Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:38 PM
INPUT INSTRUCTIONS
TITLE: Monte Carlo for a two-level path
analysis model with a continuous and a
categorical dependent variable ????
montecarlo:
names are y u x w z;
generate = u(1);
categorical = u;
nobservations = 1000;
ncsizes = 3;
csizes = 40 (5) 50 (10) 20 (15);
seed = 58459;
nreps = 1;
within = x;
between = w z;
save = ex9.4.dat;
ANALYSIS:
TYPE = TWOLEVEL;
algo = int;
estimator = wlsm;
model population:
%WITHIN%
x@1;
u ON y*.75 x*.5;
y ON x*.25;
y*1;
%BETWEEN%
w@1;
u ON w*1 y*.5 z*.7;
y ON w*.5;
z ON w*.7;
y with z*.25;
y*.5; z*.5; u*.4;
model:
%WITHIN%
u ON y*.75 x*.5;
y ON x*.25;
y*1;
%BETWEEN%
u ON w*1 y*.5 z*.7;
y ON w*.5;
z ON w*.7;
y with z*.25;
y*.5; z*.5; u*.4;
output:
tech9;
INPUT READING TERMINATED NORMALLY
Monte Carlo for a two-level path
analysis model with a continuous and a
categorical dependent variable ????
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 3
Number of independent variables 2
Number of continuous latent variables 0
Observed dependent variables
Continuous
Z Y
Binary and ordered categorical (ordinal)
U
Observed independent variables
X W
Variables with special functions
Within variables
X
Between variables
W Z
Estimator WLSM
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 1000
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 10
Minimum value for logit thresholds -10
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm EMA/FS
Integration Specifications
Type STANDARD
Number of integration points 7
Dimensions of numerical integration 0
Adaptive quadrature ON
Link PROBIT
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
ESTIMATED SAMPLE STATISTICS
MEANS/INTERCEPTS/THRESHOLDS
U$1 Z Y
________ ________ ________
0.024 -0.060 0.011
SLOPES
X W
________ ________
U 0.481 1.376
Z 0.000 0.683
Y 0.221 0.549
WITHIN LEVEL VARIANCE/COVARIANCE
U Z Y
________ ________ ________
U 1.000
Z 0.000 0.000
Y 0.530 0.000 0.965
WITHIN LEVEL CORRELATION
U Z Y
________ ________ ________
U 1.000
Z 0.000 0.000
Y 0.540 0.000 1.000
BETWEEN LEVEL VARIANCE/COVARIANCE
U Z Y
________ ________ ________
U 0.541
Z 0.426 0.567
Y 0.369 0.278 0.530
BETWEEN LEVEL CORRELATION
U Z Y
________ ________ ________
U 1.000
Z 0.769 1.000
Y 0.689 0.506 1.000
MODEL FIT INFORMATION
Number of Free Parameters 16
Chi-Square Test of Model Fit
Degrees of freedom 0
Mean 0.000
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.000 0.000
0.980 1.000 0.000 0.000
0.950 1.000 0.000 0.000
0.900 1.000 0.000 0.000
0.800 1.000 0.000 0.000
0.700 1.000 0.000 0.000
0.500 1.000 0.000 0.000
0.300 1.000 0.000 0.000
0.200 1.000 0.000 0.000
0.100 1.000 0.000 0.000
0.050 1.000 0.000 0.000
0.020 1.000 0.000 0.000
0.010 1.000 0.000 0.000
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 1.000
0.010 1.000
CFI/TLI
CFI
Mean 1.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 0.000
0.980 0.000
0.950 0.000
0.900 0.000
0.800 0.000
0.700 0.000
0.500 0.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
TLI
Mean 1.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 0.000
0.980 0.000
0.950 0.000
0.900 0.000
0.800 0.000
0.700 0.000
0.500 0.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
SRMR (Standardized Root Mean Square Residual) for the WITHIN level
Mean 0.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 1.000
0.010 1.000
SRMR (Standardized Root Mean Square Residual) for the BETWEEN level
Mean 0.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 1.000
0.010 1.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
U ON
Y 0.750 0.6525 0.0000 0.0736 0.0095 1.000 1.000
X 0.500 0.4277 0.0000 0.0682 0.0052 1.000 1.000
Y ON
X 0.250 0.2207 0.0000 0.0325 0.0009 1.000 1.000
Residual Variances
Y 1.000 0.9651 0.0000 0.0518 0.0012 1.000 1.000
Between Level
U ON
W 1.000 0.9217 0.0000 0.1277 0.0061 1.000 1.000
Y 0.500 0.4830 0.0000 0.1619 0.0003 1.000 1.000
Z 0.700 0.6556 0.0000 0.1591 0.0020 1.000 1.000
Y ON
W 0.500 0.5488 0.0000 0.0702 0.0024 1.000 1.000
Z ON
W 0.700 0.6832 0.0000 0.0615 0.0003 1.000 1.000
Y WITH
Z 0.250 0.2776 0.0000 0.0698 0.0008 1.000 1.000
Intercepts
Z 0.000 -0.0604 0.0000 0.0722 0.0036 1.000 0.000
Y 0.000 0.0110 0.0000 0.0787 0.0001 1.000 0.000
Thresholds
U$1 0.000 -0.0058 0.0000 0.1715 0.0000 1.000 0.000
Residual Variances
U 0.400 0.2199 0.0000 0.0998 0.0324 1.000 1.000
Z 0.500 0.5667 0.0000 0.0838 0.0045 1.000 1.000
Y 0.500 0.5301 0.0000 0.1095 0.0009 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.391E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U$1
________
0
NU
U Y X
________ ________ ________
0 0 0
LAMBDA
U Y X
________ ________ ________
U 0 0 0
Y 0 0 0
X 0 0 0
THETA
U Y X
________ ________ ________
U 0
Y 0 0
X 0 0 0
ALPHA
U Y X
________ ________ ________
0 0 0
BETA
U Y X
________ ________ ________
U 0 1 2
Y 0 0 3
X 0 0 0
PSI
U Y X
________ ________ ________
U 0
Y 0 4
X 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
TAU
U$1
________
16
NU
U Z Y W
________ ________ ________ ________
0 0 0 0
LAMBDA
U Z Y W
________ ________ ________ ________
U 0 0 0 0
Z 0 0 0 0
Y 0 0 0 0
W 0 0 0 0
THETA
U Z Y W
________ ________ ________ ________
U 0
Z 0 0
Y 0 0 0
W 0 0 0 0
ALPHA
U Z Y W
________ ________ ________ ________
0 5 6 0
BETA
U Z Y W
________ ________ ________ ________
U 0 7 8 9
Z 0 0 0 10
Y 0 0 0 11
W 0 0 0 0
PSI
U Z Y W
________ ________ ________ ________
U 12
Z 0 13
Y 0 14 15
W 0 0 0 0
STARTING VALUES FOR WITHIN
TAU
U$1
________
0.000
NU
U Y X
________ ________ ________
0.000 0.000 0.000
LAMBDA
U Y X
________ ________ ________
U 1.000 0.000 0.000
Y 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
U Y X
________ ________ ________
U 0.000
Y 0.000 0.000
X 0.000 0.000 0.000
ALPHA
U Y X
________ ________ ________
0.000 0.000 0.000
BETA
U Y X
________ ________ ________
U 0.000 0.750 0.500
Y 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
U Y X
________ ________ ________
U 1.000
Y 0.000 1.000
X 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
TAU
U$1
________
0.000
NU
U Z Y W
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
U Z Y W
________ ________ ________ ________
U 1.000 0.000 0.000 0.000
Z 0.000 1.000 0.000 0.000
Y 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 1.000
THETA
U Z Y W
________ ________ ________ ________
U 0.000
Z 0.000 0.000
Y 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
ALPHA
U Z Y W
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
U Z Y W
________ ________ ________ ________
U 0.000 0.700 0.500 1.000
Z 0.000 0.000 0.000 0.700
Y 0.000 0.000 0.000 0.500
W 0.000 0.000 0.000 0.000
PSI
U Z Y W
________ ________ ________ ________
U 0.400
Z 0.000 0.500
Y 0.000 0.250 0.500
W 0.000 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
TAU
U$1
________
0.000
NU
U Y X
________ ________ ________
0.000 0.000 0.000
LAMBDA
U Y X
________ ________ ________
U 1.000 0.000 0.000
Y 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
U Y X
________ ________ ________
U 0.000
Y 0.000 0.000
X 0.000 0.000 0.000
ALPHA
U Y X
________ ________ ________
0.000 0.000 0.000
BETA
U Y X
________ ________ ________
U 0.000 0.750 0.500
Y 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
U Y X
________ ________ ________
U 0.000
Y 0.000 1.000
X 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
TAU
U$1
________
0.000
NU
U Z Y W
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
U Z Y W
________ ________ ________ ________
U 1.000 0.000 0.000 0.000
Z 0.000 1.000 0.000 0.000
Y 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 1.000
THETA
U Z Y W
________ ________ ________ ________
U 0.000
Z 0.000 0.000
Y 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
ALPHA
U Z Y W
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
U Z Y W
________ ________ ________ ________
U 0.000 0.700 0.500 1.000
Z 0.000 0.000 0.000 0.700
Y 0.000 0.000 0.000 0.500
W 0.000 0.000 0.000 0.000
PSI
U Z Y W
________ ________ ________ ________
U 0.400
Z 0.000 0.500
Y 0.000 0.250 0.500
W 0.000 0.000 0.000 1.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U
Z
Y
X
W
CLUSTER
Save file
ex9.4.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:38:31
Ending Time: 22:38:31
Elapsed Time: 00:00:00
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