Mplus VERSION 5.1
MUTHEN & MUTHEN
05/05/2008 8:26 PM
INPUT INSTRUCTIONS
TITLE:
cont12
A 2-GROUP MIMIC model
with specific across-group equality constraints
applied to the factor residual variance
and to the y residual variance
DATA:
FILE IS school.dat;
VARIABLE:
NAMES ARE x1 y1-y16 x2 school x3 x4;
USEV ARE y6-y9 x1 x2 x3;
! relative to the input of wMimic1, x4 is moved
! from the USEV analysis variable list to the
! multiple-group definition below:
GROUPING IS x4 (1 = groupA 2= groupB);
ANALYSIS: TYPE = MEANSTRUCTURE;
MODEL:
! with multiple-group analysis the statement MODEL: refers
! to the general model structure that holds for all groups
! which can then be modified by group-specific model
! statements. The default is measurement invariance for
! the y intercepts and the loadings.
f BY y6-y9;
! the statement above refers to the measurement
! part of the model. The y6 loading is fixed to 1
! by default because y6 is the first variable in
! the BY statement list; the other loadings are free.
! The residuals are automatically included and are
! uncorrelated by default (a correlation betweeen
! the residuals of, say y6 and y9 is stated as
! y6 WITH y9).
f ON x1-x3;
! the statement above refers to the structural part
! of the model. The residual is automatically included.
! The x variables are not modelled and their
! covariance matrix is held fixed at the sample values.
f (1);
! the statement above constrains the residual factor variance
! to be equal across groups
y6 (2); y7 (3); y8 (4); y9 (5);
! the statements above constrain the y residual variances
! to be equal across groups
! The intercept of y8 has been found not group-invariant
! in a previous analysis. In the current analysis
! the default invariance setting is therefore modified
! using the group 2 (typeB) model statement below
MODEL groupB:
[y8];
! the statement above lets the intercept of y8 differ
! across the 2 groups
OUTPUT: SAMPSTAT STANDARDIZED MODINDICES(0.0);
*** WARNING in ANALYSIS command
Starting with Version 5, TYPE=MEANSTRUCTURE is the default for all
analyses. To remove means from the model, use
MODEL=NOMEANSTRUCTURE in the ANALYSIS command.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
cont12
A 2-GROUP MIMIC model
with specific across-group equality constraints
applied to the factor residual variance
and to the y residual variance
SUMMARY OF ANALYSIS
Number of groups 2
Number of observations
Group GROUPA 4154
Group GROUPB 1044
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 1
Observed dependent variables
Continuous
Y6 Y7 Y8 Y9
Observed independent variables
X1 X2 X3
Continuous latent variables
F
Variables with special functions
Grouping variable X4
Estimator ML
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Input data file(s)
school.dat
Input data format FREE
SAMPLE STATISTICS
SAMPLE STATISTICS FOR GROUPA
Means
Y6 Y7 Y8 Y9 X1
________ ________ ________ ________ ________
1 2.405 2.528 2.146 2.832 2.231
Means
X2 X3
________ ________
1 0.493 4.960
Covariances
Y6 Y7 Y8 Y9 X1
________ ________ ________ ________ ________
Y6 1.376
Y7 1.066 1.378
Y8 0.687 0.689 1.825
Y9 1.087 1.143 0.693 3.696
X1 0.486 0.499 0.356 0.525 1.163
X2 0.001 0.029 0.024 0.054 0.019
X3 -0.586 -0.631 -0.419 -0.668 -0.716
Covariances
X2 X3
________ ________
X2 0.250
X3 -0.008 3.016
Correlations
Y6 Y7 Y8 Y9 X1
________ ________ ________ ________ ________
Y6 1.000
Y7 0.775 1.000
Y8 0.434 0.435 1.000
Y9 0.482 0.506 0.267 1.000
X1 0.384 0.394 0.244 0.253 1.000
X2 0.001 0.049 0.035 0.056 0.036
X3 -0.288 -0.309 -0.178 -0.200 -0.382
Correlations
X2 X3
________ ________
X2 1.000
X3 -0.010 1.000
SAMPLE STATISTICS FOR GROUPB
Means
Y6 Y7 Y8 Y9 X1
________ ________ ________ ________ ________
1 2.787 2.929 2.215 3.319 2.898
Means
X2 X3
________ ________
1 0.488 2.492
Covariances
Y6 Y7 Y8 Y9 X1
________ ________ ________ ________ ________
Y6 1.172
Y7 0.904 1.267
Y8 0.585 0.690 1.793
Y9 0.729 0.864 0.494 3.209
X1 0.299 0.255 0.243 0.261 0.985
X2 0.004 0.009 0.023 0.058 0.014
X3 -0.560 -0.765 -0.451 -0.604 -0.198
Covariances
X2 X3
________ ________
X2 0.250
X3 0.014 5.760
Correlations
Y6 Y7 Y8 Y9 X1
________ ________ ________ ________ ________
Y6 1.000
Y7 0.742 1.000
Y8 0.404 0.458 1.000
Y9 0.376 0.429 0.206 1.000
X1 0.278 0.229 0.183 0.147 1.000
X2 0.007 0.016 0.034 0.065 0.028
X3 -0.215 -0.283 -0.140 -0.141 -0.083
Correlations
X2 X3
________ ________
X2 1.000
X3 0.011 1.000
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
Value 89.352
Degrees of Freedom 32
P-Value 0.0000
Chi-Square Contributions From Each Group
GROUPA 44.407
GROUPB 44.945
Chi-Square Test of Model Fit for the Baseline Model
Value 8638.602
Degrees of Freedom 36
P-Value 0.0000
CFI/TLI
CFI 0.993
TLI 0.992
Loglikelihood
H0 Value -53339.849
H1 Value -53295.173
Information Criteria
Number of Free Parameters 20
Akaike (AIC) 106719.697
Bayesian (BIC) 106850.818
Sample-Size Adjusted BIC 106787.264
(n* = (n + 2) / 24)
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.026
90 Percent C.I. 0.020 0.033
SRMR (Standardized Root Mean Square Residual)
Value 0.021
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Group GROUPA
F BY
Y6 1.000 0.000 999.000 999.000
Y7 1.053 0.016 67.787 0.000
Y8 0.673 0.019 35.974 0.000
Y9 1.050 0.026 40.822 0.000
F ON
X1 0.342 0.015 22.646 0.000
X2 0.047 0.029 1.609 0.108
X3 -0.117 0.009 -12.714 0.000
Intercepts
Y6 2.197 0.069 31.998 0.000
Y7 2.309 0.072 32.040 0.000
Y8 2.008 0.049 40.631 0.000
Y9 2.632 0.075 35.021 0.000
F 0.000 0.000 999.000 999.000
Residual Variances
Y6 0.354 0.013 27.128 0.000
Y7 0.268 0.013 20.265 0.000
Y8 1.374 0.028 48.815 0.000
Y9 2.528 0.053 48.143 0.000
F 0.765 0.022 35.210 0.000
Group GROUPB
F BY
Y6 1.000 0.000 999.000 999.000
Y7 1.053 0.016 67.787 0.000
Y8 0.673 0.019 35.974 0.000
Y9 1.050 0.026 40.822 0.000
F ON
X1 0.251 0.030 8.430 0.000
X2 0.034 0.059 0.578 0.563
X3 -0.105 0.012 -8.571 0.000
Intercepts
Y6 2.197 0.069 31.998 0.000
Y7 2.309 0.072 32.040 0.000
Y8 1.816 0.060 30.265 0.000
Y9 2.632 0.075 35.021 0.000
F 0.111 0.122 0.908 0.364
Residual Variances
Y6 0.354 0.013 27.128 0.000
Y7 0.268 0.013 20.265 0.000
Y8 1.374 0.028 48.815 0.000
Y9 2.528 0.053 48.143 0.000
F 0.765 0.022 35.210 0.000
STANDARDIZED MODEL RESULTS
STDYX Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Group GROUPA
F BY
Y6 0.860 0.006 143.028 0.000
Y7 0.897 0.006 159.378 0.000
Y8 0.498 0.012 43.237 0.000
Y9 0.551 0.011 51.808 0.000
F ON
X1 0.368 0.015 24.696 0.000
X2 0.024 0.015 1.609 0.108
X3 -0.203 0.016 -12.997 0.000
Intercepts
Y6 1.888 0.063 29.919 0.000
Y7 1.968 0.066 29.950 0.000
Y8 1.485 0.040 37.003 0.000
Y9 1.381 0.043 32.415 0.000
F 0.000 0.000 999.000 999.000
Residual Variances
Y6 0.261 0.010 25.263 0.000
Y7 0.195 0.010 19.261 0.000
Y8 0.752 0.011 65.610 0.000
Y9 0.696 0.012 59.353 0.000
F 0.765 0.012 62.087 0.000
Group GROUPB
F BY
Y6 0.848 0.007 123.430 0.000
Y7 0.888 0.006 138.251 0.000
Y8 0.478 0.012 39.826 0.000
Y9 0.531 0.011 46.936 0.000
F ON
X1 0.262 0.030 8.875 0.000
X2 0.018 0.031 0.578 0.563
X3 -0.266 0.030 -9.001 0.000
Intercepts
Y6 1.961 0.066 29.600 0.000
Y7 2.051 0.070 29.488 0.000
Y8 1.360 0.048 28.285 0.000
Y9 1.402 0.043 32.554 0.000
F 0.117 0.129 0.904 0.366
Residual Variances
Y6 0.282 0.012 24.194 0.000
Y7 0.212 0.011 18.542 0.000
Y8 0.771 0.011 67.067 0.000
Y9 0.718 0.012 59.674 0.000
F 0.849 0.021 39.781 0.000
STDY Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Group GROUPA
F BY
Y6 0.860 0.006 143.028 0.000
Y7 0.897 0.006 159.378 0.000
Y8 0.498 0.012 43.237 0.000
Y9 0.551 0.011 51.808 0.000
F ON
X1 0.342 0.014 25.259 0.000
X2 0.047 0.029 1.609 0.108
X3 -0.117 0.009 -13.099 0.000
Intercepts
Y6 1.888 0.063 29.919 0.000
Y7 1.968 0.066 29.950 0.000
Y8 1.485 0.040 37.003 0.000
Y9 1.381 0.043 32.415 0.000
F 0.000 0.000 999.000 999.000
Residual Variances
Y6 0.261 0.010 25.263 0.000
Y7 0.195 0.010 19.261 0.000
Y8 0.752 0.011 65.610 0.000
Y9 0.696 0.012 59.353 0.000
F 0.765 0.012 62.087 0.000
Group GROUPB
F BY
Y6 0.848 0.007 123.430 0.000
Y7 0.888 0.006 138.251 0.000
Y8 0.478 0.012 39.826 0.000
Y9 0.531 0.011 46.936 0.000
F ON
X1 0.264 0.029 9.018 0.000
X2 0.036 0.062 0.578 0.563
X3 -0.111 0.012 -9.150 0.000
Intercepts
Y6 1.961 0.066 29.600 0.000
Y7 2.051 0.070 29.488 0.000
Y8 1.360 0.048 28.285 0.000
Y9 1.402 0.043 32.554 0.000
F 0.117 0.129 0.904 0.366
Residual Variances
Y6 0.282 0.012 24.194 0.000
Y7 0.212 0.011 18.542 0.000
Y8 0.771 0.011 67.067 0.000
Y9 0.718 0.012 59.674 0.000
F 0.849 0.021 39.781 0.000
STD Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Group GROUPA
F BY
Y6 1.000 0.014 69.703 0.000
Y7 1.053 0.014 73.768 0.000
Y8 0.673 0.019 35.656 0.000
Y9 1.050 0.026 40.568 0.000
F ON
X1 0.342 0.014 25.259 0.000
X2 0.047 0.029 1.609 0.108
X3 -0.117 0.009 -13.099 0.000
Intercepts
Y6 2.197 0.069 31.998 0.000
Y7 2.309 0.072 32.040 0.000
Y8 2.008 0.049 40.631 0.000
Y9 2.632 0.075 35.021 0.000
F 0.000 0.000 999.000 999.000
Residual Variances
Y6 0.354 0.013 27.128 0.000
Y7 0.268 0.013 20.265 0.000
Y8 1.374 0.028 48.815 0.000
Y9 2.528 0.053 48.143 0.000
F 0.765 0.012 62.087 0.000
Group GROUPB
F BY
Y6 0.950 0.017 55.932 0.000
Y7 1.000 0.017 57.556 0.000
Y8 0.639 0.019 33.305 0.000
Y9 0.997 0.027 37.246 0.000
F ON
X1 0.264 0.029 9.018 0.000
X2 0.036 0.062 0.578 0.563
X3 -0.111 0.012 -9.150 0.000
Intercepts
Y6 2.197 0.069 31.998 0.000
Y7 2.309 0.072 32.040 0.000
Y8 1.816 0.060 30.265 0.000
Y9 2.632 0.075 35.021 0.000
F 0.117 0.129 0.904 0.366
Residual Variances
Y6 0.354 0.013 27.128 0.000
Y7 0.268 0.013 20.265 0.000
Y8 1.374 0.028 48.815 0.000
Y9 2.528 0.053 48.143 0.000
F 0.849 0.021 39.781 0.000
R-SQUARE
Group GROUPA
Observed Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
Y6 0.739 0.010 71.514 0.000
Y7 0.805 0.010 79.689 0.000
Y8 0.248 0.011 21.618 0.000
Y9 0.304 0.012 25.904 0.000
Latent Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
F 0.235 0.012 19.109 0.000
Group GROUPB
Observed Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
Y6 0.718 0.012 61.715 0.000
Y7 0.788 0.011 69.126 0.000
Y8 0.229 0.011 19.913 0.000
Y9 0.282 0.012 23.468 0.000
Latent Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
F 0.151 0.021 7.099 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.278E-03
(ratio of smallest to largest eigenvalue)
MODEL MODIFICATION INDICES
Minimum M.I. value for printing the modification index 0.000
M.I. E.P.C. Std E.P.C. StdYX E.P.C.
Group GROUPA
BY Statements
F BY Y6 3.775 0.046 0.046 0.040
F BY Y7 1.490 -0.007 -0.007 -0.006
F BY Y8 1.357 -0.010 -0.010 -0.007
F BY Y9 3.097 0.021 0.021 0.011
ON/BY Statements
F ON F /
F BY F 1.524 0.035 0.035 0.035
WITH Statements
Y7 WITH Y6 0.489 0.009 0.009 0.031
Y8 WITH Y6 2.645 0.025 0.025 0.036
Y8 WITH Y7 6.041 -0.038 -0.038 -0.063
Y9 WITH Y6 0.059 -0.005 -0.005 -0.006
Y9 WITH Y7 1.060 0.023 0.023 0.028
Y9 WITH Y8 0.913 -0.029 -0.029 -0.016
Variances/Residual Variances
Y6 0.002 0.000 0.000 0.000
Y7 0.050 -0.001 -0.001 -0.001
Y8 0.155 0.006 0.006 0.003
Y9 0.103 0.008 0.008 0.002
F 1.524 0.011 0.011 0.011
Means/Intercepts/Thresholds
[ Y6 ] 0.072 0.001 0.001 0.001
[ Y7 ] 0.223 0.001 0.001 0.001
[ Y9 ] 2.358 -0.015 -0.015 -0.008
Group GROUPB
BY Statements
F BY Y6 3.780 -0.046 -0.044 -0.039
F BY Y7 1.490 0.022 0.021 0.018
F BY Y8 1.357 0.044 0.041 0.031
F BY Y9 3.088 -0.075 -0.071 -0.038
ON/BY Statements
F ON F /
F BY F 1.523 -0.035 -0.035 -0.035
WITH Statements
Y7 WITH Y6 0.019 -0.002 -0.002 -0.007
Y8 WITH Y6 0.944 -0.026 -0.026 -0.038
Y8 WITH Y7 4.501 0.057 0.057 0.093
Y9 WITH Y6 3.256 -0.067 -0.067 -0.071
Y9 WITH Y7 0.204 0.017 0.017 0.020
Y9 WITH Y8 1.978 -0.085 -0.085 -0.046
Variances/Residual Variances
Y6 0.002 -0.001 -0.001 -0.001
Y7 0.050 0.004 0.004 0.003
Y8 0.155 -0.022 -0.022 -0.012
Y9 0.103 -0.033 -0.033 -0.009
F 1.523 -0.043 -0.048 -0.048
Means/Intercepts/Thresholds
[ Y6 ] 0.072 -0.006 -0.006 -0.006
[ Y7 ] 0.223 -0.012 -0.012 -0.011
[ Y9 ] 2.357 0.073 0.073 0.039
Beginning Time: 20:26:27
Ending Time: 20:26:28
Elapsed Time: 00:00:01
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