11.2 Prevention of faulty teeth in children: Modeling overdispersion
Table 11.2 on page 352 using dfmt.dat data.
Model 1: Poisson Model
Data: File is c:genlathttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/dmft.dat ; Variable: Names are dmft1 y male ethnic school educ all1 s3 enrich rinse hygiene eth1 white black; Missing are all (-9999) ; usevar are y educ enrich rinse hygiene all1 male white black; count is y; Analysis: estimator = ml; model: y on educ enrich rinse hygiene all1 male white black;
TESTS OF MODEL FIT Loglikelihood H0 Value -1469.046 Information Criteria Number of Free Parameters 9 Akaike (AIC) 2956.092 Bayesian (BIC) 2998.220 Sample-Size Adjusted BIC 2969.640 (n* = (n + 2) / 24) MODEL RESULTS Estimates S.E. Est./S.E. Y ON EDUC -0.233 0.087 -2.662 ENRICH -0.089 0.082 -1.093 RINSE -0.349 0.084 -4.139 HYGIENE -0.299 0.089 -3.361 ALL1 -0.588 0.096 -6.136 MALE 0.131 0.053 2.483 WHITE 0.099 0.058 1.717 BLACK -0.138 0.087 -1.591 Intercepts Y 0.759 0.072 10.583
Model 2: Normal Intercept
Data: File is c:genlathttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/dmft.dat ; Variable: Names are dmft1 y male ethnic school educ all1 s3 enrich rinse hygiene eth1 white black; Missing are all (-9999) ; usevar are y educ enrich rinse hygiene all1 male white black; count is y; Analysis: type = random; estimator = ml; model: i | y ; i on educ enrich rinse hygiene all1 male white black;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -1432.534
Information Criteria
Number of Free Parameters 10 Akaike (AIC) 2885.068 Bayesian (BIC) 2931.876 Sample-Size Adjusted BIC 2900.121 (n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
I | Y 1.000 0.000 0.000
I ON EDUC -0.229 0.113 -2.033 ENRICH -0.092 0.107 -0.855 RINSE -0.367 0.108 -3.398 HYGIENE -0.318 0.115 -2.773 ALL1 -0.607 0.119 -5.091 MALE 0.132 0.067 1.985 WHITE 0.098 0.073 1.341 BLACK -0.155 0.109 -1.424
Intercepts I 0.629 0.095 6.630 Y 0.000 0.000 0.000
Residual Variances I 0.288 0.048 6.054
Model 3: Two-class Intercept
Data: File is c:genlathttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/dmft.dat ; Variable: Names are dmft1 y male ethnic school educ all1 s3 enrich rinse hygiene eth1 white black; Missing are all (-9999) ; usevar are y educ enrich rinse hygiene all1 male white black; count is y; classes = c(2); Analysis: type = mixture; estimator = ml; model: %overall% y on educ enrich rinse hygiene all1 male white black; [y]; %c#1% [y];TESTS OF MODEL FIT Loglikelihood H0 Value -1406.032 Information Criteria Number of Free Parameters 11 Akaike (AIC) 2834.064 Bayesian (BIC) 2885.553 Sample-Size Adjusted BIC 2850.622 (n* = (n + 2) / 24) Entropy 0.539 MODEL RESULTS Estimates S.E. Est./S.E. Latent Class 1 Y ON EDUC -0.240 0.101 -2.383 ENRICH -0.080 0.095 -0.839 RINSE -0.260 0.100 -2.607 HYGIENE -0.222 0.106 -2.094 ALL1 -0.493 0.113 -4.364 MALE 0.104 0.061 1.694 WHITE 0.089 0.067 1.320 BLACK -0.116 0.102 -1.136 Intercepts Y 1.035 0.090 11.497 Latent Class 2 Y ON EDUC -0.240 0.101 -2.383 ENRICH -0.080 0.095 -0.839 RINSE -0.260 0.100 -2.607 HYGIENE -0.222 0.106 -2.094 ALL1 -0.493 0.113 -4.364 MALE 0.104 0.061 1.694 WHITE 0.089 0.067 1.320 BLACK -0.116 0.102 -1.136 Intercepts Y -1.108 0.372 -2.982 Categorical Latent Variables Means C#1 0.861 0.206 4.177
Model 4: ZIP
Data: File is c:genlathttps://stats.idre.ucla.edu/wp-content/uploads/2016/02/dmft.dat ; Variable: Names are dmft1 y male ethnic school educ all1 s3 enrich rinse hygiene eth1 white black; Missing are all (-9999) ; usevar are y educ enrich rinse hygiene all1 male white black; count is y (i); Analysis: estimator = ml; model: y on educ enrich rinse hygiene all1 male white black; [y#1];TESTS OF MODEL FITLoglikelihoodH0 Value -1410.270Information CriteriaNumber of Free Parameters 10 Akaike (AIC) 2840.541 Bayesian (BIC) 2887.349 Sample-Size Adjusted BIC 2855.594 (n* = (n + 2) / 24)MODEL RESULTSEstimates S.E. Est./S.E.Y ON EDUC -0.222 0.093 -2.382 ENRICH -0.064 0.087 -0.736 RINSE -0.223 0.094 -2.374 HYGIENE -0.226 0.097 -2.318 ALL1 -0.470 0.108 -4.355 MALE 0.098 0.058 1.692 WHITE 0.084 0.063 1.329 BLACK -0.117 0.096 -1.222Means Y#1 -1.395 0.122 -11.404Intercepts Y 0.943 0.078 12.128
Table 11.4 on page 354 modeling the same data as binomial logistic regression models.