AN INTRODUCTION TO GENERALIZED LINEAR MODELS

1. Why Generalized Linear Models are "Useful"

Advances in computing technology and combined with the development of 
statistical theory into applications offer many more choices for data 
analysis today programs than existed even a few years ago. Researchers 
are now in the position to make informed decisions about which 
particular technique to apply. However, the fundamental steps to data 
analysis remain unchanged:

1. State hypothesis based on your research objects
2. Develop a statistical design to collect data
3. Conceptualize a model based on your design and hypothesis
4. Estimate parameters for this model from sample data
5. Test your hypothesis for significance 

The industrial statistician George Box, perhaps best known for his books 
on time series and experimental design, once wrote, "All models are 
wrong, but some models are useful" (Box, 1979). Reflecting on item #3 
above, I would also add to that statement "some models are more useful 
than others" and even more to the point, "some models are more 
appropriate than others."

One of the potential weaknesses of any statistical model is accepting 
the output at face value without a review of the assumptions that form 
the foundation of it. Just because SAS (or any other program) produced 
results doesn't mean it is necessarily correct or the best technique you 
could utilize. The premise is that one should always be able to 
understand and be able to explain the technique applied; however, the 
tradeoff is that you should not ignore the "appropriateness" of the 
model compared with other possibilities.


Analysis of Data from non-normal Distributions as if they were Normal

One of the seven "problematic" areas in statistical analysis summarized 
at

http://www.uoregon.edu/~robinh/seven_prblms.txt

is closely connected with another problematic area, "Indiscriminant 
Application of Regression and Analysis of Variance", that is, techniques 
based on the normal distribution of the residuals for inference. Failure 
to select an appropriate model based on the distributional assumptions of 
the data is the real concern. That is data are not necessarily "normally" 
distributed over an "infinite" range with "constant" variance.  Response 
data, whether they are dichotomous, ordinal, counts, proportions, certain 
types of continuous measurements, or data in general whether they follow 
the normal or some other distribution are more appropriately analyzed 
under the terminology of generalized linear models.

A simple example to be explained in Section 6 concerns the computation 
of an odds ratio which is a convenient way to summarize dichotomous, 
ordinal, and multinomial data along with a mixture of categorical or 
continuous covariaties. If you have collected only one observation for 
each subject these techniques have been incorporated into PROC LOGISTIC. 
However, many types of generalized linear models can be analyzed with 
PROC GENMOD, including discrete data collected as repeated measures.