Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
title: this is an example of a CFA with continuous,
censored, categorical, and count factor indicators
montecarlo:
names = y1-y6 u1-u6;
generate = y4-y6(cb 0) u1-u3(1) u4-u6(c);
censored = y4-y6(b);
categorical = u1-u3;
count = u4-u6;
nobs = 500;
nreps = 1;
save = ex4.3.dat;
model population:
f1 by y1-y3*.7;
f2 by y4-y6*.7;
f3 by u1-u3*.7;
f4 by u4-u6*.7;
y1-y6*.51;
f1-f4@1;
analysis:
estimator = mlr;
integration = 7;
model:
f1 by y1-y3*.7;
f2 by y4-y6*.7;
f3 by u1-u3*.7;
f4 by u4-u6*.7;
y1-y6*.51;
f1-f4@1;
output:
tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a CFA with continuous,
censored, categorical, and count factor indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 0
Number of dependent variables 12
Number of independent variables 0
Number of continuous latent variables 4
Observed dependent variables
Continuous
Y1 Y2 Y3
Censored
Y4 Y5 Y6
Binary and ordered categorical (ordinal)
U1 U2 U3
Count
U4 U5 U6
Continuous latent variables
F1 F2 F3 F4
Estimator MLR
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 100
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Maximum value for logit thresholds 15
Minimum value for logit thresholds -15
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 7
Dimensions of numerical integration 3
Adaptive quadrature ON
Link LOGIT
Cholesky OFF
SUMMARY OF CENSORED LIMITS
Y4 0.000
Y5 0.000
Y6 0.000
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3
________ ________ ________
-0.009 0.071 0.061
Covariances
Y1 Y2 Y3
________ ________ ________
Y1 0.962
Y2 0.460 1.012
Y3 0.439 0.518 1.033
Correlations
Y1 Y2 Y3
________ ________ ________
Y1 1.000
Y2 0.466 1.000
Y3 0.440 0.506 1.000
MODEL FIT INFORMATION
Number of Free Parameters 36
Loglikelihood
H0 Value
Mean -6672.862
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -6672.862 -6672.862
0.980 0.000 -6672.862 -6672.862
0.950 0.000 -6672.862 -6672.862
0.900 0.000 -6672.862 -6672.862
0.800 0.000 -6672.862 -6672.862
0.700 0.000 -6672.862 -6672.862
0.500 0.000 -6672.862 -6672.862
0.300 0.000 -6672.862 -6672.862
0.200 0.000 -6672.862 -6672.862
0.100 0.000 -6672.862 -6672.862
0.050 0.000 -6672.862 -6672.862
0.020 0.000 -6672.862 -6672.862
0.010 0.000 -6672.862 -6672.862
Information Criteria
Akaike (AIC)
Mean 13417.723
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 13417.723 13417.723
0.980 0.000 13417.723 13417.723
0.950 0.000 13417.723 13417.723
0.900 0.000 13417.723 13417.723
0.800 0.000 13417.723 13417.723
0.700 0.000 13417.723 13417.723
0.500 0.000 13417.723 13417.723
0.300 0.000 13417.723 13417.723
0.200 0.000 13417.723 13417.723
0.100 0.000 13417.723 13417.723
0.050 0.000 13417.723 13417.723
0.020 0.000 13417.723 13417.723
0.010 0.000 13417.723 13417.723
Bayesian (BIC)
Mean 13569.449
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 13569.449 13569.449
0.980 0.000 13569.449 13569.449
0.950 0.000 13569.449 13569.449
0.900 0.000 13569.449 13569.449
0.800 0.000 13569.449 13569.449
0.700 0.000 13569.449 13569.449
0.500 0.000 13569.449 13569.449
0.300 0.000 13569.449 13569.449
0.200 0.000 13569.449 13569.449
0.100 0.000 13569.449 13569.449
0.050 0.000 13569.449 13569.449
0.020 0.000 13569.449 13569.449
0.010 0.000 13569.449 13569.449
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 13455.183
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 13455.183 13455.183
0.980 0.000 13455.183 13455.183
0.950 0.000 13455.183 13455.183
0.900 0.000 13455.183 13455.183
0.800 0.000 13455.183 13455.183
0.700 0.000 13455.183 13455.183
0.500 0.000 13455.183 13455.183
0.300 0.000 13455.183 13455.183
0.200 0.000 13455.183 13455.183
0.100 0.000 13455.183 13455.183
0.050 0.000 13455.183 13455.183
0.020 0.000 13455.183 13455.183
0.010 0.000 13455.183 13455.183
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 2.694
Std Dev 0.000
Degrees of freedom 0
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2.694 2.694
0.980 0.000 2.694 2.694
0.950 0.000 2.694 2.694
0.900 0.000 2.694 2.694
0.800 0.000 2.694 2.694
0.700 0.000 2.694 2.694
0.500 0.000 2.694 2.694
0.300 0.000 2.694 2.694
0.200 0.000 2.694 2.694
0.100 0.000 2.694 2.694
0.050 0.000 2.694 2.694
0.020 0.000 2.694 2.694
0.010 0.000 2.694 2.694
Likelihood Ratio Chi-Square
Mean 2.670
Std Dev 0.000
Degrees of freedom 0
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2.670 2.670
0.980 0.000 2.670 2.670
0.950 0.000 2.670 2.670
0.900 0.000 2.670 2.670
0.800 0.000 2.670 2.670
0.700 0.000 2.670 2.670
0.500 0.000 2.670 2.670
0.300 0.000 2.670 2.670
0.200 0.000 2.670 2.670
0.100 0.000 2.670 2.670
0.050 0.000 2.670 2.670
0.020 0.000 2.670 2.670
0.010 0.000 2.670 2.670
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
F1 BY
Y1 0.700 0.6269 0.0000 0.0461 0.0053 1.000 1.000
Y2 0.700 0.7437 0.0000 0.0500 0.0019 1.000 1.000
Y3 0.700 0.6931 0.0000 0.0514 0.0000 1.000 1.000
F2 BY
Y4 0.700 0.6095 0.0000 0.0627 0.0082 1.000 1.000
Y5 0.700 0.6040 0.0000 0.0618 0.0092 1.000 1.000
Y6 0.700 0.7771 0.0000 0.0688 0.0059 1.000 1.000
F3 BY
U1 0.700 1.0741 0.0000 0.6672 0.1399 1.000 0.000
U2 0.700 0.5771 0.0000 0.3590 0.0151 1.000 0.000
U3 0.700 0.4004 0.0000 0.3030 0.0897 1.000 0.000
F4 BY
U4 0.700 0.6929 0.0000 0.0482 0.0001 1.000 1.000
U5 0.700 0.7136 0.0000 0.0509 0.0002 1.000 1.000
U6 0.700 0.6465 0.0000 0.0511 0.0029 1.000 1.000
F2 WITH
F1 0.000 0.0443 0.0000 0.0641 0.0020 1.000 0.000
F3 WITH
F1 0.000 -0.2957 0.0000 0.1094 0.0874 0.000 1.000
F2 0.000 -0.0829 0.0000 0.1336 0.0069 1.000 0.000
F4 WITH
F1 0.000 -0.0844 0.0000 0.0678 0.0071 1.000 0.000
F2 0.000 -0.0039 0.0000 0.0729 0.0000 1.000 0.000
F3 0.000 0.1716 0.0000 0.1212 0.0294 1.000 0.000
Intercepts
Y1 0.000 -0.0090 0.0000 0.0439 0.0001 1.000 0.000
Y2 0.000 0.0715 0.0000 0.0450 0.0051 1.000 0.000
Y3 0.000 0.0612 0.0000 0.0454 0.0037 1.000 0.000
U4 0.000 0.1065 0.0000 0.0552 0.0113 1.000 0.000
U5 0.000 0.0034 0.0000 0.0608 0.0000 1.000 0.000
U6 0.000 0.0860 0.0000 0.0565 0.0074 1.000 0.000
Y4 0.000 -0.0526 0.0000 0.0526 0.0028 1.000 0.000
Y5 0.000 -0.0790 0.0000 0.0571 0.0062 1.000 0.000
Y6 0.000 -0.0166 0.0000 0.0545 0.0003 1.000 0.000
Thresholds
U1$1 0.000 0.0205 0.0000 0.1107 0.0004 1.000 0.000
U2$1 0.000 -0.1206 0.0000 0.0971 0.0145 1.000 0.000
U3$1 0.000 -0.0998 0.0000 0.0932 0.0100 1.000 0.000
Variances
F1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 0.510 0.5688 0.0000 0.0497 0.0035 1.000 1.000
Y2 0.510 0.4591 0.0000 0.0577 0.0026 1.000 1.000
Y3 0.510 0.5523 0.0000 0.0573 0.0018 1.000 1.000
Y4 0.510 0.4868 0.0000 0.0683 0.0005 1.000 1.000
Y5 0.510 0.6205 0.0000 0.0753 0.0122 1.000 1.000
Y6 0.510 0.3795 0.0000 0.0802 0.0170 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.384E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1 U2$1 U3$1
________ ________ ________
34 35 36
NU
U4#1 U4 U5#1 U5 U6#1
________ ________ ________ ________ ________
0 1 0 2 0
NU
U6 Y4#1 Y4 Y5#1 Y5
________ ________ ________ ________ ________
3 0 4 0 5
NU
Y6#1 Y6 U1 U2 U3
________ ________ ________ ________ ________
0 6 0 0 0
NU
Y1 Y2 Y3
________ ________ ________
7 8 9
LAMBDA
F1 F2 F3 F4
________ ________ ________ ________
U4#1 0 0 0 0
U4 0 0 0 10
U5#1 0 0 0 0
U5 0 0 0 11
U6#1 0 0 0 0
U6 0 0 0 12
Y4#1 0 0 0 0
Y4 0 13 0 0
Y5#1 0 0 0 0
Y5 0 14 0 0
Y6#1 0 0 0 0
Y6 0 15 0 0
U1 0 0 16 0
U2 0 0 17 0
U3 0 0 18 0
Y1 19 0 0 0
Y2 20 0 0 0
Y3 21 0 0 0
THETA
U4#1 U4 U5#1 U5 U6#1
________ ________ ________ ________ ________
U4#1 0
U4 0 0
U5#1 0 0 0
U5 0 0 0 0
U6#1 0 0 0 0 0
U6 0 0 0 0 0
Y4#1 0 0 0 0 0
Y4 0 0 0 0 0
Y5#1 0 0 0 0 0
Y5 0 0 0 0 0
Y6#1 0 0 0 0 0
Y6 0 0 0 0 0
U1 0 0 0 0 0
U2 0 0 0 0 0
U3 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
THETA
U6 Y4#1 Y4 Y5#1 Y5
________ ________ ________ ________ ________
U6 0
Y4#1 0 0
Y4 0 0 22
Y5#1 0 0 0 0
Y5 0 0 0 0 23
Y6#1 0 0 0 0 0
Y6 0 0 0 0 0
U1 0 0 0 0 0
U2 0 0 0 0 0
U3 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
THETA
Y6#1 Y6 U1 U2 U3
________ ________ ________ ________ ________
Y6#1 0
Y6 0 24
U1 0 0 0
U2 0 0 0 0
U3 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
THETA
Y1 Y2 Y3
________ ________ ________
Y1 25
Y2 0 26
Y3 0 0 27
ALPHA
F1 F2 F3 F4
________ ________ ________ ________
0 0 0 0
BETA
F1 F2 F3 F4
________ ________ ________ ________
F1 0 0 0 0
F2 0 0 0 0
F3 0 0 0 0
F4 0 0 0 0
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 0
F2 28 0
F3 29 30 0
F4 31 32 33 0
STARTING VALUES
TAU
U1$1 U2$1 U3$1
________ ________ ________
0.000 0.000 0.000
NU
U4#1 U4 U5#1 U5 U6#1
________ ________ ________ ________ ________
-20.000 0.000 -20.000 0.000 -20.000
NU
U6 Y4#1 Y4 Y5#1 Y5
________ ________ ________ ________ ________
0.000 -20.000 0.000 -20.000 0.000
NU
Y6#1 Y6 U1 U2 U3
________ ________ ________ ________ ________
-20.000 0.000 0.000 0.000 0.000
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
F1 F2 F3 F4
________ ________ ________ ________
U4#1 0.000 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.700
U5#1 0.000 0.000 0.000 0.000
U5 0.000 0.000 0.000 0.700
U6#1 0.000 0.000 0.000 0.000
U6 0.000 0.000 0.000 0.700
Y4#1 0.000 0.000 0.000 0.000
Y4 0.000 0.700 0.000 0.000
Y5#1 0.000 0.000 0.000 0.000
Y5 0.000 0.700 0.000 0.000
Y6#1 0.000 0.000 0.000 0.000
Y6 0.000 0.700 0.000 0.000
U1 0.000 0.000 0.700 0.000
U2 0.000 0.000 0.700 0.000
U3 0.000 0.000 0.700 0.000
Y1 0.700 0.000 0.000 0.000
Y2 0.700 0.000 0.000 0.000
Y3 0.700 0.000 0.000 0.000
THETA
U4#1 U4 U5#1 U5 U6#1
________ ________ ________ ________ ________
U4#1 0.000
U4 0.000 0.000
U5#1 0.000 0.000 0.000
U5 0.000 0.000 0.000 0.000
U6#1 0.000 0.000 0.000 0.000 0.000
U6 0.000 0.000 0.000 0.000 0.000
Y4#1 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5#1 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
Y6#1 0.000 0.000 0.000 0.000 0.000
Y6 0.000 0.000 0.000 0.000 0.000
U1 0.000 0.000 0.000 0.000 0.000
U2 0.000 0.000 0.000 0.000 0.000
U3 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
THETA
U6 Y4#1 Y4 Y5#1 Y5
________ ________ ________ ________ ________
U6 0.000
Y4#1 0.000 0.000
Y4 0.000 0.000 0.510
Y5#1 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.510
Y6#1 0.000 0.000 0.000 0.000 0.000
Y6 0.000 0.000 0.000 0.000 0.000
U1 0.000 0.000 0.000 0.000 0.000
U2 0.000 0.000 0.000 0.000 0.000
U3 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
THETA
Y6#1 Y6 U1 U2 U3
________ ________ ________ ________ ________
Y6#1 0.000
Y6 0.000 0.510
U1 0.000 0.000 1.000
U2 0.000 0.000 0.000 1.000
U3 0.000 0.000 0.000 0.000 1.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 0.510
Y2 0.000 0.510
Y3 0.000 0.000 0.510
ALPHA
F1 F2 F3 F4
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4
________ ________ ________ ________
F1 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000
F3 0.000 0.000 0.000 0.000
F4 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 1.000
F4 0.000 0.000 0.000 1.000
POPULATION VALUES
TAU
U1$1 U2$1 U3$1
________ ________ ________
0.000 0.000 0.000
NU
U4#1 U4 U5#1 U5 U6#1
________ ________ ________ ________ ________
-20.000 0.000 -20.000 0.000 -20.000
NU
U6 Y4#1 Y4 Y5#1 Y5
________ ________ ________ ________ ________
0.000 -20.000 0.000 -20.000 0.000
NU
Y6#1 Y6 U1 U2 U3
________ ________ ________ ________ ________
-20.000 0.000 0.000 0.000 0.000
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
F1 F2 F3 F4
________ ________ ________ ________
U4#1 0.000 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.700
U5#1 0.000 0.000 0.000 0.000
U5 0.000 0.000 0.000 0.700
U6#1 0.000 0.000 0.000 0.000
U6 0.000 0.000 0.000 0.700
Y4#1 0.000 0.000 0.000 0.000
Y4 0.000 0.700 0.000 0.000
Y5#1 0.000 0.000 0.000 0.000
Y5 0.000 0.700 0.000 0.000
Y6#1 0.000 0.000 0.000 0.000
Y6 0.000 0.700 0.000 0.000
U1 0.000 0.000 0.700 0.000
U2 0.000 0.000 0.700 0.000
U3 0.000 0.000 0.700 0.000
Y1 0.700 0.000 0.000 0.000
Y2 0.700 0.000 0.000 0.000
Y3 0.700 0.000 0.000 0.000
THETA
U4#1 U4 U5#1 U5 U6#1
________ ________ ________ ________ ________
U4#1 0.000
U4 0.000 0.000
U5#1 0.000 0.000 0.000
U5 0.000 0.000 0.000 0.000
U6#1 0.000 0.000 0.000 0.000 0.000
U6 0.000 0.000 0.000 0.000 0.000
Y4#1 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5#1 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
Y6#1 0.000 0.000 0.000 0.000 0.000
Y6 0.000 0.000 0.000 0.000 0.000
U1 0.000 0.000 0.000 0.000 0.000
U2 0.000 0.000 0.000 0.000 0.000
U3 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
THETA
U6 Y4#1 Y4 Y5#1 Y5
________ ________ ________ ________ ________
U6 0.000
Y4#1 0.000 0.000
Y4 0.000 0.000 0.510
Y5#1 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.510
Y6#1 0.000 0.000 0.000 0.000 0.000
Y6 0.000 0.000 0.000 0.000 0.000
U1 0.000 0.000 0.000 0.000 0.000
U2 0.000 0.000 0.000 0.000 0.000
U3 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
THETA
Y6#1 Y6 U1 U2 U3
________ ________ ________ ________ ________
Y6#1 0.000
Y6 0.000 0.510
U1 0.000 0.000 0.000
U2 0.000 0.000 0.000 0.000
U3 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 0.510
Y2 0.000 0.510
Y3 0.000 0.000 0.510
ALPHA
F1 F2 F3 F4
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4
________ ________ ________ ________
F1 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000
F3 0.000 0.000 0.000 0.000
F4 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 1.000
F4 0.000 0.000 0.000 1.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U4
U5
U6
Y4
Y5
Y6
U1
U2
U3
Y1
Y2
Y3
Save file
ex4.3.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:39
Ending Time: 22:22:51
Elapsed Time: 00:00:12
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