Table 3.2 on page 28 using pleural thickening data. In general, the AIC and BIC displayed in the book is the difference between the AIC for the specific model and the AIC for the unconstrained model and Mplus displays the AIC and BIC for each specific model alone. We can convert Mplus version of AIC and BIC back to the results in the book by taking the difference. For example, for unconstrained model, Mplus gives AIC as 1796.286 and for homogeneous 1815.697. The difference of these two gives 19.411 which is what in Table 3.2 for AIC of homogeneous model.
Model I: unconstrained
data:
file is https://stats.idre.ucla.edu/wp-content/uploads/2016/02/table3_1.dat ;
variable:
names are
a b c freq;
missing are all (-9999) ;
categorical are a b c;
classes=cl(2);
weight is freq (freq);
analysis:
type = mixture ;
starts = 0;
model:
%overall%
[A$1*10 B$1*10 C$1*10];
%cl#1%
[A$1*-10 B$1*-10 C$1*-10];
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -891.143
Information Criteria
Number of Free Parameters 7
Akaike (AIC) 1796.286
Bayesian (BIC) 1834.321
Sample-Size Adjusted BIC 1812.083
(n* = (n + 2) / 24)
Entropy 0.949
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 0.000
Degrees of Freedom 0
P-Value 1.0000
Likelihood Ratio Chi-Square
Value 0.000
Degrees of Freedom 0
P-Value 1.0000
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 92.18101 0.05448
2 1599.81899 0.94552
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.251 0.067 3.727
Category 2 0.749 0.067 11.127
B
Category 1 0.356 0.067 5.357
Category 2 0.644 0.067 9.670
C
Category 1 0.235 0.067 3.531
Category 2 0.765 0.067 11.495
Latent Class 2
A
Category 1 0.990 0.003 285.156
Category 2 0.010 0.003 2.871
B
Category 1 0.965 0.005 194.842
Category 2 0.035 0.005 7.157
C
Category 1 0.989 0.004 271.551
Category 2 0.011 0.004 3.000
Model II: Homogeneous
data:
file is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table3_1.dat ;
variable:
names are
a b c freq;
missing are all (-9999) ;
categorical are a b c;
classes=cl(2);
weight is freq (freq);
analysis:
type = mixture ;
starts = 0;
model:
%overall%
[A$1*10 B$1*10 C$1*10] (1);
%cl#1%
[A$1*-10 B$1*-10 C$1*-10] (2);
TESTS OF MODEL FIT
Loglikelihood
H0 Value -904.848
Information Criteria
Number of Free Parameters 3
Akaike (AIC) 1815.697
Bayesian (BIC) 1831.998
Sample-Size Adjusted BIC 1822.467
(n* = (n + 2) / 24)
Entropy 0.942
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 29.355
Degrees of Freedom 4
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 27.411
Degrees of Freedom 4
P-Value 0.0000
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 92.36555 0.05459
2 1599.63445 0.94541
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.283 0.049 5.801
Category 2 0.717 0.049 14.668
B
Category 1 0.283 0.049 5.801
Category 2 0.717 0.049 14.668
C
Category 1 0.283 0.049 5.801
Category 2 0.717 0.049 14.668
Latent Class 2
A
Category 1 0.981 0.003 377.675
Category 2 0.019 0.003 7.254
B
Category 1 0.981 0.003 377.675
Category 2 0.019 0.003 7.254
C
Category 1 0.981 0.003 377.675
Category 2 0.019 0.003 7.254
Model III: Reader B, heterogeneous
data:
file is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table3_1.dat ;
variable:
names are
a b c freq;
missing are all (-9999) ;
categorical are a b c;
classes=cl(2);
weight is freq (freq);
analysis:
type = mixture ;
starts = 0;
model:
%overall%
[A$1*10 C$1*10] (1);
[B$1*10];
%cl#1%
[A$1*-10 C$1*-10] (2);
[B$1*-10];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -891.210
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 1792.420
Bayesian (BIC) 1819.588
Sample-Size Adjusted BIC 1803.704
(n* = (n + 2) / 24)
Entropy 0.949
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 0.134
Degrees of Freedom 2
P-Value 0.9350
Likelihood Ratio Chi-Square
Value 0.134
Degrees of Freedom 2
P-Value 0.9350
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 92.19087 0.05449
2 1599.80913 0.94551
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.243 0.053 4.612
Category 2 0.757 0.053 14.363
B
Category 1 0.356 0.067 5.357
Category 2 0.644 0.067 9.670
C
Category 1 0.243 0.053 4.612
Category 2 0.757 0.053 14.363
Latent Class 2
A
Category 1 0.990 0.003 372.068
Category 2 0.010 0.003 3.928
B
Category 1 0.965 0.005 194.830
Category 2 0.035 0.005 7.155
C
Category 1 0.990 0.003 372.068
Category 2 0.010 0.003 3.928
Model IV: Reader B, false negative
data:
file is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table3_1.dat ;
variable:
names are
a b c freq;
missing are all (-9999) ;
categorical are a b c;
classes=cl(2);
weight is freq (freq);
analysis:
type = mixture ;
starts = 0;
model:
model:
%overall%
[A$1*10 B$1*10 C$1*10] (1);
%cl#1%
[A$1*-10 C$1*-10] (2);
[B$1*-10];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -904.768
Information Criteria
Number of Free Parameters 4
Akaike (AIC) 1817.536
Bayesian (BIC) 1839.271
Sample-Size Adjusted BIC 1826.563
(n* = (n + 2) / 24)
Entropy 0.947
Chi-Square Test of Model Fit for the Binary and Ordered Categorical (Ordinal) Outcomes
Pearson Chi-Square
Value 29.180
Degrees of Freedom 3
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 27.251
Degrees of Freedom 3
P-Value 0.0000
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES BASED ON THE ESTIMATED MODEL
Latent Classes
1 90.14024 0.05327
2 1601.85976 0.94673
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.262 0.088 2.998
Category 2 0.738 0.088 8.430
B
Category 1 0.295 0.054 5.475
Category 2 0.705 0.054 13.072
C
Category 1 0.262 0.088 2.998
Category 2 0.738 0.088 8.430
Latent Class 2
A
Category 1 0.981 0.003 339.540
Category 2 0.019 0.003 6.663
B
Category 1 0.981 0.003 339.540
Category 2 0.019 0.003 6.663
C
Category 1 0.981 0.003 339.540
Category 2 0.019 0.003 6.663
Model V: Reader B, false positive
data:
file is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table3_1.dat ;
variable:
names are
a b c freq;
missing are all (-9999) ;
categorical are a b c;
classes=cl(2);
weight is freq (freq);
analysis:
type = mixture ;
starts = 0;
model:
%overall%
[A$1*10 C$1*10] (1);
[B$1*10];
%cl#1%
[A$1*-10 B$1*-10 C$1*-10] (2);
TESTS OF MODEL FIT
Loglikelihood
H0 Value -892.636
Information Criteria
Number of Free Parameters 4
Akaike (AIC) 1793.273
Bayesian (BIC) 1815.007
Sample-Size Adjusted BIC 1802.300
(n* = (n + 2) / 24)
Entropy 0.945
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 3.111
Degrees of Freedom 3
P-Value 0.3748
Likelihood Ratio Chi-Square
Value 2.987
Degrees of Freedom 3
P-Value 0.3936
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 93.50052 0.05526
2 1598.49948 0.94474
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.287 0.049 5.839
Category 2 0.713 0.049 14.532
B
Category 1 0.287 0.049 5.839
Category 2 0.713 0.049 14.532
C
Category 1 0.287 0.049 5.839
Category 2 0.713 0.049 14.532
Latent Class 2
A
Category 1 0.989 0.003 382.510
Category 2 0.011 0.003 4.168
B
Category 1 0.966 0.005 194.568
Category 2 0.034 0.005 6.860
C
Category 1 0.989 0.003 382.510
Category 2 0.011 0.003 4.168
Cheating Data Example on page 30 using raw data https://stats.idre.ucla.edu/wp-content/uploads/2016/02/table3_4.dat.
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table3_4.dat ;
Variable:
names are a b c d freq;
missing are all (-9999) ;
weight is freq (freq);
categorical are a b c d;
classes = cl(2);
Analysis:
Type = mixture ;
starts = 0;
Model:
%overall%
[a$1*10 b$1*10 c$1*10 d$1*10];
%cl#1%
[a$1*-10 b$1*-10 c$1*-10 d$1*-10];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -440.027
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 898.054
Bayesian (BIC) 931.941
Sample-Size Adjusted BIC 903.395
(n* = (n + 2) / 24)
Entropy 0.737
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 8.323
Degrees of Freedom 6
P-Value 0.2154
Likelihood Ratio Chi-Square
Value 7.764
Degrees of Freedom 6
P-Value 0.2559
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.423 0.180 2.346
Category 2 0.577 0.180 3.199
B
Category 1 0.411 0.175 2.350
Category 2 0.589 0.175 3.369
C
Category 1 0.784 0.085 9.272
Category 2 0.216 0.085 2.555
D
Category 1 0.624 0.100 6.218
Category 2 0.376 0.100 3.752
Latent Class 2
A
Category 1 0.983 0.029 34.212
Category 2 0.017 0.029 0.578
B
Category 1 0.971 0.030 31.849
Category 2 0.029 0.030 0.959
C
Category 1 0.963 0.015 63.319
Category 2 0.037 0.015 2.439
D
Category 1 0.818 0.026 31.148
Category 2 0.182 0.026 6.928
We can also obtain Bootstrap estimates of standard error by using the option "bootstrap =" in the analysis statement as shown below. Here we used "bootstrap = 50" to request 50 bootstrap draws to be used in the computation.
Data:
File is c:daytonstata_data_fileshttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table3_4.dat ;
Variable:
names are
a b c d freq;
missing are all (-9999) ;
weight is freq (freq);
categorical are a b c d;
classes = cl(2);
Analysis:
Type = mixture ;
starts = 0;
bootstrap = 50;
estimator = ML;
Model:
%overall%
[a$1*10 b$1*10 c$1*10 d$1*10];
%cl#1%
[a$1*-10 b$1*-10 c$1*-10 d$1*-10];
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.423 0.190 2.228
Category 2 0.577 0.190 3.038
B
Category 1 0.411 0.172 2.395
Category 2 0.589 0.172 3.433
C
Category 1 0.784 0.076 10.371
Category 2 0.216 0.076 2.858
D
Category 1 0.624 0.114 5.487
Category 2 0.376 0.114 3.312
Latent Class 2
A
Category 1 0.983 0.019 51.328
Category 2 0.017 0.019 0.867
B
Category 1 0.971 0.026 37.457
Category 2 0.029 0.026 1.128
C
Category 1 0.963 0.016 58.393
Category 2 0.037 0.016 2.250
D
Category 1 0.818 0.026 32.035
Category 2 0.182 0.026 7.125
Table 3.5, 3.6 and 3.7 are omitted for now since Mplus does not provide those estimates.
Table 3.8 on page 39 using the academic cheating data with a single latent variable of two classes.
We first create a data file containing the latent classification probabilities and the modal class using the savedata statement of Mplus.
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table3_4.dat ;
Variable:
names are
a b c d freq;
missing are all (-9999) ;
weight is freq (freq);
categorical are a b c d;
classes = cl(2);
Analysis:
Type = mixture ;
starts = 0;
Model:
%overall%
[a$1*10 b$1*10 c$1*10 d$1*10];
%cl#1%
[a$1*-10 b$1*-10 c$1*-10 d$1*-10];
savedata:
file = cprob.dat;
save = cprob;
Next, we simply copy and paste the content of data file cprob.dat to Stata do file editor and input it as a data set. Based on the output from the Mplus run, we create a sequence of variables representing the conditional probabilities. Based on the conditional probabilities and the latent class probabilities, we then create column 3 and 4 of Table 3.8.
clear
input a b c d observed p1 p2 class
0.000 0.000 0.000 0.000 207.000 0.021 0.979 2.000
1.000 0.000 0.000 0.000 10.000 0.636 0.364 1.000
0.000 1.000 0.000 0.000 13.000 0.507 0.493 1.000
1.000 1.000 0.000 0.000 11.000 0.988 0.012 1.000
0.000 0.000 1.000 0.000 7.000 0.134 0.866 2.000
1.000 0.000 1.000 0.000 1.000 0.926 0.074 1.000
0.000 1.000 1.000 0.000 1.000 0.880 0.120 1.000
1.000 1.000 1.000 0.000 1.000 0.998 0.002 1.000
0.000 0.000 0.000 1.000 46.000 0.055 0.945 2.000
1.000 0.000 0.000 1.000 3.000 0.826 0.174 1.000
0.000 1.000 0.000 1.000 4.000 0.736 0.264 1.000
1.000 1.000 0.000 1.000 4.000 0.996 0.004 1.000
0.000 0.000 1.000 1.000 5.000 0.296 0.704 2.000
1.000 0.000 1.000 1.000 2.000 0.971 0.029 1.000
0.000 1.000 1.000 1.000 2.000 0.952 0.048 1.000
1.000 1.000 1.000 1.000 2.000 0.999 0.001 1.000
end
gen a11 = .983
gen a12 = .423
gen b11 = .971
gen b12 = .411
gen c11 = .963
gen c12 = .784
gen d11 = .818
gen d12 = .624
gen px1 = .839
gen py1 = 1
gen py2 = 1
foreach var of varlist a b c d {
replace py1 = py1*`var'11 if `var'==0
replace py2 = py2*`var'12 if `var'==0
replace py1 = py1*(1-`var'11) if `var'==1
replace py2 = py2*(1-`var'12) if `var'==1
}
replace py1 = py1*px1
replace py2 = py2*(1-px1)
gen odds = p1/p2
sort d c b a
list a b c d observed py1 py2 class p2 odds, clean
a b c d observed py1 py2 class p2 odds 1. 0 0 0 0 207 .6308329 .0136933 2 .979 .0214505 2. 1 0 0 0 10 .0109096 .0186786 1 .364 1.747253 3. 0 1 0 0 13 .0188405 .0196238 1 .493 1.028398 4. 1 1 0 0 11 .0003258 .0267681 1 .012 82.33333 5. 0 0 1 0 7 .0242376 .0037726 2 .866 .1547344 6. 1 0 1 0 1 .0004192 .0051461 1 .074 12.51351 7. 0 1 1 0 1 .0007239 .0054065 1 .12 7.333333 8. 1 1 1 0 1 .0000125 .0073749 1 .002 499 9. 0 0 0 1 46 .1403564 .0082511 2 .945 .0582011 10. 1 0 0 1 3 .0024273 .0112551 1 .174 4.747127 11. 0 1 0 1 4 .0041919 .0118246 1 .264 2.787879 12. 1 1 0 1 4 .0000725 .0161295 1 .004 249 13. 0 0 1 1 5 .0053927 .0022733 2 .704 .4204546 14. 1 0 1 1 2 .0000933 .0031009 1 .029 33.48276 15. 0 1 1 1 2 .0001611 .0032578 1 .048 19.83333 16. 1 1 1 1 2 2.79e-06 .0044438 1 .001 998.9999
Table 3. 9 and Table 3.10 are omitted for the time being.
Table 4.1 on page 50 and Table 4.2 on page 51 using left-right clinical scale data using raw data file https://stats.idre.ucla.edu/wp-content/uploads/2016/02/table4_1_nozero.dat. Notice that we requested TECH10 output to display the estimated frequencies.
Model I: Proctor
data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table4_1_nozero.dat ;
variable:
names are
a b c freq;
missing are all (-9999) ;
categorical are a b c;
classes = cl(4);
weight is freq (freq);
analysis:
Type = mixture ;
model:
%overall%
[a$1*1 b$1*1 c$1*1] (p1);
%cl#1%
[a$1*-1 b$1*-1 c$1*-1] (p2);
%cl#2%
[a$1*1] (p1)
[b$1*-1 c$1*-1] (p2);
%cl#3%
[a$1*1 b$1*1] (p1)
[c$1*-1] (p2);
model constraint:
p2 = -p1;
output: tech10;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -746.102
Information Criteria
Number of Free Parameters 4
Akaike (AIC) 1500.203
Bayesian (BIC) 1517.607
Sample-Size Adjusted BIC 1504.908
(n* = (n + 2) / 24)
Entropy 0.944
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 3.586
Degrees of Freedom 3
P-Value 0.3098
Likelihood Ratio Chi-Square
Value 5.440
Degrees of Freedom 3
P-Value 0.1422
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 173.25843 0.30237
2 71.02449 0.12395
3 260.89574 0.45532
4 67.82134 0.11836
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.991 0.003 349.008
Category 2 0.009 0.003 3.035
B
Category 1 0.991 0.003 349.008
Category 2 0.009 0.003 3.035
C
Category 1 0.991 0.003 349.008
Category 2 0.009 0.003 3.035
Latent Class 2
A
Category 1 0.009 0.003 3.035
Category 2 0.991 0.003 349.008
B
Category 1 0.991 0.003 349.008
Category 2 0.009 0.003 3.035
C
Category 1 0.991 0.003 349.008
Category 2 0.009 0.003 3.035
Latent Class 3
A
Category 1 0.009 0.003 3.035
Category 2 0.991 0.003 349.008
B
Category 1 0.009 0.003 3.035
Category 2 0.991 0.003 349.008
C
Category 1 0.991 0.003 349.008
Category 2 0.009 0.003 3.035
Latent Class 4
A
Category 1 0.009 0.003 3.035
Category 2 0.991 0.003 349.008
B
Category 1 0.009 0.003 3.035
Category 2 0.991 0.003 349.008
C
Category 1 0.009 0.003 3.035
Category 2 0.991 0.003 349.008
MODEL FIT INFORMATION FOR THE LATENT CLASS INDICATOR MODEL PART
RESPONSE PATTERNS
No. Pattern No. Pattern No. Pattern No. Pattern
1 000 2 100 3 010 4 110
5 101 6 111
RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS
Response Frequency Standard Chi-square Contribution
Pattern Observed Estimated Residual Pearson Loglikelihood Deleted
1 170.00 169.44 0.05 0.00 1.13
2 73.00 72.89 0.01 0.00 0.23
3 6.00 3.69 1.21 1.45 5.84
4 254.00 255.40 0.12 0.01 -2.78
5 1.00 1.21 0.19 0.04 -0.38
6 69.00 68.30 0.09 0.01 1.41
Model II: Intrusion-Omission Error
data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table4_1_nozero.dat ;
variable:
names are
a b c freq;
missing are all (-9999) ;
categorical are a b c;
classes = cl(4);
weight is freq (freq);
analysis:
Type = mixture ;
starts = 0;
model:
%overall%
[a$1*-10 b$1*-10 c$1*-10] (1); !for class 4
%cl#1%
[a$1*10 b$1*10 c$1*10] (2);
%cl#2%
[a$1*-10] (1)
[b$1*10 c$1*10] (2);
%cl#3%
[a$1*-10 b$1*-10] (1)
[c$1*10] (2);
output: tech10;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -744.854
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 1499.707
Bayesian (BIC) 1521.462
Sample-Size Adjusted BIC 1505.589
(n* = (n + 2) / 24)
Entropy 0.959
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 1.760
Degrees of Freedom 2
P-Value 0.4148
Likelihood Ratio Chi-Square
Value 2.944
Degrees of Freedom 2
P-Value 0.2294
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 168.69989 0.29442
2 69.66926 0.12159
3 263.38416 0.45966
4 71.24670 0.12434
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 2
A
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 3
A
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
B
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 4
A
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
B
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
C
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS
Response Frequency Standard Chi-square Contribution
Pattern Observed Estimated Residual Pearson Loglikelihood Deleted
1 170.00 170.00 0.00 0.00 0.00
2 73.00 73.00 0.00 0.00 0.00
3 6.00 4.55 0.68 0.46 3.32
4 254.00 255.45 0.12 0.01 -2.89
5 1.00 1.20 0.19 0.03 -0.37
6 69.00 67.57 0.19 0.03 2.89
Model III: Variable-Specific Error
data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table4_1_nozero.dat ;
variable:
names are
a b c freq;
missing are all (-9999) ;
categorical are a b c;
classes = cl(4);
weight is freq (freq);
analysis:
Type = mixture ;
starts = 0;
model:
%overall%
[a$1*-10] (p1);
[b$1*-10] (p2);
[c$1@-15] ; !for class 4
%cl#1%
[a$1*10] (q1);
[b$1*10] (q2);
[c$1@15] ;
%cl#2%
[a$1*-10] (p1);
[b$1*10] (q2);
[c$1@15] ;
%cl#3%
[a$1*-10] (p1);
[b$1*-10] (p2);
[c$1@15] ;
model constraint:
p1 = -q1;
p2 = -q2;
output: tech10;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -743.787
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 1497.573
Bayesian (BIC) 1519.328
Sample-Size Adjusted BIC 1503.455
(n* = (n + 2) / 24)
Entropy 0.956
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 0.711
Degrees of Freedom 2
P-Value 0.7010
Likelihood Ratio Chi-Square
Value 0.810
Degrees of Freedom 2
P-Value 0.6669
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 175.99997 0.30716
2 67.53883 0.11787
3 259.46127 0.45281
4 69.99993 0.12216
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
B
Category 1 0.972 0.009 105.123
Category 2 0.028 0.009 3.079
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 2
A
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
B
Category 1 0.972 0.009 105.123
Category 2 0.028 0.009 3.079
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 3
A
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
B
Category 1 0.028 0.009 3.079
Category 2 0.972 0.009 105.123
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 4
A
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
B
Category 1 0.028 0.009 3.079
Category 2 0.972 0.009 105.123
C
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS
Response Frequency Standard Chi-square Contribution
Pattern Observed Estimated Residual Pearson Loglikelihood Deleted
1 170.00 170.99 0.09 0.01 -1.98
2 73.00 73.00 0.00 0.00 0.00
3 6.00 5.01 0.45 0.20 2.17
4 254.00 254.00 0.00 0.00 0.00
5 1.00 1.99 0.70 0.49 -1.38
6 69.00 68.01 0.13 0.01 2.00
Model IV: Latent-Class Specific Error
data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table4_1_nozero.dat ;
variable:
names are
a b c freq;
missing are all (-9999) ;
categorical are a b c;
classes = cl(4);
weight is freq (freq);
analysis:
Type = mixture ;
starts = 0;
model:
%overall%
[a$1@15 b$1@10 c$1@15]; !for class 4
%cl#1%
[a$1@-15 b$1@-15 c$1@-15];
%cl#2%
[a$1*-5 ] (p1);
[b$1*5 c$1*5] (p2);
%cl#3%
[a$1*5 b$1*5] (q1);
[c$1*-5] (q2);
model constraint:
p1 = -p2;
q1 = -q2;
output: tech10;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -743.531
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 1497.061
Bayesian (BIC) 1518.816
Sample-Size Adjusted BIC 1502.943
(n* = (n + 2) / 24)
Entropy 0.934
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 0.156
Degrees of Freedom 2
P-Value 0.9252
Likelihood Ratio Chi-Square
Value 0.298
Degrees of Freedom 2
P-Value 0.8615
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 63.27073 0.11042
2 69.86503 0.12193
3 270.83218 0.47266
4 169.03207 0.29499
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
B
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
C
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
Latent Class 2
A
Category 1 0.012 0.006 2.075
Category 2 0.988 0.006 164.884
B
Category 1 0.988 0.006 164.884
Category 2 0.012 0.006 2.075
C
Category 1 0.988 0.006 164.884
Category 2 0.012 0.006 2.075
Latent Class 3
A
Category 1 0.022 0.007 3.011
Category 2 0.978 0.007 133.362
B
Category 1 0.022 0.007 3.011
Category 2 0.978 0.007 133.362
C
Category 1 0.978 0.007 133.362
Category 2 0.022 0.007 3.011
Latent Class 4
A
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS
Response Frequency Standard Chi-square Contribution
Pattern Observed Estimated Residual Pearson Loglikelihood Deleted
1 170.00 170.00 0.00 0.00 0.00
2 73.00 73.01 0.00 0.00 -0.02
3 6.00 5.74 0.11 0.01 0.54
4 254.00 254.13 0.01 0.00 -0.26
5 1.00 0.98 0.02 0.00 0.05
6 69.00 69.00 0.00 0.00 0.00
Table 4.3 on page 56 using Lazarsfeld-Stouffer Attitude data with raw data file https://stats.idre.ucla.edu/wp-content/uploads/2016/02/laz_sto.dat.
Model I: One intrinsically unscalable class model
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/laz_sto.dat ;
Variable:
names are a b c d freq;
missing are all (-9999) ;
categorical are a b c d;
classes = cl(6);
weight is freq (freq);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*-1 b$1*-1 c$1*-1 d$1*-1]; !for class 6
%cl#1%
[a$1@15 b$1@15 c$1@15 d$1@15];
%cl#2%
[a$1@-15 ];
[b$1@15 c$1@15 d$1@15];;
%cl#3%
[a$1@-15 b$1@-15];
[c$1@15 d$1@15];
%cl#4%
[a$1@-15 b$1@-15 c$1@-15];
[d$1@15];
%cl#5%
[a$1@-15 b$1@-15 c$1@-15 d$1@-15];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2357.211
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 4732.421
Bayesian (BIC) 4776.591
Sample-Size Adjusted BIC 4748.006
(n* = (n + 2) / 24)
Entropy 0.822
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 26.085
Degrees of Freedom 6
P-Value 0.0002
Likelihood Ratio Chi-Square
Value 26.500
Degrees of Freedom 6
P-Value 0.0002
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 49.78701 0.04979
2 11.23731 0.01124
3 0.00000 0.00000
4 78.89503 0.07890
5 188.01697 0.18802
6 672.06370 0.67206
RESULTS IN PROBABILITY SCALE
Latent Class 1-5 (omitted here)
Latent Class 6
A
Category 1 0.304 0.024 12.866
Category 2 0.696 0.024 29.475
B
Category 1 0.356 0.030 11.978
Category 2 0.644 0.030 21.708
C
Category 1 0.466 0.030 15.346
Category 2 0.534 0.030 17.607
D
Category 1 0.746 0.021 34.745
Category 2 0.254 0.021 11.856
Model II: Two intrinsically unscalable classes model. Notice that Mplus gets a better log likelihood. The estimated probabilities are somewhat different from the result in the book. This may be due to the different algorithms used in ML estimation.
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/laz_sto.dat ;
Variable:
names are a b c d freq;
missing are all (-9999) ;
categorical are a b c d;
classes = cl(7);
weight is freq (freq);
Analysis:
Type = mixture ;
starts = 0;
model:
%overall%
[a$1*-1 b$1*-1 c$1*-1 d$1*-2]; !for class 7
%cl#1%
[a$1@15 b$1@15 c$1@15 d$1@15];
%cl#2%
[a$1@-15 ];
[b$1@15 c$1@15 d$1@15];
%cl#3%
[a$1@-15 b$1@-15];
[c$1@15 d$1@15];
%cl#4%
[a$1@-15 b$1@-15 c$1@-15];
[d$1@15];
%cl#5%
[a$1@-15 b$1@-15 c$1@-15 d$1@-15];
%cl#6%
[a$1*1 b$1*1 c$1*1 d$1*8];
ONE OR MORE MULTINOMIAL LOGIT PARAMETERS WERE FIXED TO AVOID SINGULARITY
OF THE INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE
MODEL IS NOT IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT
DISTRIBUTION OF THE CATEGORICAL LATENT VARIABLES AND ANY INDEPENDENT
VARIABLES. THE FOLLOWING PARAMETERS WERE FIXED:
10
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2345.748
Information Criteria
Number of Free Parameters 14
Akaike (AIC) 4719.495
Bayesian (BIC) 4788.204
Sample-Size Adjusted BIC 4743.739
(n* = (n + 2) / 24)
Entropy 0.776
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 3.975
Degrees of Freedom 1
P-Value 0.0462
Likelihood Ratio Chi-Square
Value 3.574
Degrees of Freedom 1
P-Value 0.0587
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 25.43469 0.02543
2 0.00000 0.00000
3 20.78793 0.02079
4 134.55060 0.13455
5 137.93803 0.13794
6 478.91510 0.47892
7 202.37364 0.20237
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
D
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 2
A
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
D
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 3
A
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
B
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
D
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 4
A
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
B
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
C
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
D
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 5
A
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
B
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
C
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
D
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
Latent Class 6
A
Category 1 0.416 0.046 9.069
Category 2 0.584 0.046 12.706
B
Category 1 0.480 0.049 9.887
Category 2 0.520 0.049 10.703
C
Category 1 0.539 0.037 14.389
Category 2 0.461 0.037 12.322
D
Category 1 0.961 0.125 7.707
Category 2 0.039 0.125 0.316
Latent Class 7
A
Category 1 0.144 0.116 1.244
Category 2 0.856 0.116 7.408
B
Category 1 0.220 0.138 1.594
Category 2 0.780 0.138 5.639
C
Category 1 0.345 0.110 3.132
Category 2 0.655 0.110 5.951
D
Category 1 0.001 0.011 0.077
Category 2 0.999 0.011 87.746
Model III: intrusion-omission error model
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/laz_sto.dat ;
Variable:
names are a b c d freq;
missing are all (-9999) ;
categorical are a b c d;
classes = cl(5);
weight is freq (freq);
Analysis:
Type = mixture ;
starts = 0;
model:
%overall%
[a$1*-5 b$1*-5 c$1*-5 d$1*-5] (1) ; !for class 5
%cl#1%
[a$1*5 b$1*5 c$1*5 d$1*5] (2);
%cl#2%
[a$1*-5] (1);
[b$1*5 c$1*5 d$1*5] (2);
%cl#3%
[a$1*-5 b$1*-5] (1);
[c$1*5 d$1*5] (2);
%cl#4%
[a$1*-5 b$1*-5 c$1*-5] (1);
[d$1*5] (2);
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2379.713
Information Criteria
Number of Free Parameters 6
Akaike (AIC) 4771.426
Bayesian (BIC) 4800.872
Sample-Size Adjusted BIC 4781.816
(n* = (n + 2) / 24)
Entropy 0.461
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 63.313
Degrees of Freedom 9
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 71.505
Degrees of Freedom 9
P-Value 0.0000
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 192.62219 0.19262
2 80.34766 0.08035
3 127.35833 0.12736
4 337.63774 0.33764
5 262.03407 0.26203
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.787 0.026 30.031
Category 2 0.213 0.026 8.125
B
Category 1 0.787 0.026 30.031
Category 2 0.213 0.026 8.125
C
Category 1 0.787 0.026 30.031
Category 2 0.213 0.026 8.125
D
Category 1 0.787 0.026 30.031
Category 2 0.213 0.026 8.125
Latent Class 2
A
Category 1 0.128 0.018 7.078
Category 2 0.872 0.018 48.232
B
Category 1 0.787 0.026 30.031
Category 2 0.213 0.026 8.125
C
Category 1 0.787 0.026 30.031
Category 2 0.213 0.026 8.125
D
Category 1 0.787 0.026 30.031
Category 2 0.213 0.026 8.125
Latent Class 3
A
Category 1 0.128 0.018 7.078
Category 2 0.872 0.018 48.232
B
Category 1 0.128 0.018 7.078
Category 2 0.872 0.018 48.232
C
Category 1 0.787 0.026 30.031
Category 2 0.213 0.026 8.125
D
Category 1 0.787 0.026 30.031
Category 2 0.213 0.026 8.125
Latent Class 4
A
Category 1 0.128 0.018 7.078
Category 2 0.872 0.018 48.232
B
Category 1 0.128 0.018 7.078
Category 2 0.872 0.018 48.232
C
Category 1 0.128 0.018 7.078
Category 2 0.872 0.018 48.232
D
Category 1 0.787 0.026 30.031
Category 2 0.213 0.026 8.125
Latent Class 5
A
Category 1 0.128 0.018 7.078
Category 2 0.872 0.018 48.232
B
Category 1 0.128 0.018 7.078
Category 2 0.872 0.018 48.232
C
Category 1 0.128 0.018 7.078
Category 2 0.872 0.018 48.232
D
Category 1 0.128 0.018 7.078
Category 2 0.872 0.018 48.232
Model IV: variable-specific error model
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/laz_sto.dat ;
Variable:
names are a b c d freq;
missing are all (-9999) ;
categorical are a b c d;
classes = cl(5);
weight is freq (freq);
Analysis:
Type = mixture ;
starts = 0;
model:
%overall%
[a$1*-5] (p1);
[b$1*-5] (p2);
[c$1*-5] (p3);
[d$1*-5] (p4); !for class 5
%cl#1%
[a$1*5] (q1);
[b$1*5] (q2);
[c$1*5] (q3);
[d$1*5] (q4);
%cl#2%
[a$1*-5] (p1);
[b$1*5] (q2);
[c$1*5] (q3);
[d$1*5] (q4);
%cl#3%
[a$1*-5] (p1);
[b$1*-5] (p2);
[c$1*5] (q3);
[d$1*5] (q4);
%cl#4%
[a$1*-5] (p1);
[b$1*-5] (p2);
[c$1*-5] (p3);
[d$1*5] (q4);
model constraint:
p1 = -q1;
p2 = -q2;
p3 = -q3;
p4 = -q4;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2365.771
Information Criteria
Number of Free Parameters 8
Akaike (AIC) 4747.542
Bayesian (BIC) 4786.804
Sample-Size Adjusted BIC 4761.396
(n* = (n + 2) / 24)
Entropy 0.692
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 42.633
Degrees of Freedom 7
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 43.622
Degrees of Freedom 7
P-Value 0.0000
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 158.52423 0.15852
2 62.02713 0.06203
3 67.23843 0.06724
4 356.18533 0.35619
5 356.02489 0.35602
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.860 0.016 55.149
Category 2 0.140 0.016 8.963
B
Category 1 0.819 0.018 46.149
Category 2 0.181 0.018 10.222
C
Category 1 0.766 0.020 38.099
Category 2 0.234 0.020 11.668
D
Category 1 0.990 0.004 234.405
Category 2 0.010 0.004 2.447
Latent Class 2
A
Category 1 0.140 0.016 8.963
Category 2 0.860 0.016 55.149
B
Category 1 0.819 0.018 46.149
Category 2 0.181 0.018 10.222
C
Category 1 0.766 0.020 38.099
Category 2 0.234 0.020 11.668
D
Category 1 0.990 0.004 234.405
Category 2 0.010 0.004 2.447
Latent Class 3
A
Category 1 0.140 0.016 8.963
Category 2 0.860 0.016 55.149
B
Category 1 0.181 0.018 10.222
Category 2 0.819 0.018 46.149
C
Category 1 0.766 0.020 38.099
Category 2 0.234 0.020 11.668
D
Category 1 0.990 0.004 234.405
Category 2 0.010 0.004 2.447
Latent Class 4
A
Category 1 0.140 0.016 8.963
Category 2 0.860 0.016 55.149
B
Category 1 0.181 0.018 10.222
Category 2 0.819 0.018 46.149
C
Category 1 0.234 0.020 11.668
Category 2 0.766 0.020 38.099
D
Category 1 0.990 0.004 234.405
Category 2 0.010 0.004 2.447
Latent Class 5
A
Category 1 0.140 0.016 8.963
Category 2 0.860 0.016 55.149
B
Category 1 0.181 0.018 10.222
Category 2 0.819 0.018 46.149
C
Category 1 0.234 0.020 11.668
Category 2 0.766 0.020 38.099
D
Category 1 0.010 0.004 2.447
Category 2 0.990 0.004 234.405
Model V: Intrusion-omission error and one intrinsically unscalable class model. Notice that Mplus gets a better log likelihood. The estimated probabilities are somewhat different from the result in the book. This may be due to the different algorithms used in ML estimation.
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/laz_sto.dat ;
Variable:
names are a b c d freq;
missing are all (-9999) ;
categorical are a b c d;
classes = cl(6);
weight is freq (freq);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*10 b$1*10 c$1*9 d$1*5]; ! for class 6;
%cl#1%
[a$1*-10 b$1*-10 c$1*-10 d$1*-10] (1);
%cl#2%
[a$1*5] (2);
[b$1*-10 c$1*-10 d$1*-10] (1);
%cl#3%
[a$1*5 b$1*5] (2);
[c$1*-10 d$1*-10] (1);
%cl#4%
[a$1*5 b$1*5 c$1*5] (2);
[d$1*-10] (1);
%cl#5%
[a$1*5 b$1*5 c$1*5 d$1*5] (2);
IN THE OPTIMIZATION, ONE OR MORE LOGIT THRESHOLDS APPROACHED AND WERE SET
AT THE EXTREME VALUES. EXTREME VALUES ARE -15.000 AND 15.000.
THE FOLLOWING THRESHOLDS WERE SET AT THESE VALUES:
* THRESHOLD 1 OF CLASS INDICATOR D FOR CLASS 6 AT ITERATION 72
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE
TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE
FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING
VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE
CONDITION NUMBER IS 0.470D-10. PROBLEM INVOLVING PARAMETER 11.
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2345.938
Information Criteria
Number of Free Parameters 11
Akaike (AIC) 4713.876
Bayesian (BIC) 4767.862
Sample-Size Adjusted BIC 4732.925
(n* = (n + 2) / 24)
Entropy 0.511
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 3.909
Degrees of Freedom 4
P-Value 0.4185
Likelihood Ratio Chi-Square
Value 3.956
Degrees of Freedom 4
P-Value 0.4121
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 110.86584 0.11087
2 73.79787 0.07380
3 129.17772 0.12918
4 313.11373 0.31311
5 0.01108 0.00001
6 373.03377 0.37303
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.424 0.033 12.929
Category 2 0.576 0.033 17.528
B
Category 1 0.424 0.033 12.929
Category 2 0.576 0.033 17.528
C
Category 1 0.424 0.033 12.929
Category 2 0.576 0.033 17.528
D
Category 1 0.424 0.033 12.929
Category 2 0.576 0.033 17.528
Latent Class 2
A
Category 1 0.033 0.026 1.274
Category 2 0.967 0.026 37.240
B
Category 1 0.424 0.033 12.929
Category 2 0.576 0.033 17.528
C
Category 1 0.424 0.033 12.929
Category 2 0.576 0.033 17.528
D
Category 1 0.424 0.033 12.929
Category 2 0.576 0.033 17.528
Latent Class 3
A
Category 1 0.033 0.026 1.274
Category 2 0.967 0.026 37.240
B
Category 1 0.033 0.026 1.274
Category 2 0.967 0.026 37.240
C
Category 1 0.424 0.033 12.929
Category 2 0.576 0.033 17.528
D
Category 1 0.424 0.033 12.929
Category 2 0.576 0.033 17.528
Latent Class 4
A
Category 1 0.033 0.026 1.274
Category 2 0.967 0.026 37.240
B
Category 1 0.033 0.026 1.274
Category 2 0.967 0.026 37.240
C
Category 1 0.033 0.026 1.274
Category 2 0.967 0.026 37.240
D
Category 1 0.424 0.033 12.929
Category 2 0.576 0.033 17.528
Latent Class 5
A
Category 1 0.033 0.026 1.274
Category 2 0.967 0.026 37.240
B
Category 1 0.033 0.026 1.274
Category 2 0.967 0.026 37.240
C
Category 1 0.033 0.026 1.274
Category 2 0.967 0.026 37.240
D
Category 1 0.033 0.026 1.274
Category 2 0.967 0.026 37.240
Latent Class 6
A
Category 1 0.509 0.040 12.807
Category 2 0.491 0.040 12.347
B
Category 1 0.553 0.038 14.409
Category 2 0.447 0.038 11.627
C
Category 1 0.624 0.035 17.792
Category 2 0.376 0.035 10.726
D
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Model VI: Variable-specific error and one intrinsically unscalable class model
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/laz_sto.dat ;
Variable:
names are a b c d freq;
missing are all (-9999) ;
categorical are a b c d;
classes = cl(6);
weight is freq (freq);
Analysis:
Type = mixture ;
starts = 20 5; !use random starts;
stseed = 123457;
model:
%overall%
[a$1*-7 b$1*-5 c$1*-3 d$1*-1]; ! for class 6;
%cl#1%
[a$1*-5] (p1);
[b$1*-5] (p2);
[c$1*-5] (p3);
[d$1*-5] (p4);
%cl#2%
[a$1*5] (q1);
[b$1*-5] (p2);
[c$1*-5] (p3);
[d$1*-5] (p4);
%cl#3%
[a$1*5] (q1);
[b$1*5] (q2);
[c$1*-5] (p3);
[d$1*-5] (p4);
%cl#4%
[a$1*5] (q1);
[b$1*5] (q2);
[c$1*5] (q3);
[d$1*-5] (p4);
%cl#5%
[a$1*5] (q1);
[b$1*5] (q2);
[c$1*5] (q3);
[d$1*5] (q4);
model constraint:
p1 = -q1;
p2 = -q2;
p3 = -q3;
p4 = -q4;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2344.772
Information Criteria
Number of Free Parameters 13
Akaike (AIC) 4715.543
Bayesian (BIC) 4779.344
Sample-Size Adjusted BIC 4738.056
(n* = (n + 2) / 24)
Entropy 0.505
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 1.593
Degrees of Freedom 2
P-Value 0.4510
Likelihood Ratio Chi-Square
Value 1.623
Degrees of Freedom 2
P-Value 0.4442
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 179.78671 0.17979
2 50.80390 0.05080
3 90.36266 0.09036
4 185.10047 0.18510
5 145.45897 0.14546
6 348.48729 0.34849
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.757 0.050 15.159
Category 2 0.243 0.050 4.858
B
Category 1 0.630 0.087 7.208
Category 2 0.370 0.087 4.233
C
Category 1 0.665 0.051 13.174
Category 2 0.335 0.051 6.624
D
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 2
A
Category 1 0.243 0.050 4.858
Category 2 0.757 0.050 15.159
B
Category 1 0.630 0.087 7.208
Category 2 0.370 0.087 4.233
C
Category 1 0.665 0.051 13.174
Category 2 0.335 0.051 6.624
D
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 3
A
Category 1 0.243 0.050 4.858
Category 2 0.757 0.050 15.159
B
Category 1 0.370 0.087 4.233
Category 2 0.630 0.087 7.208
C
Category 1 0.665 0.051 13.174
Category 2 0.335 0.051 6.624
D
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 4
A
Category 1 0.243 0.050 4.858
Category 2 0.757 0.050 15.159
B
Category 1 0.370 0.087 4.233
Category 2 0.630 0.087 7.208
C
Category 1 0.335 0.051 6.624
Category 2 0.665 0.051 13.174
D
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 5
A
Category 1 0.243 0.050 4.858
Category 2 0.757 0.050 15.159
B
Category 1 0.370 0.087 4.233
Category 2 0.630 0.087 7.208
C
Category 1 0.335 0.051 6.624
Category 2 0.665 0.051 13.174
D
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
Latent Class 6
A
Category 1 0.010 0.049 0.197
Category 2 0.990 0.049 20.195
B
Category 1 0.000 0.000 0.000
Category 2 1.000 0.000 0.000
C
Category 1 0.135 0.041 3.304
Category 2 0.865 0.041 21.114
D
Category 1 0.387 0.063 6.135
Category 2 0.613 0.063 9.709
Table 4.4 on page 58 using Model VI in the example above. Notice that it should be model VI as explained in previous page instead of model V. This is the output requested with TECH10 in the above Mplus program for Model VI.
RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS
Response Frequency Standard Chi-square Contribution
Pattern Observed Estimated Residual Pearson Loglikelihood Deleted
1 75.00 73.21 0.22 0.04 3.62
2 69.00 68.62 0.05 0.00 0.76
3 55.00 55.40 0.05 0.00 -0.79
4 96.00 96.53 0.06 0.00 -1.07
5 42.00 45.07 0.47 0.21 -5.93
6 60.00 60.29 0.04 0.00 -0.58
7 45.00 42.96 0.32 0.10 4.17
8 199.00 198.92 0.01 0.00 0.16
9 3.00 4.37 0.66 0.43 -2.26
10 16.00 13.64 0.64 0.41 5.12
11 8.00 7.72 0.10 0.01 0.57
12 52.00 51.83 0.02 0.00 0.33
13 10.00 8.69 0.45 0.20 2.81
14 25.00 27.12 0.41 0.17 -4.07
15 16.00 16.58 0.14 0.02 -1.14
16 229.00 229.05 0.00 0.00 -0.10
Result on page 60 using Stouffer-Toby role conflict data of Table 4.6 on page 61. In this example, we show how to specify using a data set with individual records. You can download the data file following the link here.
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table4_6-1.dat ;
Variable:
Names are a b c d freq;
missing are all (-9999) ;
categorical are a b c d;
classes = cl(5);
weight is freq (freq);
Analysis:
Type = mixture ;
starts = 0;
model:
Analysis:
Type = mixture ;
starts = 0;
model:
%overall%
[a$1*-5] (p1);
[b$1*-5] (p2);
[c$1*-5] (p3);
[d$1*-5] (p4); !for class 5
%cl#1%
[a$1*5] (q1);
[b$1*5] (q2);
[c$1*5] (q3);
[d$1*5] (q4);
%cl#2%
[a$1*-5] (p1);
[b$1*5] (q2);
[c$1*5] (q3);
[d$1*5] (q4);
%cl#3%
[a$1*-5] (p1);
[b$1*-5] (p2);
[c$1*5] (q3);
[d$1*5] (q4);
%cl#4%
[a$1*-5] (p1);
[b$1*-5] (p2);
[c$1*-5] (p3);
[d$1*5] (q4);
model constraint:
p1 = -q1;
p4 = -q4;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -503.568
Information Criteria
Number of Free Parameters 10
Akaike (AIC) 1027.136
Bayesian (BIC) 1060.889
Sample-Size Adjusted BIC 1029.201
(n* = (n + 2) / 24)
Entropy 0.724
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 0.895
Degrees of Freedom 5
P-Value 0.9706
Likelihood Ratio Chi-Square
Value 0.921
Degrees of Freedom 5
P-Value 0.9687
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 51.64449 0.23909
2 3.80927 0.01764
3 22.18693 0.10272
4 94.84487 0.43910
5 43.51444 0.20146
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.864 0.035 24.530
Category 2 0.136 0.035 3.869
B
Category 1 0.948 0.068 13.882
Category 2 0.052 0.068 0.763
C
Category 1 0.940 0.066 14.310
Category 2 0.060 0.066 0.914
D
Category 1 0.988 0.004 239.974
Category 2 0.012 0.004 2.796
Latent Class 2
A
Category 1 0.136 0.035 3.869
Category 2 0.864 0.035 24.530
B
Category 1 0.948 0.068 13.882
Category 2 0.052 0.068 0.763
C
Category 1 0.940 0.066 14.310
Category 2 0.060 0.066 0.914
D
Category 1 0.988 0.004 239.974
Category 2 0.012 0.004 2.796
Latent Class 3
A
Category 1 0.136 0.035 3.869
Category 2 0.864 0.035 24.530
B
Category 1 0.364 0.050 7.314
Category 2 0.636 0.050 12.782
C
Category 1 0.940 0.066 14.310
Category 2 0.060 0.066 0.914
D
Category 1 0.988 0.004 239.974
Category 2 0.012 0.004 2.796
Latent Class 4
A
Category 1 0.136 0.035 3.869
Category 2 0.864 0.035 24.530
B
Category 1 0.364 0.050 7.314
Category 2 0.636 0.050 12.782
C
Category 1 0.253 0.069 3.678
Category 2 0.747 0.069 10.852
D
Category 1 0.988 0.004 239.974
Category 2 0.012 0.004 2.796
Latent Class 5
A
Category 1 0.136 0.035 3.869
Category 2 0.864 0.035 24.530
B
Category 1 0.364 0.050 7.314
Category 2 0.636 0.050 12.782
C
Category 1 0.253 0.069 3.678
Category 2 0.747 0.069 10.852
D
Category 1 0.012 0.004 2.796
Category 2 0.988 0.004 239.974
Model of one intrinsically unscalable class is fitted to Stouffer-Toby data (page 61).
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table4_6-1.dat ;
Variable:
Names are a b c d freq;
missing are all (-9999) ;
categorical are a b c d;
classes = cl(6);
weight is freq (freq);
Analysis:
Type = mixture ;
starts = 0;
model:
Analysis:
Type = mixture ;
starts = 0;
model:
%overall%
[a$1*-5 b$1*-5 c$1*-5 d$1*-5] ; !for class 6
%cl#1%
[a$1@15 b$1@15 c$1@15 d$1@15];
%cl#2%
[a$1@-15 b$1@15 c$1@15 d$1@15];
%cl#3%
[a$1@-15 b$1@-15 c$1@15 d$1@15];
%cl#4%
[a$1@-15 b$1@-15 c$1@-15 d$1@15];
%cl#5%
[a$1@-15 b$1@-15 c$1@-15 d$1@-15];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -503.602
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 1025.204
Bayesian (BIC) 1055.581
Sample-Size Adjusted BIC 1027.062
(n* = (n + 2) / 24)
Entropy 0.814
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 1.005
Degrees of Freedom 6
P-Value 0.9854
Likelihood Ratio Chi-Square
Value 0.988
Degrees of Freedom 6
P-Value 0.9860
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 38.26154 0.17714
2 7.55784 0.03499
3 5.51063 0.02551
4 6.78175 0.03140
5 10.44380 0.04835
6 147.44445 0.68261
Latent markov model example — to be done
Located latent class model example — to be done
T-class mixture model example — to be done
Table 5.1 on page 69 using IEA bus data. We requested TECH10 for expected frequencies. Column labeled as "Disc" can be obtained by squaring the column below labeled as "Standard Residual" in the part of the output titled as RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS.
Model I: linear scale
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table5_1.dat ;
Variable:
Names are
a b c d freq;
Missing are all (-9999) ;
categorical are a b c d;
weight is freq (freq);
classes = cl(5);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*10] (p3);
[d$1*10] (p4);
%cl#1%
[a$1*-10] (q1);
[b$1*-10] (q2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#2%
[a$1*10] (p1);
[b$1*-10] (q2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#3%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#4%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*10] (p3);
[d$1*-10] (q4);
model constraint:
p1 = -q1;
p2 = -q2;
p3 = -q3;
p4 = -q4;
output: TECH10;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -12930.791
Information Criteria
Number of Free Parameters 8
Akaike (AIC) 25877.581
Bayesian (BIC) 25931.643
Sample-Size Adjusted BIC 25906.221
(n* = (n + 2) / 24)
Entropy 0.600
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 40.367
Degrees of Freedom 7
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 46.849
Degrees of Freedom 7
P-Value 0.0000
TECHNICAL 10 OUTPUT
MODEL FIT INFORMATION FOR THE LATENT CLASS INDICATOR MODEL PART
RESPONSE PATTERNS
No. Pattern No. Pattern No. Pattern No. Pattern
1 0000 2 1000 3 0100 4 1100
5 0010 6 1010 7 0110 8 1110
9 0001 10 1001 11 0101 12 1101
13 0011 14 1011 15 0111 16 1111
RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS
Response Frequency Standard Chi-square Contribution
Pattern Observed Estimated Residual Pearson Loglikelihood Deleted
1 1138.00 1148.73 0.35 0.10 -21.37
2 1532.00 1532.94 0.03 0.00 -1.87
3 502.00 467.06 1.68 2.61 72.43
4 1354.00 1376.74 0.69 0.38 -45.10
5 75.00 69.79 0.63 0.39 10.81
6 200.00 220.75 1.42 1.95 -39.48
7 198.00 182.67 1.15 1.29 31.91
8 852.00 852.32 0.01 0.00 -0.65
9 13.00 23.31 2.14 4.56 -15.18
10 43.00 32.27 1.89 3.57 24.69
11 9.00 10.89 0.57 0.33 -3.42
12 37.00 34.95 0.35 0.12 4.21
13 15.00 13.10 0.53 0.28 4.07
14 59.00 60.60 0.21 0.04 -3.15
15 23.00 57.46 4.57 20.67 -42.12
16 309.00 275.43 2.07 4.09 71.08
Model II: biform scale
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table5_1.dat ;
Variable:
Names are
a b c d freq;
Missing are all (-9999) ;
categorical are a b c d;
weight is freq (freq);
classes = cl(6);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*10] (p3);
[d$1*10] (p4);
%cl#1%
[a$1*-10] (q1);
[b$1*-10] (q2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#2%
[a$1*10] (p1);
[b$1*-10] (q2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#3%
[a$1*-10] (q1);
[b$1*10] (p2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#4%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#5%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*10] (p3);
[d$1*-10] (q4);
model constraint:
p1 = -q1;
p2 = -q2;
p3 = -q3;
p4 = -q4;
output: tech10;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -12927.166
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 25872.333
Bayesian (BIC) 25933.151
Sample-Size Adjusted BIC 25904.552
(n* = (n + 2) / 24)
Entropy 0.613
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 35.277
Degrees of Freedom 6
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 39.601
Degrees of Freedom 6
P-Value 0.0000
RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS
Response Frequency Standard Chi-square Contribution
Pattern Observed Estimated Residual Pearson Loglikelihood Deleted
1 1138.00 1130.55 0.24 0.05 14.94
2 1532.00 1538.86 0.20 0.03 -13.70
3 502.00 503.06 0.05 0.00 -2.11
4 1354.00 1353.05 0.03 0.00 1.89
5 75.00 73.24 0.21 0.04 3.57
6 200.00 213.59 0.95 0.86 -26.29
7 198.00 169.07 2.26 4.95 62.55
8 852.00 869.58 0.64 0.36 -34.80
9 13.00 22.06 1.93 3.72 -13.75
10 43.00 31.55 2.04 4.15 26.62
11 9.00 11.65 0.78 0.60 -4.64
12 37.00 36.89 0.02 0.00 0.23
13 15.00 10.61 1.35 1.81 10.38
14 59.00 54.54 0.61 0.36 9.28
15 23.00 52.76 4.11 16.79 -38.20
16 309.00 287.94 1.27 1.54 43.62
Model III: augmented biform
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table5_1.dat ;
Variable:
Names are
a b c d freq;
Missing are all (-9999) ;
categorical are a b c d;
weight is freq (freq);
classes = cl(7);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*-10] (q1);
[b$1*10] (p2);
[c$1*10] (p3);
[d$1*-10] (q4);
%cl#1%
[a$1*-10] (q1);
[b$1*-10] (q2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#2%
[a$1*10] (p1);
[b$1*-10] (q2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#3%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#4%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*10] (p3);
[d$1*-10] (q4);
%cl#5%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*10] (p3);
[d$1*10] (p4);
%cl#6%
[a$1*-10] (q1);
[b$1*10] (p2);
[c$1*-10] (q3);
[d$1*-10] (q4);
model constraint:
p1 = -q1;
p2 = -q2;
p3 = -q3;
p4 = -q4;
output: tech10;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -12916.633
Information Criteria
Number of Free Parameters 10
Akaike (AIC) 25853.266
Bayesian (BIC) 25920.843
Sample-Size Adjusted BIC 25889.065
(n* = (n + 2) / 24)
Entropy 0.665
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 20.806
Degrees of Freedom 5
P-Value 0.0009
Likelihood Ratio Chi-Square
Value 18.534
Degrees of Freedom 5
P-Value 0.0023
RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS
Response Frequency Standard Chi-square Contribution
Pattern Observed Estimated Residual Pearson Loglikelihood Deleted
1 1138.00 1130.04 0.26 0.06 15.98
2 1532.00 1539.78 0.23 0.04 -15.52
3 502.00 500.24 0.08 0.01 3.52
4 1354.00 1354.60 0.02 0.00 -1.20
5 75.00 74.04 0.11 0.01 1.93
6 200.00 208.66 0.61 0.36 -16.96
7 198.00 198.53 0.04 0.00 -1.07
8 852.00 845.10 0.25 0.06 13.85
9 13.00 22.50 2.01 4.01 -14.27
10 43.00 32.36 1.87 3.50 24.44
11 9.00 10.78 0.54 0.29 -3.25
12 37.00 36.70 0.05 0.00 0.60
13 15.00 6.61 3.27 10.66 24.60
14 59.00 61.00 0.26 0.07 -3.93
15 23.00 30.25 1.32 1.74 -12.61
16 309.00 307.79 0.07 0.00 2.43
Table 5.2 on page 70 based on model III in the previous example. We will only display the relevant part of the output from the previous Mplus run.
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 1321.35246 0.20779
2 1702.89005 0.26779
3 1444.95636 0.22723
4 1077.81020 0.16949
5 400.30746 0.06295
6 260.16087 0.04091
7 151.52261 0.02383
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.917 0.015 61.663
Category 2 0.083 0.015 5.577
B
Category 1 0.837 0.013 63.040
Category 2 0.163 0.013 12.317
C
Category 1 0.967 0.008 123.853
Category 2 0.033 0.008 4.229
D
Category 1 0.981 0.002 444.472
Category 2 0.019 0.002 8.782
Table 5.3 on page 71 based on model III in the previous example. We use the SAVEDATA command of Mplus to save the posterior class probabilities along with the most likely class for each individual. The first five columns are manifest variables and their frequencies. The next seven columns are posterior probabilities for each class. Based on the posterior probabilities, the classification is determined. The modal posterior probabilities is the maximum of the seven probabilities.
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table5_1.dat ;
Variable:
Names are
a b c d freq;
Missing are all (-9999) ;
categorical are a b c d;
weight is freq (freq);
classes = cl(7);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*-10] (q1);
[b$1*10] (p2);
[c$1*10] (p3);
[d$1*-10] (q4);
%cl#1%
[a$1*-10] (q1);
[b$1*-10] (q2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#2%
[a$1*10] (p1);
[b$1*-10] (q2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#3%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*-10] (q3);
[d$1*-10] (q4);
%cl#4%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*10] (p3);
[d$1*-10] (q4);
%cl#5%
[a$1*10] (p1);
[b$1*10] (p2);
[c$1*10] (p3);
[d$1*10] (p4);
%cl#6%
[a$1*-10] (q1);
[b$1*10] (p2);
[c$1*-10] (q3);
[d$1*-10] (q4);
model constraint:
p1 = -q1;
p2 = -q2;
p3 = -q3;
p4 = -q4;
output: tech10;
savedata:
file is table5_3.dat;
save = cprob;
0.000 0.000 0.000 0.000 1138.000 0.851 0.099 0.016 0.000 0.000 0.033 0.001 1.000
1.000 0.000 0.000 0.000 1532.000 0.056 0.805 0.133 0.003 0.000 0.002 0.000 2.000
0.000 1.000 0.000 0.000 502.000 0.375 0.044 0.190 0.005 0.000 0.378 0.008 6.000
1.000 1.000 0.000 0.000 1354.000 0.013 0.179 0.776 0.020 0.000 0.013 0.000 3.000
0.000 0.000 1.000 0.000 75.000 0.443 0.052 0.009 0.187 0.001 0.017 0.291 1.000
1.000 0.000 1.000 0.000 200.000 0.014 0.203 0.034 0.734 0.005 0.001 0.009 4.000
0.000 1.000 1.000 0.000 198.000 0.032 0.004 0.016 0.357 0.003 0.033 0.555 7.000
1.000 1.000 1.000 0.000 852.000 0.001 0.010 0.042 0.928 0.007 0.001 0.012 4.000
0.000 0.000 0.000 1.000 13.000 0.844 0.098 0.016 0.000 0.008 0.032 0.001 1.000
1.000 0.000 0.000 1.000 43.000 0.053 0.756 0.125 0.003 0.060 0.002 0.000 2.000
0.000 1.000 0.000 1.000 9.000 0.344 0.040 0.174 0.004 0.083 0.347 0.007 6.000
1.000 1.000 0.000 1.000 37.000 0.009 0.130 0.566 0.014 0.271 0.009 0.000 3.000
0.000 0.000 1.000 1.000 15.000 0.098 0.011 0.002 0.041 0.779 0.004 0.064 5.000
1.000 0.000 1.000 1.000 59.000 0.001 0.014 0.002 0.050 0.933 0.000 0.001 5.000
0.000 1.000 1.000 1.000 23.000 0.004 0.000 0.002 0.046 0.871 0.004 0.072 5.000
1.000 1.000 1.000 1.000 309.000 0.000 0.001 0.002 0.050 0.946 0.000 0.001 5.000
Table 6. 2 on page 76 using https://stats.idre.ucla.edu/wp-content/uploads/2016/02/table6_1_g-1.dat, https://stats.idre.ucla.edu/wp-content/uploads/2016/02/table6_1_f-1.dat and https://stats.idre.ucla.edu/wp-content/uploads/2016/02/table6_1_m-1.dat.
Model I: Combined group analysis
Data:
File is c:daytontable6_1_g.dat ;
Variable:
Names are
a b c d g freq;
Missing are all (-9999) ;
usevariables are a b c d g freq;
weight is freq (freq);
categorical are a b c d g;
classes =x(2);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*-10 b$1*-10 c$1*-10 d$1*-10];
[g$1] (1);
%x#1%
[g$1] (1);
TESTS OF MODEL FIT
Loglikelihood
H0 Value -653.101
Information Criteria
Number of Free Parameters 10
Akaike (AIC) 1326.202
Bayesian (BIC) 1363.791
Sample-Size Adjusted BIC 1332.074
(n* = (n + 2) / 24)
Entropy 0.736
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 24.868
Degrees of Freedom 21
P-Value 0.2529
Likelihood Ratio Chi-Square
Value 28.887
Degrees of Freedom 21
P-Value 0.1167
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 264.93321 0.83575
2 52.06679 0.16425
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.984 0.029 34.408
Category 2 0.016 0.029 0.574
B
Category 1 0.976 0.031 31.767
Category 2 0.024 0.031 0.784
C
Category 1 0.963 0.016 61.892
Category 2 0.037 0.016 2.385
D
Category 1 0.817 0.027 30.566
Category 2 0.183 0.027 6.829
G
Category 1 0.432 0.028 15.533
Category 2 0.568 0.028 20.408
Latent Class 2
A
Category 1 0.431 0.172 2.507
Category 2 0.569 0.172 3.316
B
Category 1 0.412 0.169 2.443
Category 2 0.588 0.169 3.487
C
Category 1 0.785 0.089 8.793
Category 2 0.215 0.089 2.402
D
Category 1 0.623 0.108 5.761
Category 2 0.377 0.108 3.482
G
Category 1 0.432 0.028 15.533
Category 2 0.568 0.028 20.408
Model II: Analysis on female group
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table6_1_f-1.dat ;
Variable:
Names are
a b c d freq;
Missing are all (-9999) ;
usevariables are a b c d freq;
weight is freq (freq);
categorical are a b c d ;
classes =x(2);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*-10 b$1*-10 c$1*-10 d$1*-10];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -273.207
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 564.415
Bayesian (BIC) 593.151
Sample-Size Adjusted BIC 564.648
(n* = (n + 2) / 24)
Entropy 0.761
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 7.300
Degrees of Freedom 6
P-Value 0.2940
Likelihood Ratio Chi-Square
Value 8.660
Degrees of Freedom 6
P-Value 0.1936
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 26.27241 0.14596
2 153.72759 0.85404
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.356 0.301 1.183
Category 2 0.644 0.301 2.144
B
Category 1 0.307 0.259 1.185
Category 2 0.693 0.259 2.671
C
Category 1 0.812 0.120 6.766
Category 2 0.188 0.120 1.564
D
Category 1 0.625 0.147 4.241
Category 2 0.375 0.147 2.544
Latent Class 2
A
Category 1 0.980 0.043 22.900
Category 2 0.020 0.043 0.467
B
Category 1 0.936 0.053 17.775
Category 2 0.064 0.053 1.210
C
Category 1 0.941 0.021 44.072
Category 2 0.059 0.021 2.762
D
Category 1 0.791 0.035 22.358
Category 2 0.209 0.035 5.912
Model III: Analysis on male group
Data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table6_1_m-1.dat ;
Variable:
Names are
a b c d freq;
Missing are all (-9999) ;
usevariables are a b c d freq;
weight is freq (freq);
categorical are a b c d ;
classes =x(2);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*-10 b$1*-10 c$1*-10 d$1*-10];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -156.177
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 330.354
Bayesian (BIC) 356.634
Sample-Size Adjusted BIC 328.162
(n* = (n + 2) / 24)
Entropy 0.797
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 5.526
Degrees of Freedom 6
P-Value 0.4784
Likelihood Ratio Chi-Square
Value 6.398
Degrees of Freedom 6
P-Value 0.3801
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 117.08534 0.85464
2 19.91466 0.14536
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 0.977 0.027 36.663
Category 2 0.023 0.027 0.846
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 0.994 0.022 45.732
Category 2 0.006 0.022 0.259
D
Category 1 0.855 0.039 21.915
Category 2 0.145 0.039 3.710
Latent Class 2
A
Category 1 0.430 0.206 2.087
Category 2 0.570 0.206 2.771
B
Category 1 0.548 0.197 2.776
Category 2 0.452 0.197 2.289
C
Category 1 0.682 0.129 5.293
Category 2 0.318 0.129 2.472
D
Category 1 0.546 0.148 3.686
Category 2 0.454 0.148 3.069
Table 6.4 on page 80 using spatial data, https://stats.idre.ucla.edu/wp-content/uploads/2016/02/table6_3-1.dat, https://stats.idre.ucla.edu/wp-content/uploads/2016/02/table6_3_f-1.dat and https://stats.idre.ucla.edu/wp-content/uploads/2016/02/table6_3_m-1.dat.
Model I: analysis on male group
data:
File is c:daytonhttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/table6_3_m-1.dat ;
Variable:
Names are
a b c freq;
Missing are all (-9999) ;
usevariables are a b c freq;
weight is freq (freq);
categorical are a b c ;
classes =x(4);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*-10] (2);
[b$1*-10] (2);
[c$1*-10] (2);
%x#1%
[a$1*10] (1);
[b$1*10] (1);
[c$1*10] (1);
%x#2%
[a$1*10] (2);
[b$1*-10] (1);
[c$1*-10] (1);
%x#3%
[a$1*10] (2);
[b$1*10] (2);
[c$1*-10] (1);
TESTS OF MODEL FIT
Loglikelihood
H0 Value -360.823
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 731.647
Bayesian (BIC) 749.564
Sample-Size Adjusted BIC 733.712
(n* = (n + 2) / 24)
Entropy 0.935
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 2.837
Degrees of Freedom 2
P-Value 0.2420
Likelihood Ratio Chi-Square
Value 4.436
Degrees of Freedom 2
P-Value 0.1089
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 80.66675 0.30326
2 42.00001 0.15789
3 112.42420 0.42265
4 30.90904 0.11620
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 2
A
Category 1 0.029 0.013 2.258
Category 2 0.971 0.013 74.503
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 3
A
Category 1 0.029 0.013 2.258
Category 2 0.971 0.013 74.503
B
Category 1 0.029 0.013 2.258
Category 2 0.971 0.013 74.503
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 4
A
Category 1 0.029 0.013 2.258
Category 2 0.971 0.013 74.503
B
Category 1 0.029 0.013 2.258
Category 2 0.971 0.013 74.503
C
Category 1 0.029 0.013 2.258
Category 2 0.971 0.013 74.503
Model II: analysis on female group
data:
File is c:daytontable6_3_f.dat ;
Variable:
Names are
a b c freq;
Missing are all (-9999) ;
usevariables are a b c freq;
weight is freq (freq);
categorical are a b c ;
classes =x(4);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*-10] (2);
[b$1*-10] (2);
[c$1*-10] (2);
%x#1%
[a$1*10] (1);
[b$1*10] (1);
[c$1*10] (1);
%x#2%
[a$1*10] (2);
[b$1*-10] (1);
[c$1*-10] (1);
%x#3%
[a$1*10] (2);
[b$1*10] (2);
[c$1*-10] (1);
TESTS OF MODEL FIT
Loglikelihood
H0 Value -378.816
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 767.631
Bayesian (BIC) 786.266
Sample-Size Adjusted BIC 770.408
(n* = (n + 2) / 24)
Entropy 0.977
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 1.667
Degrees of Freedom 2
P-Value 0.4345
Likelihood Ratio Chi-Square
Value 1.595
Degrees of Freedom 2
P-Value 0.4504
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 87.74567 0.28582
2 27.93863 0.09101
3 150.96490 0.49174
4 40.35080 0.13144
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 2
A
Category 1 0.009 0.006 1.424
Category 2 0.991 0.006 162.391
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 3
A
Category 1 0.009 0.006 1.424
Category 2 0.991 0.006 162.391
B
Category 1 0.009 0.006 1.424
Category 2 0.991 0.006 162.391
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
Latent Class 4
A
Category 1 0.009 0.006 1.424
Category 2 0.991 0.006 162.391
B
Category 1 0.009 0.006 1.424
Category 2 0.991 0.006 162.391
C
Category 1 0.009 0.006 1.424
Category 2 0.991 0.006 162.391
Model III: Combined analysis. The results here are a little off here, especially the p-value.
data:
File is c:daytontable6_3.dat ;
Variable:
Names are
a b c g freq;
Missing are all (-9999) ;
usevariables are a b c g freq;
weight is freq (freq);
categorical are a b c g;
classes =x(4);
Analysis:
Type = mixture ;
model:
%overall%
[a$1*-10] (2);
[b$1*-10] (2);
[c$1*-10] (2);
[g$1@0];
%x#1%
[a$1*10] (1);
[b$1*10] (1);
[c$1*10] (1);
%x#2%
[a$1*10] (2);
[b$1*-10] (1);
[c$1*-10] (1);
%x#3%
[a$1*10] (2);
[b$1*10] (2);
[c$1*-10] (1);
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -1142.027
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 2294.054
Bayesian (BIC) 2315.808
Sample-Size Adjusted BIC 2299.936
(n* = (n + 2) / 24)
Entropy 0.959
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 18.179
Degrees of Freedom 10
P-Value 0.0520
Likelihood Ratio Chi-Square
Value 19.396
Degrees of Freedom 10
P-Value 0.0355
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 168.69989 0.29442
2 69.66925 0.12159
3 263.38416 0.45966
4 71.24670 0.12434
RESULTS IN PROBABILITY SCALE
Latent Class 1
A
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
G
Category 1 0.500 0.000 0.000
Category 2 0.500 0.000 0.000
Latent Class 2
A
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
B
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
G
Category 1 0.500 0.000 0.000
Category 2 0.500 0.000 0.000
Latent Class 3
A
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
B
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
C
Category 1 1.000 0.000 0.000
Category 2 0.000 0.000 0.000
G
Category 1 0.500 0.000 0.000
Category 2 0.500 0.000 0.000
Latent Class 4
A
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
B
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
C
Category 1 0.017 0.007 2.668
Category 2 0.983 0.007 149.771
G
Category 1 0.500 0.000 0.000
Category 2 0.500 0.000 0.000