Mplus Textbook Examples
Applied Latent Class Analysis
Chapter
3 Latent Cluster Analysis by Jeroen K. Vermunt and Jay Magidson
Table 1 on page 100 using diabetes data. Notice that we only did the first three columns. Technically, the rest is the same.
Model 1:1 Class-dep unrestricted Σk with 1 cluster
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(1);
Analysis:
Type = mixture ;
model:
%overall%
glucose with insulin;
glucose with sspg;
insulin with sspg;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2545.828
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 5109.655
Bayesian (BIC) 5136.446
Sample-Size Adjusted BIC 5107.967
(n* = (n + 2) / 24)
Model 2:1 Class-ind unrestricted Σk with 1 cluster
This is the same as Model 1:1 since there is only one cluster.
Model 3:1 Class-dep. diagonal Σk with 1 cluster
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(1);
Analysis:
Type = mixture ;
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2750.135
Information Criteria
Number of Free Parameters 6
Akaike (AIC) 5512.269
Bayesian (BIC) 5530.130
Sample-Size Adjusted BIC 5511.144
(n* = (n + 2) / 24)
Model 4:1 Class-ind. diagonal Σk with 1 cluster
This is the same as Model 3:1 since there is only one cluster.
Model 5:1 class-dep Σk with only σ12 free with one cluster
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(1);
Analysis:
Type = mixture ;
model:
%overall%
glucose with insulin;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2559.462
Information Criteria
Number of Free Parameters 7
Akaike (AIC) 5132.924
Bayesian (BIC) 5153.761
Sample-Size Adjusted BIC 5131.611
(n* = (n + 2) / 24)
Model 6:1 class-ind Σk with only σ12 free with one cluster
This is the same as Model 5:1 since there is only one cluster.
Model 1:2 Class-dep unrestricted Σk with 2 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(2);
Analysis:
Type = mixture ;
model:
%overall%
glucose with insulin sspg;
insulin with sspg;
%c#1%
glucose-sspg;
glucose with insulin sspg;
insulin with sspg;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2355.905
Information Criteria
Number of Free Parameters 19
Akaike (AIC) 4749.811
Bayesian (BIC) 4806.369
Sample-Size Adjusted BIC 4746.246
(n* = (n + 2) / 24)
Entropy 0.935
Model 2:2 Class-ind unrestricted Σk with 2 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(2);
Analysis:
Type = mixture ;
model:
%overall%
glucose with insulin sspg;
insulin with sspg;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2473.144
Information Criteria
Number of Free Parameters 13
Akaike (AIC) 4972.288
Bayesian (BIC) 5010.985
Sample-Size Adjusted BIC 4969.849
(n* = (n + 2) / 24)
Entropy 0.980
Model 3:2 Class-dep. diagonal Σk with 2 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(2);
Analysis:
Type = mixture ;
model:
%overall%
glucose-sspg;
%c#1%
glucose-sspg;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2445.312
Information Criteria
Number of Free Parameters 13
Akaike (AIC) 4916.624
Bayesian (BIC) 4955.322
Sample-Size Adjusted BIC 4914.185
(n* = (n + 2) / 24)
Entropy 0.980
Model 4:2 Class-ind. diagonal Σk with 2 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(2);
Analysis:
Type = mixture ;
model:
%overall%
glucose-sspg;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2559.816
Information Criteria
Number of Free Parameters 10
Akaike (AIC) 5139.632
Bayesian (BIC) 5169.399
Sample-Size Adjusted BIC 5137.756
(n* = (n + 2) / 24)
Entropy 0.994
Model 5:2 class-dep Σk with only σ12 free with 2 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(2);
Analysis:
Type = mixture ;
! starts = 150 5;
model:
%overall%
glucose insulin sspg;
glucose with insulin;
%c#1%
glucose insulin sspg;
glucose with insulin;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2377.427
Information Criteria
Number of Free Parameters 15
Akaike (AIC) 4784.853
Bayesian (BIC) 4829.504
Sample-Size Adjusted BIC 4782.039
(n* = (n + 2) / 24)
Entropy 0.962
Model 6:2 class-ind Σk with only σ12 free with 2 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(2);
Analysis:
Type = mixture ;
model:
%overall%
glucose insulin sspg;
glucose with insulin;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2475.119
Information Criteria
Number of Free Parameters 11
Akaike (AIC) 4972.237
Bayesian (BIC) 5004.981
Sample-Size Adjusted BIC 4970.173
(n* = (n + 2) / 24)
Entropy 0.981
Model 1:3 Class-dep unrestricted Σk with 3 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(3);
Analysis:
Type = mixture ;
model:
%overall%
glucose insulin sspg;
glucose with insulin;
glucose with sspg;
insulin with sspg;
%c#1%
glucose insulin sspg;
glucose with insulin;
glucose with sspg;
insulin with sspg;
%c#2%
glucose insulin sspg;
glucose with insulin;
glucose with sspg;
insulin with sspg;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2303.492
Information Criteria
Number of Free Parameters 29
Akaike (AIC) 4664.984
Bayesian (BIC) 4751.309
Sample-Size Adjusted BIC 4659.543
(n* = (n + 2) / 24)
Entropy 0.855
Model 2:3 Class-ind unrestricted Σk with 3 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(3);
Analysis:
Type = mixture ;
model:
%overall%
glucose insulin sspg;
glucose with insulin;
glucose with sspg;
insulin with sspg;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2417.341
Information Criteria
Number of Free Parameters 17
Akaike (AIC) 4868.683
Bayesian (BIC) 4919.287
Sample-Size Adjusted BIC 4865.493
(n* = (n + 2) / 24)
Entropy 0.993
Model 3:3 Class-dep. diagonal Σk with 3 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(3);
Analysis:
Type = mixture ;
model:
%overall%
glucose insulin sspg;
%c#1%
glucose insulin sspg;
%c#2%
glucose insulin sspg;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2364.137
Information Criteria
Number of Free Parameters 20
Akaike (AIC) 4768.274
Bayesian (BIC) 4827.809
Sample-Size Adjusted BIC 4764.522
(n* = (n + 2) / 24)
Entropy 0.902
Model 4:3 Class-ind. diagonal Σk with 3 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(3);
Analysis:
Type = mixture ;
model:
%overall%
glucose insulin sspg;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2464.383
Information Criteria
Number of Free Parameters 14
Akaike (AIC) 4956.766
Bayesian (BIC) 4998.440
Sample-Size Adjusted BIC 4954.139
(n* = (n + 2) / 24)
Entropy 0.994
Model 5:3 class-dep Σk with only σ12 free with 3 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(3);
Analysis:
Type = mixture ;
model:
%overall%
glucose insulin sspg;
glucose with insulin;
%c#1%
glucose insulin sspg;
glucose with insulin;
%c#2%
glucose insulin sspg;
glucose with insulin;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2315.965
Information Criteria
Number of Free Parameters 23
Akaike (AIC) 4677.930
Bayesian (BIC) 4746.395
Sample-Size Adjusted BIC 4673.615
(n* = (n + 2) / 24)
Entropy 0.844
Model 6:3 class-ind Σk with only σ12 free with 3 clusters
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(3);
Analysis:
Type = mixture ;
! starts = 150 2;
model:
%overall%
glucose insulin sspg;
glucose with insulin;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2439.523
Information Criteria
Number of Free Parameters 15
Akaike (AIC) 4909.046
Bayesian (BIC) 4953.697
Sample-Size Adjusted BIC 4906.232
(n* = (n + 2) / 24)
Entropy 0.975
Table 2 on page 100 using model 5:3, a three-class model with class-dependent variance-covariance matrices and with only a local dependence between y1 and y2.
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(3);
Analysis:
Type = mixture ;
model:
%overall%
glucose insulin sspg;
glucose with insulin;
%c#1%
glucose insulin sspg;
glucose with insulin;
%c#2%
glucose insulin sspg;
glucose with insulin;
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 75.34772 0.51964
2 41.21362 0.28423
3 28.43866 0.19613
MODEL RESULTS
Estimates S.E. Est./S.E.
Latent Class 1
GLUCOSE WITH
INSULIN 70.840 47.839 1.481
Means
GLUCOSE 90.956 0.987 92.109
INSULIN 356.212 7.055 50.493
SSPG 161.930 6.762 23.946
Variances
GLUCOSE 57.299 10.546 5.433
INSULIN 1993.055 450.743 4.422
SSPG 2267.268 441.327 5.137
Latent Class 2
GLUCOSE WITH
INSULIN 1185.211 451.959 2.622
Means
GLUCOSE 103.193 2.496 41.342
INSULIN 487.963 21.674 22.514
SSPG 304.644 27.319 11.151
Variances
GLUCOSE 175.814 50.943 3.451
INSULIN 13292.888 ******* 2.366
SSPG 22383.512 ******* 3.805
Latent Class 3
GLUCOSE WITH
INSULIN 19226.834 ******* 5.990
Means
GLUCOSE 231.436 16.011 14.455
INSULIN 1106.372 63.013 17.558
SSPG 78.448 9.764 8.035
Variances
GLUCOSE 5246.220 836.749 6.270
INSULIN 78353.539 ******* 5.341
SSPG 2111.967 404.087 5.227
Categorical Latent Variables
Means
C#1 0.974 0.233 4.179
C#2 0.371 0.283 1.313
Table 3 on page 101. We output the class-membership to a data file called table3.dat in the following Mplus run. We then have to merge it back to the original data set and perform a crosstabulation between the class-membership based on the cluster analysis and the true membership in the original data set. This is done in Stata here.
Data:
File is c:alcachapter3diabetes.dat ;
Variable:
Names are
true glucose insulin sspg;
Missing are all (-9999) ;
Usev are glucose insulin sspg;
classes = c(3);
Analysis:
Type = mixture ;
model:
%overall%
glucose insulin sspg;
glucose with insulin;
%c#1%
glucose insulin sspg;
glucose with insulin;
%c#2%
glucose insulin sspg;
glucose with insulin;
savedata:
file is c:alcachapter3table3.dat;
save = cprob;
Stata Code for crosstabulation
Notice that we used the label command to label the three classes predicted by the model.
. infile glucose insulin sspg cprob1 cprob2 cprob3 c using table3.dat (145 observations read) . sort glucose insulin sspg . merge glucose insulin sspg using exam1
. label define g 1 "chemical" 2"normal" 3"overt"
. label values c g
. tab true c
| c
true | chemical normal overt | Total
-----------+---------------------------------+----------
1 | 8 27 1 | 36
2 | 71 5 0 | 76
3 | 0 5 28 | 33
-----------+---------------------------------+----------
Total | 79 37 29 | 145
Table 4 using prostate cancer data.
Model 1:1 local independence with 1 cluster
Data:
File is c:alcachapter3https://stats.idre.ucla.edu/wp-content/uploads/2016/02/prostate.dat ;
Variable:
Names are
y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12;
Missing are all (-9999) ;
usev are y1 - y12;
classes = c(1);
nominal are y3 y4 y7 y12;
Analysis:
Type = mixture ;
model:
%overall%
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15607.612
Information Criteria
Number of Free Parameters 27
Akaike (AIC) 31269.223
Bayesian (BIC) 31381.633
Sample-Size Adjusted BIC 31295.939
(n* = (n + 2) / 24)
Model 2:1 Model 1:1 + σ56k
Data:
File is c:alcachapter3https://stats.idre.ucla.edu/wp-content/uploads/2016/02/prostate.dat ;
Variable:
Names are
y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12;
Missing are all (-9999) ;
usev are y1 - y12;
classes = c(1);
nominal are y3 y4 y7 y12;
Analysis:
Type = mixture ;
! starts = 100 10;
model:
%overall%
y5 with y6;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15488.042
Information Criteria
Number of Free Parameters 28
Akaike (AIC) 31032.083
Bayesian (BIC) 31148.656
Sample-Size Adjusted BIC 31059.788
(n* = (n + 2) / 24)
Model 3:1 Model 2:1 + σ28k
Data:
File is c:alcachapter3https://stats.idre.ucla.edu/wp-content/uploads/2016/02/prostate.dat ;
Variable:
Names are
y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12;
Missing are all (-9999) ;
usev are y1 - y12;
classes = c(1);
nominal are y3 y4 y7 y12;
Analysis:
Type = mixture ;
model:
%overall%
y5 with y6;
y2 with y8;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15471.263
Information Criteria
Number of Free Parameters 29
Akaike (AIC) 31000.527
Bayesian (BIC) 31121.263
Sample-Size Adjusted BIC 31029.221
(n* = (n + 2) / 24)
Model 1:2 local independence with 2 clusters
Note: The code follows below does not work with Mplus 3.01. It works with Mplus 3.1. (Aug. 4, 2004).
Data:
File is c:alcachapter3https://stats.idre.ucla.edu/wp-content/uploads/2016/02/prostate.dat ;
Variable:
Names are
y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12;
Missing are all (-9999) ;
usev are y1 - y12;
classes = c(2);
nominal are y3 y4 y7 y12;
Analysis:
Type = mixture ;
model:
%overall%
y1 y2 y5 y6 y8 y9 y10 y11;
%c#1%
y1 y2 y5 y6 y8 y9 y10 y11;
output: tech1 ;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -13836.484
Information Criteria
Number of Free Parameters 95
Akaike (AIC) 27862.968
Bayesian (BIC) 28258.483
Sample-Size Adjusted BIC 27956.967
(n* = (n + 2) / 24)
Entropy 0.971