Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:48 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level LCGA for a three-category outcome
DATA: FILE IS ex10.11.dat;
VARIABLE: NAMES ARE u1-u4 class clus;
USEVARIABLES = u1-u4;
CATEGORICAL = u1-u4;
CLASSES = c(2);
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL MIXTURE;
MODEL:
%WITHIN%
%OVERALL%
i s | u1@0 u2@1 u3@2 u4@3;
i-s@0;
%c#1%
[i*1 s*1];
%c#2%
[i@0 s];
%BETWEEN%
%OVERALL%
c#1*1;
[u1$1-u4$1*1] (1);
[u1$2-u4$2*1.5] (2);
*** 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
U1 5 16 27 29
U2 17 25
U3 4 10 15 16 18 26 30 32 36 40
U4 11 18 32 33 36
*** WARNING in MODEL command
All continuous latent variable covariances involving I on the within level
have been fixed to 0 because the variance of I is fixed at 0.
2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of a two-level LCGA for a three-category outcome
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 4
Number of independent variables 0
Number of continuous latent variables 2
Number of categorical latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Continuous latent variables
I S
Categorical latent variables
C
Variables with special functions
Cluster variable CLUS
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
Link LOGIT
Cholesky ON
Input data file(s)
ex10.11.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 110
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.608 608.000
Category 2 0.099 99.000
Category 3 0.293 293.000
U2
Category 1 0.515 515.000
Category 2 0.090 90.000
Category 3 0.395 395.000
U3
Category 1 0.455 455.000
Category 2 0.064 64.000
Category 3 0.481 481.000
U4
Category 1 0.425 425.000
Category 2 0.054 54.000
Category 3 0.521 521.000
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:
-3317.328 285380 1
-3317.328 76974 16
-3317.329 unperturbed 0
-3441.891 903420 5
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 7
Loglikelihood
H0 Value -3317.328
H0 Scaling Correction Factor 0.9810
for MLR
Information Criteria
Akaike (AIC) 6648.657
Bayesian (BIC) 6683.011
Sample-Size Adjusted BIC 6660.779
(n* = (n + 2) / 24)
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 527.88727 0.52789
2 472.11273 0.47211
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 529 0.52900
2 471 0.47100
CLASSIFICATION QUALITY
Entropy 0.723
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.929 0.071
2 0.078 0.922
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.931 0.069
2 0.080 0.920
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 2.599 0.000
2 -2.446 0.000
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
Latent Class 1
I |
U1 1.000 0.000 999.000 999.000
U2 1.000 0.000 999.000 999.000
U3 1.000 0.000 999.000 999.000
U4 1.000 0.000 999.000 999.000
S |
U1 0.000 0.000 999.000 999.000
U2 1.000 0.000 999.000 999.000
U3 2.000 0.000 999.000 999.000
U4 3.000 0.000 999.000 999.000
Means
I -0.722 0.120 -5.996 0.000
S -0.133 0.054 -2.453 0.014
Variances
I 0.000 0.000 999.000 999.000
S 0.000 0.000 999.000 999.000
Latent Class 2
I |
U1 1.000 0.000 999.000 999.000
U2 1.000 0.000 999.000 999.000
U3 1.000 0.000 999.000 999.000
U4 1.000 0.000 999.000 999.000
S |
U1 0.000 0.000 999.000 999.000
U2 1.000 0.000 999.000 999.000
U3 2.000 0.000 999.000 999.000
U4 3.000 0.000 999.000 999.000
Means
I 0.000 0.000 999.000 999.000
S 1.037 0.072 14.418 0.000
Variances
I 0.000 0.000 999.000 999.000
S 0.000 0.000 999.000 999.000
Between Level
Latent Class 1
Thresholds
U1$1 0.083 0.081 1.021 0.307
U1$2 0.540 0.080 6.725 0.000
U2$1 0.083 0.081 1.021 0.307
U2$2 0.540 0.080 6.725 0.000
U3$1 0.083 0.081 1.021 0.307
U3$2 0.540 0.080 6.725 0.000
U4$1 0.083 0.081 1.021 0.307
U4$2 0.540 0.080 6.725 0.000
Latent Class 2
Thresholds
U1$1 0.083 0.081 1.021 0.307
U1$2 0.540 0.080 6.725 0.000
U2$1 0.083 0.081 1.021 0.307
U2$2 0.540 0.080 6.725 0.000
U3$1 0.083 0.081 1.021 0.307
U3$2 0.540 0.080 6.725 0.000
U4$1 0.083 0.081 1.021 0.307
U4$2 0.540 0.080 6.725 0.000
Categorical Latent Variables
Within Level
Means
C#1 0.141 0.156 0.901 0.367
Between Level
Variances
C#1 1.027 0.304 3.384 0.001
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.805E-02
(ratio of smallest to largest eigenvalue)
RESULTS IN PROBABILITY SCALE
Estimate
Within Level
Between Level
Latent Class 1
U1
Category 1 0.691
Category 2 0.088
Category 3 0.221
U2
Category 1 0.719
Category 2 0.083
Category 3 0.199
U3
Category 1 0.745
Category 2 0.077
Category 3 0.178
U4
Category 1 0.769
Category 2 0.071
Category 3 0.160
Latent Class 2
U1
Category 1 0.521
Category 2 0.111
Category 3 0.368
U2
Category 1 0.278
Category 2 0.100
Category 3 0.622
U3
Category 1 0.120
Category 2 0.057
Category 3 0.823
U4
Category 1 0.046
Category 2 0.025
Category 3 0.929
Beginning Time: 22:48:55
Ending Time: 22:48:59
Elapsed Time: 00:00:04
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