Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:57 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level CFA
mixture model with continuous factor
indicators
DATA: FILE IS ex10.4.dat;
VARIABLE: NAMES ARE y1-y5 class clus;
USEVARIABLES = y1-y5;
CLASSES = c (2);
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL MIXTURE;
STARTS = 0;
MODEL:
%WITHIN%
%OVERALL%
fw BY y1-y5;
%BETWEEN%
%OVERALL%
fb BY y1-y5;
c#1*1;
%c#1%
[fb*2];
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level CFA
mixture model with continuous factor
indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 5
Number of independent variables 0
Number of continuous latent variables 2
Number of categorical latent variables 1
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5
Continuous latent variables
FW FB
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 2
Adaptive quadrature ON
Cholesky OFF
Input data file(s)
ex10.4.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
Y1 1.081 0.005 -3.441 0.10% -0.342 0.637 1.070
1000.000 2.601 -0.351 5.535 0.10% 1.544 2.405
Y2 0.836 -0.042 -2.756 0.10% -0.333 0.493 0.850
1000.000 1.746 -0.417 4.350 0.10% 1.199 1.992
Y3 0.833 -0.027 -3.209 0.10% -0.341 0.466 0.842
1000.000 1.707 -0.422 4.296 0.10% 1.187 2.016
Y4 0.856 -0.002 -3.088 0.10% -0.293 0.500 0.867
1000.000 1.655 -0.366 4.582 0.10% 1.223 2.009
Y5 0.820 -0.027 -3.165 0.10% -0.360 0.443 0.800
1000.000 1.712 -0.372 4.649 0.10% 1.192 1.974
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 23
Loglikelihood
H0 Value -5334.228
H0 Scaling Correction Factor 0.9313
for MLR
Information Criteria
Akaike (AIC) 10714.456
Bayesian (BIC) 10827.334
Sample-Size Adjusted BIC 10754.285
(n* = (n + 2) / 24)
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 503.78930 0.50379
2 496.21070 0.49621
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 505 0.50500
2 495 0.49500
CLASSIFICATION QUALITY
Entropy 0.538
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.861 0.139
2 0.139 0.861
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.863 0.137
2 0.142 0.858
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.841 0.000
2 -1.803 0.000
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
Latent Class 1
FW BY
Y1 1.000 0.000 999.000 999.000
Y2 0.859 0.045 19.226 0.000
Y3 0.720 0.038 18.919 0.000
Y4 0.794 0.043 18.548 0.000
Y5 0.746 0.041 18.213 0.000
Variances
FW 0.781 0.096 8.156 0.000
Residual Variances
Y1 0.263 0.018 14.340 0.000
Y2 0.240 0.015 16.219 0.000
Y3 0.245 0.013 18.948 0.000
Y4 0.242 0.014 17.447 0.000
Y5 0.264 0.013 20.631 0.000
Latent Class 2
FW BY
Y1 1.000 0.000 999.000 999.000
Y2 0.859 0.045 19.226 0.000
Y3 0.720 0.038 18.919 0.000
Y4 0.794 0.043 18.548 0.000
Y5 0.746 0.041 18.213 0.000
Variances
FW 0.781 0.096 8.156 0.000
Residual Variances
Y1 0.263 0.018 14.340 0.000
Y2 0.240 0.015 16.219 0.000
Y3 0.245 0.013 18.948 0.000
Y4 0.242 0.014 17.447 0.000
Y5 0.264 0.013 20.631 0.000
Between Level
Latent Class 1
FB BY
Y1 1.000 0.000 999.000 999.000
Y2 0.773 0.024 31.776 0.000
Y3 0.824 0.024 34.227 0.000
Y4 0.769 0.023 33.965 0.000
Y5 0.807 0.025 31.935 0.000
Means
FB 2.180 0.119 18.344 0.000
Intercepts
Y1 -0.020 0.116 -0.172 0.864
Y2 -0.015 0.092 -0.163 0.871
Y3 -0.074 0.095 -0.777 0.437
Y4 0.010 0.089 0.117 0.907
Y5 -0.067 0.096 -0.702 0.483
Variances
FB 0.411 0.097 4.238 0.000
Latent Class 2
FB BY
Y1 1.000 0.000 999.000 999.000
Y2 0.773 0.024 31.776 0.000
Y3 0.824 0.024 34.227 0.000
Y4 0.769 0.023 33.965 0.000
Y5 0.807 0.025 31.935 0.000
Means
FB 0.000 0.000 999.000 999.000
Intercepts
Y1 -0.020 0.116 -0.172 0.864
Y2 -0.015 0.092 -0.163 0.871
Y3 -0.074 0.095 -0.777 0.437
Y4 0.010 0.089 0.117 0.907
Y5 -0.067 0.096 -0.702 0.483
Variances
FB 0.411 0.097 4.238 0.000
Categorical Latent Variables
Within Level
Means
C#1 0.038 0.206 0.186 0.853
Between Level
Variances
C#1 0.986 0.379 2.600 0.009
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.300E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN LEVEL, LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
FW C#1 FB
________ ________ ________
Y1 0 0 0
Y2 1 0 0
Y3 2 0 0
Y4 3 0 0
Y5 4 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 5
Y2 0 6
Y3 0 0 7
Y4 0 0 0 8
Y5 0 0 0 0 9
ALPHA
FW C#1 FB
________ ________ ________
0 0 0
BETA
FW C#1 FB
________ ________ ________
FW 0 0 0
C#1 0 0 0
FB 0 0 0
PSI
FW C#1 FB
________ ________ ________
FW 10
C#1 0 0
FB 0 0 0
PARAMETER SPECIFICATION FOR WITHIN LEVEL, LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
FW C#1 FB
________ ________ ________
Y1 0 0 0
Y2 1 0 0
Y3 2 0 0
Y4 3 0 0
Y5 4 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 5
Y2 0 6
Y3 0 0 7
Y4 0 0 0 8
Y5 0 0 0 0 9
ALPHA
FW C#1 FB
________ ________ ________
0 0 0
BETA
FW C#1 FB
________ ________ ________
FW 0 0 0
C#1 0 0 0
FB 0 0 0
PSI
FW C#1 FB
________ ________ ________
FW 10
C#1 0 0
FB 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL, LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
11 12 13 14 15
LAMBDA
FW C#1 FB
________ ________ ________
Y1 0 0 0
Y2 0 0 16
Y3 0 0 17
Y4 0 0 18
Y5 0 0 19
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
Y5 0 0 0 0 0
ALPHA
FW C#1 FB
________ ________ ________
0 0 20
BETA
FW C#1 FB
________ ________ ________
FW 0 0 0
C#1 0 0 0
FB 0 0 0
PSI
FW C#1 FB
________ ________ ________
FW 0
C#1 0 21
FB 0 0 22
PARAMETER SPECIFICATION FOR BETWEEN LEVEL, LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
11 12 13 14 15
LAMBDA
FW C#1 FB
________ ________ ________
Y1 0 0 0
Y2 0 0 16
Y3 0 0 17
Y4 0 0 18
Y5 0 0 19
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
Y5 0 0 0 0 0
ALPHA
FW C#1 FB
________ ________ ________
0 0 0
BETA
FW C#1 FB
________ ________ ________
FW 0 0 0
C#1 0 0 0
FB 0 0 0
PSI
FW C#1 FB
________ ________ ________
FW 0
C#1 0 21
FB 0 0 22
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
23 0
GAMMA(C)
FW C#1 FB
________ ________ ________
C#1 0 0 0
C#2 0 0 0
STARTING VALUES FOR WITHIN LEVEL, LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
FW C#1 FB
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 1.000 0.000 0.000
Y5 1.000 0.000 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.301
Y2 0.000 0.873
Y3 0.000 0.000 0.854
Y4 0.000 0.000 0.000 0.827
Y5 0.000 0.000 0.000 0.000 0.856
ALPHA
FW C#1 FB
________ ________ ________
0.000 0.000 0.000
BETA
FW C#1 FB
________ ________ ________
FW 0.000 0.000 0.000
C#1 0.000 0.000 0.000
FB 0.000 0.000 0.000
PSI
FW C#1 FB
________ ________ ________
FW 0.050
C#1 0.000 0.000
FB 0.000 0.000 0.000
STARTING VALUES FOR WITHIN LEVEL, LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
FW C#1 FB
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 1.000 0.000 0.000
Y5 1.000 0.000 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.301
Y2 0.000 0.873
Y3 0.000 0.000 0.854
Y4 0.000 0.000 0.000 0.827
Y5 0.000 0.000 0.000 0.000 0.856
ALPHA
FW C#1 FB
________ ________ ________
0.000 0.000 0.000
BETA
FW C#1 FB
________ ________ ________
FW 0.000 0.000 0.000
C#1 0.000 0.000 0.000
FB 0.000 0.000 0.000
PSI
FW C#1 FB
________ ________ ________
FW 0.050
C#1 0.000 0.000
FB 0.000 0.000 0.000
STARTING VALUES FOR BETWEEN LEVEL, LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1.081 0.836 0.833 0.856 0.820
LAMBDA
FW C#1 FB
________ ________ ________
Y1 0.000 0.000 1.000
Y2 0.000 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 1.000
Y5 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
ALPHA
FW C#1 FB
________ ________ ________
0.000 0.000 2.000
BETA
FW C#1 FB
________ ________ ________
FW 0.000 0.000 0.000
C#1 0.000 0.000 0.000
FB 0.000 0.000 0.000
PSI
FW C#1 FB
________ ________ ________
FW 0.000
C#1 0.000 1.000
FB 0.000 0.000 0.050
STARTING VALUES FOR BETWEEN LEVEL, LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1.081 0.836 0.833 0.856 0.820
LAMBDA
FW C#1 FB
________ ________ ________
Y1 0.000 0.000 1.000
Y2 0.000 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 1.000
Y5 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
ALPHA
FW C#1 FB
________ ________ ________
0.000 0.000 0.000
BETA
FW C#1 FB
________ ________ ________
FW 0.000 0.000 0.000
C#1 0.000 0.000 0.000
FB 0.000 0.000 0.000
PSI
FW C#1 FB
________ ________ ________
FW 0.000
C#1 0.000 1.000
FB 0.000 0.000 0.050
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
FW C#1 FB
________ ________ ________
C#1 0.000 0.000 0.000
C#2 0.000 0.000 0.000
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.71376209D+04 0.0000000 0.0000000 EM
2 -0.54016613D+04 1735.9595840 0.2432126 EM
3 -0.53657018D+04 35.9595033 0.0066571 EM
4 -0.53570703D+04 8.6314690 0.0016086 EM
5 -0.53531499D+04 3.9203881 0.0007318 EM
6 -0.53504601D+04 2.6898612 0.0005025 EM
7 -0.53483168D+04 2.1432859 0.0004006 EM
8 -0.53465319D+04 1.7849314 0.0003337 EM
9 -0.53450232D+04 1.5086586 0.0002822 EM
10 -0.53437392D+04 1.2839616 0.0002402 EM
11 -0.53426408D+04 1.0984677 0.0002056 EM
12 -0.53416956D+04 0.9451991 0.0001769 EM
13 -0.53408766D+04 0.8189280 0.0001533 EM
14 -0.53401615D+04 0.7150909 0.0001339 EM
15 -0.53395320D+04 0.6295253 0.0001179 EM
16 -0.53389736D+04 0.5584696 0.0001046 EM
17 -0.53384749D+04 0.4986872 0.0000934 EM
18 -0.53380273D+04 0.4475608 0.0000838 EM
19 -0.53376241D+04 0.4031849 0.0000755 EM
20 -0.53372599D+04 0.3642501 0.0000682 EM
21 -0.53369301D+04 0.3297436 0.0000618 EM
22 -0.53366314D+04 0.2987719 0.0000560 EM
23 -0.53363608D+04 0.2705738 0.0000507 EM
24 -0.53361162D+04 0.2445344 0.0000458 EM
25 -0.53358961D+04 0.2201562 0.0000413 EM
26 -0.53356990D+04 0.1970663 0.0000369 EM
27 -0.53355239D+04 0.1750936 0.0000328 EM
28 -0.53353695D+04 0.1543946 0.0000289 EM
29 -0.53352341D+04 0.1354270 0.0000254 EM
30 -0.53351155D+04 0.1186219 0.0000222 EM
31 -0.53350114D+04 0.1040453 0.0000195 EM
32 -0.53349200D+04 0.0914553 0.0000171 EM
33 -0.53348394D+04 0.0805473 0.0000151 EM
34 -0.53347684D+04 0.0710655 0.0000133 EM
35 -0.53347056D+04 0.0627976 0.0000118 EM
36 -0.53346500D+04 0.0555634 0.0000104 EM
37 -0.53343622D+04 0.2878291 0.0000540 FS
38 -0.53342446D+04 0.1175709 0.0000220 EM
39 -0.53342353D+04 0.0092905 0.0000017 EM
40 -0.53342316D+04 0.0037283 0.0000007 EM
41 -0.53342297D+04 0.0019164 0.0000004 EM
42 -0.53342286D+04 0.0011246 0.0000002 EM
43 -0.53342278D+04 0.0007126 0.0000001 EM
Beginning Time: 22:57:27
Ending Time: 22:57:32
Elapsed Time: 00:00:05
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