Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:46 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level CFA
with categorical factor indicators, a random
intercept factor, and covariates
montecarlo:
names are u1-u4 x1 x2 w;
generate = u1-u4(1);
categorical = u1-u4;
nobservations = 1000;
ncsizes = 3;
csizes = 40 (5) 50 (10) 20 (15);
seed = 58459;
nreps = 1;
save = ex9.7.dat;
within = x1 x2;
between = w;
ANALYSIS:
TYPE IS TWOLEVEL;
MODEL POPULATION:
%Within%
x1-x2@1;
fw BY u1@1
u2*1
u3*1
u4*1;
fw ON x1*1 x2*.5;
fw*1;
%Between%
[w@0]; w@.7;
fb BY u1@1
u2*1
u3*1
u4*1;
fb ON w*.5;
fb*.4;
MODEL:
%Within%
fw BY u1@1
u2*1
u3*1
u4*1;
fw ON x1*1 x2*.5;
fw*1;
%Between%
fb BY u1@1
u2*1
u3*1
u4*1;
fb ON w*.5;
fb*.4;
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level CFA
with categorical factor indicators, a random
intercept factor, and covariates
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of replications
Requested 1
Completed 1
Value of seed 58459
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 2
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Observed independent variables
X1 X2 W
Continuous latent variables
FW FB
Variables with special functions
Within variables
X1 X2
Between variables
W
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 15
Dimensions of numerical integration 2
Adaptive quadrature ON
Link LOGIT
Cholesky ON
SUMMARY OF DATA FOR THE FIRST REPLICATION
Cluster information
Size (s) Number of clusters of Size s
5 40
10 50
15 20
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
X1 X2 W
________ ________ ________
0.021 -0.007 -0.154
Covariances
X1 X2 W
________ ________ ________
X1 0.952
X2 -0.006 1.088
W -0.004 0.025 0.615
Correlations
X1 X2 W
________ ________ ________
X1 1.000
X2 -0.006 1.000
W -0.005 0.030 1.000
MODEL FIT INFORMATION
Number of Free Parameters 15
Loglikelihood
H0 Value
Mean -2352.335
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -2352.335 -2352.335
0.980 0.000 -2352.335 -2352.335
0.950 0.000 -2352.335 -2352.335
0.900 0.000 -2352.335 -2352.335
0.800 0.000 -2352.335 -2352.335
0.700 0.000 -2352.335 -2352.335
0.500 0.000 -2352.335 -2352.335
0.300 0.000 -2352.335 -2352.335
0.200 0.000 -2352.335 -2352.335
0.100 0.000 -2352.335 -2352.335
0.050 0.000 -2352.335 -2352.335
0.020 0.000 -2352.335 -2352.335
0.010 0.000 -2352.335 -2352.335
Information Criteria
Akaike (AIC)
Mean 4734.669
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 4734.669 4734.669
0.980 0.000 4734.669 4734.669
0.950 0.000 4734.669 4734.669
0.900 0.000 4734.669 4734.669
0.800 0.000 4734.669 4734.669
0.700 0.000 4734.669 4734.669
0.500 0.000 4734.669 4734.669
0.300 0.000 4734.669 4734.669
0.200 0.000 4734.669 4734.669
0.100 0.000 4734.669 4734.669
0.050 0.000 4734.669 4734.669
0.020 0.000 4734.669 4734.669
0.010 0.000 4734.669 4734.669
Bayesian (BIC)
Mean 4808.286
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 4808.286 4808.286
0.980 0.000 4808.286 4808.286
0.950 0.000 4808.286 4808.286
0.900 0.000 4808.286 4808.286
0.800 0.000 4808.286 4808.286
0.700 0.000 4808.286 4808.286
0.500 0.000 4808.286 4808.286
0.300 0.000 4808.286 4808.286
0.200 0.000 4808.286 4808.286
0.100 0.000 4808.286 4808.286
0.050 0.000 4808.286 4808.286
0.020 0.000 4808.286 4808.286
0.010 0.000 4808.286 4808.286
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 4760.645
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 4760.645 4760.645
0.980 0.000 4760.645 4760.645
0.950 0.000 4760.645 4760.645
0.900 0.000 4760.645 4760.645
0.800 0.000 4760.645 4760.645
0.700 0.000 4760.645 4760.645
0.500 0.000 4760.645 4760.645
0.300 0.000 4760.645 4760.645
0.200 0.000 4760.645 4760.645
0.100 0.000 4760.645 4760.645
0.050 0.000 4760.645 4760.645
0.020 0.000 4760.645 4760.645
0.010 0.000 4760.645 4760.645
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
FW BY
U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.2344 0.0000 0.1769 0.0549 1.000 1.000
U3 1.000 1.3080 0.0000 0.1705 0.0949 1.000 1.000
U4 1.000 1.2960 0.0000 0.1675 0.0876 1.000 1.000
FW ON
X1 1.000 0.8344 0.0000 0.0890 0.0274 1.000 1.000
X2 0.500 0.3870 0.0000 0.0471 0.0128 0.000 1.000
Residual Variances
FW 1.000 0.6605 0.0000 0.1353 0.1152 0.000 1.000
Between Level
FB BY
U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.5645 0.0000 0.5985 0.3187 1.000 1.000
U3 1.000 1.3676 0.0000 0.4245 0.1351 1.000 1.000
U4 1.000 1.7137 0.0000 0.5953 0.5094 1.000 1.000
FB ON
W 0.500 0.2428 0.0000 0.0828 0.0662 0.000 1.000
Thresholds
U1$1 0.000 0.0106 0.0000 0.0870 0.0001 1.000 0.000
U2$1 0.000 0.1350 0.0000 0.0962 0.0182 1.000 0.000
U3$1 0.000 0.0634 0.0000 0.0938 0.0040 1.000 0.000
U4$1 0.000 -0.0165 0.0000 0.1113 0.0003 1.000 0.000
Residual Variances
FB 0.400 0.1103 0.0000 0.0618 0.0839 0.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.160E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0 0 0 0
NU
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
0 0 0 0 0
NU
X2
________
0
LAMBDA
FW X1 X2
________ ________ ________
U1 0 0 0
U2 1 0 0
U3 2 0 0
U4 3 0 0
X1 0 0 0
X2 0 0 0
THETA
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
THETA
X2
________
X2 0
ALPHA
FW X1 X2
________ ________ ________
0 0 0
BETA
FW X1 X2
________ ________ ________
FW 0 4 5
X1 0 0 0
X2 0 0 0
PSI
FW X1 X2
________ ________ ________
FW 6
X1 0 0
X2 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
12 13 14 15
NU
U1 U2 U3 U4 W
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
FB W
________ ________
U1 0 0
U2 7 0
U3 8 0
U4 9 0
W 0 0
THETA
U1 U2 U3 U4 W
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
W 0 0 0 0 0
ALPHA
FB W
________ ________
0 0
BETA
FB W
________ ________
FB 0 10
W 0 0
PSI
FB W
________ ________
FB 11
W 0 0
STARTING VALUES FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X2
________
0.000
LAMBDA
FW X1 X2
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 0.000 0.000
U3 1.000 0.000 0.000
U4 1.000 0.000 0.000
X1 0.000 1.000 0.000
X2 0.000 0.000 1.000
THETA
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
THETA
X2
________
X2 0.000
ALPHA
FW X1 X2
________ ________ ________
0.000 0.000 0.000
BETA
FW X1 X2
________ ________ ________
FW 0.000 1.000 0.500
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
PSI
FW X1 X2
________ ________ ________
FW 1.000
X1 0.000 0.500
X2 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
FB W
________ ________
U1 1.000 0.000
U2 1.000 0.000
U3 1.000 0.000
U4 1.000 0.000
W 0.000 1.000
THETA
U1 U2 U3 U4 W
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
ALPHA
FB W
________ ________
0.000 0.000
BETA
FB W
________ ________
FB 0.000 0.500
W 0.000 0.000
PSI
FB W
________ ________
FB 0.400
W 0.000 0.500
POPULATION VALUES FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X2
________
0.000
LAMBDA
FW X1 X2
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 0.000 0.000
U3 1.000 0.000 0.000
U4 1.000 0.000 0.000
X1 0.000 1.000 0.000
X2 0.000 0.000 1.000
THETA
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
THETA
X2
________
X2 0.000
ALPHA
FW X1 X2
________ ________ ________
0.000 0.000 0.000
BETA
FW X1 X2
________ ________ ________
FW 0.000 1.000 0.500
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
PSI
FW X1 X2
________ ________ ________
FW 1.000
X1 0.000 1.000
X2 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
FB W
________ ________
U1 1.000 0.000
U2 1.000 0.000
U3 1.000 0.000
U4 1.000 0.000
W 0.000 1.000
THETA
U1 U2 U3 U4 W
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
ALPHA
FB W
________ ________
0.000 0.000
BETA
FB W
________ ________
FB 0.000 0.500
W 0.000 0.000
PSI
FB W
________ ________
FB 0.400
W 0.000 0.700
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.23613274D+04 0.0000000 0.0000000 EM
2 -0.23540324D+04 7.2949791 0.0030894 EM
3 -0.23528562D+04 1.1762740 0.0004997 EM
4 -0.23525291D+04 0.3271132 0.0001390 EM
5 -0.23524202D+04 0.1088548 0.0000463 EM
6 -0.23523760D+04 0.0441996 0.0000188 EM
7 -0.23523554D+04 0.0206495 0.0000088 EM
8 -0.23523450D+04 0.0103375 0.0000044 EM
9 -0.23523397D+04 0.0053316 0.0000023 EM
10 -0.23523369D+04 0.0027870 0.0000012 EM
11 -0.23523354D+04 0.0014677 0.0000006 EM
12 -0.23523347D+04 0.0007772 0.0000003 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
X1
X2
W
CLUSTER
Save file
ex9.7.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:46:43
Ending Time: 22:46:45
Elapsed Time: 00:00:02
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