discrete data model classification

Hi,

I am interested in the classification of discrete data models.

The classification below I came up with is strongly based on Agresti (2002), Dobson (2002) and Plan et al. (2009), the last one compares different count-data models as used in pharmacometrics.

There are probably much more complex classifications, not only restricted to GLMs, out there but that's what I found out so far based on mentioned references.

Any comments, corrections and suggestions would be very appreciated.

Best Regards,
Maciej



1 Categorical data ? Logit models 

1.1 Binary response
1.1.1 Single explanatory variabel
e.g. Linear probability model, Logistic regression model 
1.1.2 Multiple explanatory variabels
e.g. General logistic regression model 

1.2 Multi-category response
1.2.1 Nominal response variables 
e.g. Reference category logit model
1.2.2 Ordinal response variables ? cumulative logit 
e.g. Cumulative logit model, Proportional odds model, Adjacent category logit model, Continuation ratio logit model 
1.2.3 Ordinal response variables ? cumulative link

2 Categorical data ? other models 
e.g. Probit model, Log-log model 

3 Count data
e.g. Poisson model, Poisson model with Markovian elements, Poisson model with mixture distribution, Negative Binomial model, Zero inflated model, Generalized Poisson model

4 Time-to-event
? Proportional hazard model, Weibull model



Agresti, A. (2002). Categorical data analysis. Wiley-Interscience, New York, 2nd ed edition.
Dobson, A. J. (2002). An introduction to generalized linear models. Chapman & Hall/CRC texts in statistical science	8 series. Chapman & Hall/CRC, Boca Raton, 2nd ed edition.
Plan, E. L., Maloney, A., Troc?niz, I. F., and Karlsson, M. O. (2009). Performance in population models for count	15 data, part i: maximum likelihood approximations. J Pharmacokinet Pharmacodyn, 36(4):353?66.