Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:52 PM
INPUT INSTRUCTIONS
TITLE: two-level path analysis with a continuous,
a categorical, and a cluster-level observed dependent variable
DATA: FILE = ex9.4.dat;
VARIABLE: NAMES ARE u z y x w clus;
CATEGORICAL = u;
WITHIN = x;
BETWEEN = w z;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL;
ESTIMATOR = WLSM;
MODEL:
%WITHIN%
u ON y x;
y ON x;
%BETWEEN%
u ON w y z;
y ON w;
z ON w;
y WITH z;
OUTPUT: TECH1;
*** WARNING
One or more individual-level variables have no variation within a
cluster for the following clusters.
Variable Cluster IDs with no within-cluster variation
U 1 2 3 5 6 8 9 12 13 14 17 19 21 23 25 27 28 33 35 36 37 42 45 51 54 56 57 58
66 67 69 73 76 84 90 97 100 101 106 109
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
two-level path analysis with a continuous,
a categorical, and a cluster-level observed dependent variable
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
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
Cluster variable CLUS
Within variables
X
Between variables
Z W
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
Input data file(s)
ex9.4.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 110
Average cluster size 9.091
Estimated Intraclass Correlations for the Y Variables
Intraclass Intraclass Intraclass
Variable Correlation Variable Correlation Variable Correlation
U 0.695 Y 0.468
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U
Category 1 0.478 478.000
Category 2 0.522 522.000
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
Z -0.004 -0.368 -2.607 0.91% -0.830 -0.150 0.137
110.000 1.130 -0.183 2.298 0.91% 0.339 0.803
Y 0.076 -0.029 -3.709 0.10% -1.048 -0.263 0.097
1000.000 1.834 -0.114 3.756 0.10% 0.421 1.210
X 0.012 0.127 -2.984 0.10% -0.813 -0.284 -0.036
1000.000 1.046 0.010 3.794 0.10% 0.254 0.846
W 0.083 0.151 -2.558 0.91% -0.804 -0.307 -0.020
110.000 1.207 -0.332 2.859 0.91% 0.339 1.018
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 16
Chi-Square Test of Model Fit
Value 0.000*
Degrees of Freedom 0
P-Value 0.0000
Scaling Correction Factor 1.0000
for WLSM
* 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 589.633
Degrees of Freedom 9
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.000
Value for Between 0.000
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
U ON
Y 0.653 0.074 8.871 0.000
X 0.428 0.068 6.275 0.000
Y ON
X 0.221 0.033 6.785 0.000
Residual Variances
Y 0.965 0.052 18.642 0.000
Between Level
U ON
W 0.922 0.128 7.217 0.000
Y 0.483 0.162 2.984 0.003
Z 0.656 0.159 4.120 0.000
Y ON
W 0.549 0.070 7.817 0.000
Z ON
W 0.683 0.062 11.103 0.000
Y WITH
Z 0.278 0.070 3.977 0.000
Intercepts
Z -0.060 0.072 -0.836 0.403
Y 0.011 0.079 0.139 0.889
Thresholds
U$1 -0.006 0.172 -0.034 0.973
Residual Variances
U 0.220 0.100 2.204 0.028
Z 0.567 0.084 6.765 0.000
Y 0.530 0.109 4.842 0.000
QUALITY OF NUMERICAL RESULTS
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 0.000 0.000
Y 0.000 0.000 0.000
X 0.000 0.000 0.000
PSI
U Y X
________ ________ ________
U 1.000
Y 0.000 0.917
X 0.000 0.000 0.523
STARTING VALUES FOR BETWEEN
TAU
U$1
________
-0.049
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 -0.014 0.076 0.000
BETA
U Z Y W
________ ________ ________ ________
U 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
PSI
U Z Y W
________ ________ ________ ________
U 1.000
Z 0.000 0.534
Y 0.000 0.000 0.917
W 0.000 0.000 0.000 0.595
Beginning Time: 23:52:33
Ending Time: 23:52:34
Elapsed Time: 00:00:01
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