2 in Wang & Bergin (2017)
TITLE: Model2
DATA: FILE IS "data\zUSAmath.dat";
! The file has the names of five imputed datasets.
TYPE IS IMPUTATION;
VARIABLE: NAMES ARE IDCNTRY IDSCHOOL IDCLASS IDSTUD ITSEX
zBSBM16A zBSBM16B zBSBM16C zBSBM16D zBSBM16E zBSBM16F
zBSBM16G zBSBM16H zBSBM16I zmath
TOTWGT HOUWGT SENWGT WGTADJ1 WGTADJ2 WGTADJ3 WGTFAC1 WGTFAC2
WGTFAC3 JKZONE JKREP;
! wgtfac1 and wgtadj1 are school weighting factor and adjustment
! wgtfac2 and wgtadj2 are class weighting factor and adjustment
! wgtfac3 and wgtadj3 are student weighting factor and adjustment
USEVARIABLES ARE IDSCHOOL IDCLASS zBSBM16A zBSBM16C zBSBM16D zmath wt1 wt2 zmathsq;
MISSING ARE ITSEX(9) zBSBM16A-zBSBM16I(9) TOTWGT-WGTFAC3 (999999.000000)
JKZONE(99) JKREP(9);
AUXILIARY ARE IDCNTRY IDSTUD ITSEX;
WITHIN = zmathsq;
CLUSTER = IDSCHOOL IDCLASS;
WEIGHT IS wt1;
! within-level weight;
WTSCALE IS CLUSTER;
! CLUSTER is default; it rescales within level weights so that
! they sum to cluster size;
! ECLUSTER rescales within level weights so that they sum to
! effective cluster sample size;
BWEIGHT IS wt2;
! between-level weight;
BWTSCALE IS SAMPLE;
! SAMPLE is default; it adjusts the between weights so that the product
! of the between and within weights sums to the total sample size.
DEFINE: wt1 = WGTADJ3*WGTFAC3;
wt2 = WGTADJ1*WGTFAC1*WGTADJ2*WGTFAC2;
zmathsq=zmath*zmath;
ANALYSIS: TYPE = TWOLEVEL COMPLEX;
MODEL: %WITHIN%
scw BY zBSBM16A (1)
zBSBM16C (3)
zBSBM16D (4);
scw ON zmathsq (bb)
zmath (b1);
scw (var1);
zmath (var2);
zmathsq (var5);
zmath with zmathsq (cov1);
%BETWEEN%
scb BY zBSBM16A (1)
zBSBM16C (3)
zBSBM16D (4);
scb on
zmath (b2);
scb (var3);
zmath (var4);
! covariate math1 is decomposed into two unrelated latent variables
! math1ij = math1wij + math1bj (within and between)
! math1ij is used on the within level and math1bj is used on the
! between level;
MODEL CONSTRAINT:
NEW(ESw);
NEW(ESb);
NEW(ESBFLPE);
ESw=2*b1*sqrt(var2)/sqrt(b1**2*var2+bb**2*var5+2*b1*bb*cov1+var1+b2**2*var4+var3);
ESb=2*b2*sqrt(var4)/sqrt(b1**2*var2+bb**2*var5+2*b1*bb*cov1+var1+b2**2*var4+var3);
ESBFLPE=2*(b2-b1)*sqrt(var4)/sqrt(b1**2*var2+bb**2*var5+2*b1*bb*cov1+var1+b2**2*var4+var3);
! ESw is the size of within-level linear effect of math ability on sc
! ESb is the size of between-level effect of math ability on sc
! ESBFLPE is the size of contextual effect (i.e., BELPE)
MODEL TEST:
ESw=0;
ESb=0;
ESBFLPE=0;
OUTPUT: STANDARDIZED;