variable (affairs) counted the number of extramarital sexual intercourse experiences participants had in the past year. It’s likely that there’s a subgroup of faithful marital partners who would never have an affair, no matter how long the period of time studied. These are called structural zeros (primarily by the swingers in the group).

In such cases, you can analyze the data using an approach called zero-inflated Poisson regression. The approach fits two models simultaneously—one that predicts who would or would not have an affair, and the second that predicts how many affairs a participant would have if you excluded the permanently faithful. Think of this as a model that combines a logistic regression (for predicting structural zeros) and a Poisson regression model (that predicts counts for observations that aren’t structural zeros). Zero-inflated Poisson regression can be fit using the zeroinfl() function in the pscl package.

ROBUST POISSON REGRESSION

Finally, the glmRob() function in the robust package can be used to fit a robust generalized linear model, including robust Poisson regression. As mentioned previously, this can be helpful in the presence of outliers and influential observations.

Going further

Generalized linear models are a complex and mathematically sophisticated subject, but many fine resources are available for learning about them. A good, short introduction to the topic is Dunteman and Ho (2006). The classic (and advanced) text on generalized linear models is provided by McCullagh and Nelder (1989). Comprehensive and accessible presentations are provided by Dobson and Barnett (2008) and Fox (2008). Faraway (2006) and Fox (2002) provide excellent introductions within the context of R.

13.4 Summary

In this chapter, we used generalized linear models to expand the range of approaches available for helping you to understand your data. In particular, the framework allows you to analyze response variables that are decidedly non-normal, including categorical outcomes and discrete counts. After briefly describing the general approach, we focused on logistic regression (for analyzing a dichotomous outcome) and Poisson regression (for analyzing outcomes measured as counts or rates).

We also discussed the important topic of overdispersion, including how to detect it and how to adjust for it. Finally, we looked at some of the extensions and variations that are available in R.

Each of the statistical approaches covered so far has dealt with directly observed and recorded variables. In the next chapter, we’ll look at statistical models that deal with latent variables—unobserved, theoretical variables that you believe underlie and account for the behavior of the variables you do observe. In particular, you’ll see how you can use factor analytic methods to detect and test hypotheses about these unobserved variables.