Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:46 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level mixture
regression for a continuous dependent variable
DATA: FILE IS ex10.1.dat;
VARIABLE: NAMES ARE y x1 x2 w class clus;
USEVARIABLES = y x1 x2 w;
CLASSES = c (2);
WITHIN = x1 x2;
BETWEEN = w;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL MIXTURE;
STARTS = 0;
MODEL:
%WITHIN%
%OVERALL%
y ON x1 x2;
c ON x1;
%c#1%
y ON x2;
y;
%BETWEEN%
%OVERALL%
y ON w;
c#1 ON w;
c#1*1;
%c#1%
[y*2];
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level mixture
regression for a continuous dependent 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 0
Number of categorical latent variables 1
Observed dependent variables
Continuous
Y
Observed independent variables
X1 X2 W
Categorical latent variables
C
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 2
Adaptive quadrature ON
Cholesky OFF
Input data file(s)
ex10.1.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 1.239 0.307 -9.293 0.10% -1.390 0.262 1.069
1000.000 9.813 0.279 12.401 0.10% 1.863 3.758
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
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 13
Loglikelihood
H0 Value -1752.471
H0 Scaling Correction Factor 0.9041
for MLR
Information Criteria
Akaike (AIC) 3530.943
Bayesian (BIC) 3594.744
Sample-Size Adjusted BIC 3553.455
(n* = (n + 2) / 24)
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 546.36692 0.54637
2 453.63308 0.45363
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 573 0.57300
2 427 0.42700
CLASSIFICATION QUALITY
Entropy 0.402
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.808 0.192
2 0.196 0.804
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.847 0.153
2 0.243 0.757
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.711 0.000
2 -1.136 0.000
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
Latent Class 1
Y ON
X1 1.923 0.070 27.464 0.000
X2 0.970 0.080 12.193 0.000
Residual Variances
Y 1.061 0.105 10.087 0.000
Latent Class 2
Y ON
X1 1.923 0.070 27.464 0.000
X2 1.966 0.132 14.845 0.000
Residual Variances
Y 1.973 0.176 11.233 0.000
Between Level
Latent Class 1
Y ON
W 0.748 0.099 7.567 0.000
Intercepts
Y 0.963 0.148 6.502 0.000
Residual Variances
Y 0.520 0.091 5.730 0.000
Latent Class 2
Y ON
W 0.748 0.099 7.567 0.000
Intercepts
Y 1.975 0.146 13.515 0.000
Residual Variances
Y 0.520 0.091 5.730 0.000
Categorical Latent Variables
Within Level
C#1 ON
X1 -1.302 0.263 -4.951 0.000
Intercepts
C#1 0.153 0.328 0.466 0.641
Between Level
C#1 ON
W -1.134 0.332 -3.418 0.001
Residual Variances
C#1 0.013 0.132 0.102 0.919
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.199E-02
(ratio of smallest to largest eigenvalue)
LOGISTIC REGRESSION ODDS RATIO RESULTS
95% C.I.
Estimate S.E. Lower 2.5% Upper 2.5%
Categorical Latent Variables
Within Level
C#1 ON
X1 0.272 0.072 0.163 0.456
Between Level
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN LEVEL, LATENT CLASS 1
NU
Y X1 X2 W
________ ________ ________ ________
0 0 0 0
LAMBDA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
Y 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
THETA
Y X1 X2 W
________ ________ ________ ________
Y 0
X1 0 0
X2 0 0 0
W 0 0 0 0
ALPHA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
0 0 0 0 0
BETA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0 0 0 0 0
Y 0 0 1 2 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
PSI
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0
Y 0 3
X1 0 0 0
X2 0 0 0 0
W 0 0 0 0 0
PARAMETER SPECIFICATION FOR WITHIN LEVEL, LATENT CLASS 2
NU
Y X1 X2 W
________ ________ ________ ________
0 0 0 0
LAMBDA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
Y 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
THETA
Y X1 X2 W
________ ________ ________ ________
Y 0
X1 0 0
X2 0 0 0
W 0 0 0 0
ALPHA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
0 0 0 0 0
BETA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0 0 0 0 0
Y 0 0 1 4 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
PSI
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0
Y 0 5
X1 0 0 0
X2 0 0 0 0
W 0 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL, LATENT CLASS 1
NU
Y X1 X2 W
________ ________ ________ ________
0 0 0 0
LAMBDA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
Y 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
THETA
Y X1 X2 W
________ ________ ________ ________
Y 0
X1 0 0
X2 0 0 0
W 0 0 0 0
ALPHA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
0 6 0 0 0
BETA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0 0 0 0 7
Y 0 0 0 0 8
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
PSI
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 9
Y 0 10
X1 0 0 0
X2 0 0 0 0
W 0 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL, LATENT CLASS 2
NU
Y X1 X2 W
________ ________ ________ ________
0 0 0 0
LAMBDA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
Y 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
THETA
Y X1 X2 W
________ ________ ________ ________
Y 0
X1 0 0
X2 0 0 0
W 0 0 0 0
ALPHA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
0 11 0 0 0
BETA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0 0 0 0 7
Y 0 0 0 0 8
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
PSI
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 9
Y 0 10
X1 0 0 0
X2 0 0 0 0
W 0 0 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
12 0
GAMMA(C)
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0 0 13 0 0
C#2 0 0 0 0 0
STARTING VALUES FOR WITHIN LEVEL, LATENT CLASS 1
NU
Y X1 X2 W
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
Y 0.000 1.000 0.000 0.000 0.000
X1 0.000 0.000 1.000 0.000 0.000
X2 0.000 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 0.000 1.000
THETA
Y X1 X2 W
________ ________ ________ ________
Y 0.000
X1 0.000 0.000
X2 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
ALPHA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0.000
Y 0.000 4.906
X1 0.000 0.000 0.504
X2 0.000 0.000 0.000 0.480
W 0.000 0.000 0.000 0.000 0.000
STARTING VALUES FOR WITHIN LEVEL, LATENT CLASS 2
NU
Y X1 X2 W
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
Y 0.000 1.000 0.000 0.000 0.000
X1 0.000 0.000 1.000 0.000 0.000
X2 0.000 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 0.000 1.000
THETA
Y X1 X2 W
________ ________ ________ ________
Y 0.000
X1 0.000 0.000
X2 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
ALPHA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0.000
Y 0.000 4.906
X1 0.000 0.000 0.504
X2 0.000 0.000 0.000 0.480
W 0.000 0.000 0.000 0.000 0.000
STARTING VALUES FOR BETWEEN LEVEL, LATENT CLASS 1
NU
Y X1 X2 W
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
Y 0.000 1.000 0.000 0.000 0.000
X1 0.000 0.000 1.000 0.000 0.000
X2 0.000 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 0.000 1.000
THETA
Y X1 X2 W
________ ________ ________ ________
Y 0.000
X1 0.000 0.000
X2 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
ALPHA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
0.000 2.000 0.000 0.000 0.000
BETA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 1.000
Y 0.000 4.906
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.471
STARTING VALUES FOR BETWEEN LEVEL, LATENT CLASS 2
NU
Y X1 X2 W
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
Y 0.000 1.000 0.000 0.000 0.000
X1 0.000 0.000 1.000 0.000 0.000
X2 0.000 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 0.000 1.000
THETA
Y X1 X2 W
________ ________ ________ ________
Y 0.000
X1 0.000 0.000
X2 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
ALPHA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
0.000 4.371 0.000 0.000 0.000
BETA
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 1.000
Y 0.000 4.906
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.471
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
C#1 Y X1 X2 W
________ ________ ________ ________ ________
C#1 0.000 0.000 0.000 0.000 0.000
C#2 0.000 0.000 0.000 0.000 0.000
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.25901670D+04 0.0000000 0.0000000 EM
2 -0.19332348D+04 656.9322573 0.2536254 EM
3 -0.18579322D+04 75.3025259 0.0389516 EM
4 -0.18414640D+04 16.4682639 0.0088638 EM
5 -0.18298623D+04 11.6016474 0.0063002 EM
6 -0.18209031D+04 8.9591984 0.0048961 EM
7 -0.18136206D+04 7.2825391 0.0039994 EM
8 -0.18072417D+04 6.3788284 0.0035172 EM
9 -0.18013185D+04 5.9232905 0.0032775 EM
10 -0.17956427D+04 5.6757586 0.0031509 EM
11 -0.17901485D+04 5.4942160 0.0030597 EM
12 -0.17848517D+04 5.2967803 0.0029588 EM
13 -0.17798168D+04 5.0349074 0.0028209 EM
14 -0.17751353D+04 4.6814688 0.0026303 EM
15 -0.17709063D+04 4.2289861 0.0023823 EM
16 -0.17672151D+04 3.6912037 0.0020844 EM
17 -0.17641139D+04 3.1012668 0.0017549 EM
18 -0.17616091D+04 2.5047730 0.0014198 EM
19 -0.17596608D+04 1.9482749 0.0011060 EM
20 -0.17581939D+04 1.4669631 0.0008337 EM
21 -0.17571156D+04 1.0782660 0.0006133 EM
22 -0.17563334D+04 0.7821693 0.0004451 EM
23 -0.17557666D+04 0.5667837 0.0003227 EM
24 -0.17553514D+04 0.4152530 0.0002365 EM
25 -0.17550406D+04 0.3108035 0.0001771 EM
26 -0.17548012D+04 0.2394103 0.0001364 EM
27 -0.17546107D+04 0.1904817 0.0001085 EM
28 -0.17544541D+04 0.1565480 0.0000892 EM
29 -0.17543216D+04 0.1325047 0.0000755 EM
30 -0.17542066D+04 0.1150663 0.0000656 EM
31 -0.17541046D+04 0.1019615 0.0000581 EM
32 -0.17540128D+04 0.0918132 0.0000523 EM
33 -0.17539291D+04 0.0836721 0.0000477 EM
34 -0.17538522D+04 0.0769410 0.0000439 EM
35 -0.17537810D+04 0.0712015 0.0000406 EM
36 -0.17537148D+04 0.0662092 0.0000378 EM
37 -0.17536530D+04 0.0617639 0.0000352 EM
38 -0.17535953D+04 0.0577589 0.0000329 EM
39 -0.17535412D+04 0.0540959 0.0000308 EM
40 -0.17534904D+04 0.0507257 0.0000289 EM
41 -0.17534428D+04 0.0475921 0.0000271 EM
42 -0.17533982D+04 0.0446801 0.0000255 EM
43 -0.17533562D+04 0.0419510 0.0000239 EM
44 -0.17533168D+04 0.0393985 0.0000225 EM
45 -0.17532798D+04 0.0370025 0.0000211 EM
46 -0.17532451D+04 0.0347538 0.0000198 EM
47 -0.17532124D+04 0.0326382 0.0000186 EM
48 -0.17531818D+04 0.0306542 0.0000175 EM
49 -0.17531530D+04 0.0287878 0.0000164 EM
50 -0.17531259D+04 0.0270375 0.0000154 EM
51 -0.17531005D+04 0.0253927 0.0000145 EM
52 -0.17530767D+04 0.0238476 0.0000136 EM
53 -0.17530543D+04 0.0223999 0.0000128 EM
54 -0.17530333D+04 0.0210430 0.0000120 EM
55 -0.17530135D+04 0.0197708 0.0000113 EM
56 -0.17529949D+04 0.0185801 0.0000106 EM
57 -0.17529774D+04 0.0174644 0.0000100 EM
58 -0.17529610D+04 0.0164207 0.0000094 EM
59 -0.17529456D+04 0.0154443 0.0000088 EM
60 -0.17529310D+04 0.0145311 0.0000083 EM
61 -0.17529174D+04 0.0136776 0.0000078 EM
62 -0.17529045D+04 0.0128798 0.0000073 EM
63 -0.17528923D+04 0.0121345 0.0000069 EM
64 -0.17528809D+04 0.0114380 0.0000065 EM
65 -0.17528701D+04 0.0107877 0.0000062 EM
66 -0.17528599D+04 0.0101802 0.0000058 EM
67 -0.17527077D+04 0.1522273 0.0000868 QN
68 -0.17527018D+04 0.0058833 0.0000034 EM
69 -0.17526971D+04 0.0047758 0.0000027 EM
70 -0.17526927D+04 0.0043631 0.0000025 EM
71 -0.17526886D+04 0.0040803 0.0000023 EM
72 -0.17526848D+04 0.0038469 0.0000022 EM
73 -0.17526811D+04 0.0036402 0.0000021 EM
74 -0.17526777D+04 0.0034530 0.0000020 EM
75 -0.17526744D+04 0.0032815 0.0000019 EM
76 -0.17526713D+04 0.0031237 0.0000018 EM
77 -0.17526683D+04 0.0029778 0.0000017 EM
78 -0.17526654D+04 0.0028428 0.0000016 EM
79 -0.17524737D+04 0.1917156 0.0001094 QN
80 -0.17524720D+04 0.0017677 0.0000010 EM
81 -0.17524715D+04 0.0004729 0.0000003 EM
Beginning Time: 22:46:50
Ending Time: 22:46:59
Elapsed Time: 00:00:09
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