Ed231A

Multivariate Analysis

Latent Class & Mixture Models Using Latent Gold

2 & 3 Class Latent Class Models Using Latent Gold

File name: D:\latent_gold\hsb6a.sav
File size: 51508 bytes
File date: 2005-Aug-04 01:01:26 PM
LL BIC(LL) Npar Lē df p-value Class.Err.
Model6 2-Cluster -1677.2808 3424.9278 11 51.4380 20 0.00014 0.0436
Model7 3-Cluster -1661.2068 3431.1613 17 19.2900 14 0.15 0.1537
Model8

Model6 - Lē = 51.4380

2-Cluster Model
Number of cases 600
Number of parameters (Npar) 11
Random Seed 170911
Best Start Seed 2170057
Chi-squared Statistics
Degrees of freedom (df) 20 p-value
L-squared (Lē) 51.4380 0.00014
X-squared 53.9846 5.8e-5
Cressie-Read 52.7624 8.8e-5
BIC (based on Lē) -76.5006
AIC (based on Lē) 11.4380
AIC3 (based on Lē) -8.5620
CAIC (based on Lē) -96.5006
Dissimilarity Index 0.1160
Log-likelihood Statistics
Log-likelihood (LL) -1677.2808
Log-prior -5.6096
Log-posterior -1682.8904
BIC (based on LL) 3424.9278
AIC (based on LL) 3376.5616
AIC3 (based on LL) 3387.5616
CAIC (based on LL) 3435.9278
Classification Statistics Clusters
Classification errors 0.0436
Reduction of errors (Lambda) 0.9027
Entropy R-squared 0.8256
Standard R-squared 0.8589
Classification log-likelihood -1749.2245
AWE 3672.1815
Classification Table Modal
Probabilistic Cluster1 Cluster2 Total
Cluster1 319.5904 11.7230 331.3134
Cluster2 14.4096 254.2770 268.6866
Total 334.0000 266.0000 600.0000
Files
Response D:\latent_gold\hsb6a.sav

Parameters

Models for Indicators
Cluster1 Cluster2 Wald p-value Rē
hiread
0 -1.0193 1.0193 152.6336 4.6e-35 0.5847
1 1.0193 -1.0193
hiwrite
0 -0.7380 0.7380 147.3200 6.7e-34 0.3923
1 0.7380 -0.7380
himath
0 -0.8045 0.8045 148.1552 4.4e-34 0.4306
1 0.8045 -0.8045
hisci
0 -0.8311 0.8311 150.5488 1.3e-34 0.4596
1 0.8311 -0.8311
hiss
0 -0.6436 0.6436 116.0746 4.6e-27 0.2933
1 0.6436 -0.6436
Intercepts Overall Wald p-value
hiread
0 0.0735 0.7134 0.40
1 -0.0735
hiwrite
0 -0.0241 0.1563 0.69
1 0.0241
himath
0 0.1354 4.0706 0.044
1 -0.1354
hisci
0 0.0328 0.2262 0.63
1 -0.0328
hiss
0 -0.3586 36.9240 1.2e-9
1 0.3586
Model for Clusters
Intercept Cluster1 Cluster2 Wald p-value
0.1046 -0.1046 4.2413 0.039

Loadings

Loadings Clusters Rē
hiread 0.7647 0.5847
hiwrite 0.6263 0.3923
himath 0.6562 0.4306
hisci 0.6779 0.4596
hiss 0.5416 0.2933

Profile

Cluster1 Cluster2
Cluster Size 0.5521 0.4479
Indicators
hiread
0 0.1311 0.8990
1 0.8689 0.1010
hiwrite
0 0.1788 0.8066
1 0.8212 0.1934
himath
0 0.2078 0.8676
1 0.7922 0.1324
hisci
0 0.1685 0.8491
1 0.8315 0.1509
hiss
0 0.1188 0.6388
1 0.8812 0.3612

ProbMeans

Cluster1 Cluster2
Overall 0.5521 0.4479
Indicators
hiread
0 0.1517 0.8483
1 0.9145 0.0855
hiwrite
0 0.2141 0.7859
1 0.8401 0.1599
himath
0 0.2275 0.7725
1 0.8812 0.1188
hisci
0 0.1959 0.8041
1 0.8723 0.1277
hiss
0 0.1859 0.8141
1 0.7508 0.2492

Bivariate Residuals

Indicators hiread hiwrite himath hisci hiss
hiread .
hiwrite 0.0554 .
himath 0.0024 3.6039 .
hisci 1.0735 0.1496 0.9450 .
hiss 0.4397 3.6543 0.0013 0.0096 .

Model7 - Lē = 19.2900

3-Cluster Model
Number of cases 600
Number of parameters (Npar) 17
Random Seed 170911
Best Start Seed 1932825
Chi-squared Statistics
Degrees of freedom (df) 14 p-value
L-squared (Lē) 19.2900 0.15
X-squared 18.2428 0.20
Cressie-Read 18.4894 0.18
BIC (based on Lē) -70.2670
AIC (based on Lē) -8.7100
AIC3 (based on Lē) -22.7100
CAIC (based on Lē) -84.2670
Dissimilarity Index 0.0532
Log-likelihood Statistics
Log-likelihood (LL) -1661.2068
Log-prior -6.5071
Log-posterior -1667.7139
BIC (based on LL) 3431.1613
AIC (based on LL) 3356.4135
AIC3 (based on LL) 3373.4135
CAIC (based on LL) 3448.1613
Classification Statistics Clusters
Classification errors 0.1537
Reduction of errors (Lambda) 0.7587
Entropy R-squared 0.6577
Standard R-squared 0.6625
Classification log-likelihood -1886.1174
AWE 4040.7304
Classification Table Modal
Probabilistic Cluster1 Cluster2 Cluster3 Total
Cluster1 205.6318 0.1269 12.0658 217.8245
Cluster2 0.2884 179.0310 24.8007 204.1202
Cluster3 23.0797 31.8421 123.1335 178.0553
Total 229.0000 211.0000 160.0000 600.0000
Files
Response D:\latent_gold\hsb6a.sav

Parameters

Models for Indicators
Cluster1 Cluster2 Cluster3 Wald p-value Rē
hiread
0 1.5740 -1.3597 -0.2143 48.7013 2.7e-11 0.5875
1 -1.5740 1.3597 0.2143
hiwrite
0 1.1415 -1.5063 0.3648 13.4425 0.0012 0.4630
1 -1.1415 1.5063 -0.3648
himath
0 1.1387 -1.1921 0.0535 41.0728 1.2e-9 0.4741
1 -1.1387 1.1921 -0.0535
hisci
0 1.3280 -0.9006 -0.4274 59.1238 1.5e-13 0.4984
1 -1.3280 0.9006 0.4274
hiss
0 0.8542 -0.8655 0.0114 51.3733 7.0e-12 0.3008
1 -0.8542 0.8655 -0.0114
Intercepts Overall Wald p-value
hiread
0 -0.0537 0.0825 0.77
1 0.0537
hiwrite
0 -0.3495 1.0623 0.30
1 0.3495
himath
0 -0.0417 0.0667 0.80
1 0.0417
hisci
0 -0.0104 0.0066 0.94
1 0.0104
hiss
0 -0.4796 20.5861 5.7e-6
1 0.4796
Model for Clusters
Intercept Cluster1 Cluster2 Cluster3 Wald p-value
0.0887 0.0238 -0.1125 0.7626 0.68

Loadings

Loadings Clusters Rē
hiread 0.7665 0.5875
hiwrite 0.6805 0.4630
himath 0.6886 0.4741
hisci 0.7060 0.4984
hiss 0.5485 0.3008

Profile

Cluster1 Cluster2 Cluster3
Cluster Size 0.3630 0.3402 0.2968
Indicators
hiread
0 0.9544 0.0559 0.3691
1 0.0456 0.9441 0.6309
hiwrite
0 0.8298 0.0239 0.5077
1 0.1702 0.9761 0.4923
himath
0 0.8997 0.0782 0.5059
1 0.1003 0.9218 0.4941
hisci
0 0.9331 0.1392 0.2941
1 0.0669 0.8608 0.7059
hiss
0 0.6790 0.0635 0.2816
1 0.3210 0.9365 0.7184

ProbMeans

Cluster1 Cluster2 Cluster3
Overall 0.3630 0.3402 0.2968
Indicators
hiread
0 0.7299 0.0395 0.2305
1 0.0310 0.6122 0.3568
hiwrite
0 0.6552 0.0171 0.3276
1 0.1140 0.6154 0.2706
himath
0 0.6493 0.0524 0.2983
1 0.0729 0.6319 0.2953
hisci
0 0.7162 0.0996 0.1842
1 0.0456 0.5563 0.3980
hiss
0 0.7014 0.0610 0.2376
1 0.1795 0.4916 0.3289

Bivariate Residuals

Indicators hiread hiwrite himath hisci hiss
hiread .
hiwrite 0.1815 .
himath 0.1933 0.1624 .
hisci 0.3348 0.5319 0.3757 .
hiss 0.2413 1.8988 0.2336 0.0949 .

Ed231A Page
UCLA Department of Education

Phil Ender, 24apr03