Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:57 PM
INPUT INSTRUCTIONS
TITLE:this is an example of two-level mixture
regression for a continuous dependent variable
with a between-level categorical latent variable
DATA: FILE = ex10.2.dat;
VARIABLE: NAMES ARE y x1 x2 w dummy clus;
USEVARIABLES = y-w;
CLASSES = cb(2);
WITHIN = x1 x2;
BETWEEN = cb w;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL MIXTURE RANDOM;
PROCESSORS = 2;
MODEL:
%WITHIN%
%OVERALL%
s1 | y ON x1;
s2 | y ON x2;
%BETWEEN%
%OVERALL%
cb y ON w; s1-s2@0;
%cb#1%
[s1 s2];
%cb#2%
[s1 s2];
INPUT READING TERMINATED NORMALLY
this is an example of two-level mixture
regression for a continuous dependent variable
with a between-level categorical latent variable
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 1
Number of independent variables 3
Number of continuous latent variables 2
Number of categorical latent variables 1
Observed dependent variables
Continuous
Y
Observed independent variables
X1 X2 W
Continuous latent variables
S1 S2
Categorical latent variables
CB
Variables with special functions
Cluster variable CLUS
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 1
Adaptive quadrature ON
Random Starts Specifications
Number of initial stage random starts 20
Number of final stage optimizations 4
Number of initial stage iterations 10
Initial stage convergence criterion 0.100D+01
Random starts scale 0.500D+01
Random seed for generating random starts 0
Cholesky OFF
Input data file(s)
ex10.2.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 110
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
Y 1.449 -0.010 -9.293 0.10% -0.910 0.753 1.377
1000.000 7.878 0.151 11.074 0.10% 2.100 3.903
X1 -0.024 -0.022 -3.006 0.10% -0.887 -0.320 -0.036
1000.000 1.008 -0.185 3.145 0.10% 0.237 0.860
X2 -0.055 -0.036 -3.111 0.10% -0.903 -0.306 -0.051
1000.000 0.961 -0.141 2.811 0.10% 0.206 0.780
W -0.084 -0.367 -2.894 0.91% -0.853 -0.241 -0.033
110.000 0.947 0.046 1.927 0.91% 0.174 0.720
RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES
Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers:
-1574.798 608496 4
-1574.798 unperturbed 0
-1574.800 637345 19
-1574.800 27071 15
THE BEST LOGLIKELIHOOD VALUE HAS BEEN REPLICATED. RERUN WITH AT LEAST TWICE THE
RANDOM STARTS TO CHECK THAT THE BEST LOGLIKELIHOOD IS STILL OBTAINED AND REPLICATED.
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 11
Loglikelihood
H0 Value -1574.798
H0 Scaling Correction Factor 0.9503
for MLR
Information Criteria
Akaike (AIC) 3171.596
Bayesian (BIC) 3225.582
Sample-Size Adjusted BIC 3190.645
(n* = (n + 2) / 24)
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 496.52221 0.49652
2 503.47779 0.50348
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 500 0.50000
2 500 0.50000
CLASSIFICATION QUALITY
Entropy 0.929
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.975 0.025
2 0.018 0.982
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.982 0.018
2 0.025 0.975
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 3.973 0.000
2 -3.658 0.000
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
Latent Class 1
Residual Variances
Y 1.005 0.046 21.805 0.000
Latent Class 2
Residual Variances
Y 1.005 0.046 21.805 0.000
Between Level
Latent Class 1
Y ON
W 0.694 0.075 9.225 0.000
Means
S1 0.972 0.042 23.353 0.000
S2 1.944 0.059 32.855 0.000
Intercepts
Y 2.465 0.115 21.510 0.000
Variances
S1 0.000 0.000 999.000 999.000
S2 0.000 0.000 999.000 999.000
Residual Variances
Y 0.497 0.092 5.385 0.000
Latent Class 2
Y ON
W 0.694 0.075 9.225 0.000
Means
S1 1.943 0.059 33.184 0.000
S2 1.018 0.042 23.970 0.000
Intercepts
Y 0.805 0.119 6.780 0.000
Variances
S1 0.000 0.000 999.000 999.000
S2 0.000 0.000 999.000 999.000
Residual Variances
Y 0.497 0.092 5.385 0.000
Categorical Latent Variables
Within Level
Between Level
CB#1 ON
W 0.822 0.217 3.783 0.000
Intercepts
CB#1 -0.068 0.217 -0.311 0.756
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.203E-01
(ratio of smallest to largest eigenvalue)
ALTERNATIVE PARAMETERIZATIONS FOR THE CATEGORICAL LATENT VARIABLE REGRESSION
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Parameterization using Reference Class 1
CB#2 ON
W -0.822 0.217 -3.783 0.000
Intercepts
CB#2 0.068 0.217 0.311 0.756
ODDS RATIO FOR THE ALTERNATIVE PARAMETERIZATIONS FOR THE CATEGORICAL LATENT VARIABLE REGRESSION
95% C.I.
Estimate S.E. Lower 2.5% Upper 2.5%
Parameterization using Reference Class 1
CB#2 ON
W 0.440 0.096 0.287 0.673
Beginning Time: 22:57:15
Ending Time: 22:57:18
Elapsed Time: 00:00:03
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