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3 - Regression with Categorical Dependent Variables

from II - Predictive Modeling Foundations

Published online by Cambridge University Press:  05 August 2014

By
Montserrat Guillén
Edited by
Edward W. Frees ,
Richard A. Derrig  and
Glenn Meyers
Montserrat Guillén
Affiliation:
University of Barcelona
Edward W. Frees
Affiliation:
University of Wisconsin, Madison
Richard A. Derrig
Affiliation:
Temple University, Philadelphia
Glenn Meyers
Affiliation:
ISO Innovative Analytics, New Jersey
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Summary

Chapter Preview. This chapter presents regression models where the dependent variable is categorical, whereas covariates can either be categorical or continuous. In the first part binary dependent variable models are presented, and the second part is aimed at covering general categorical dependent variable models, where the dependent variable has more than two outcomes. This chapter is illustrated with datasets, inspired by real-life situations. It also provides the corresponding R programs for estimation, which are based on R packages glm and mlogit. The same output can be obtained when using SAS or similar software programs for estimating the models presented in this chapter.

Coding Categorical Variables

Categorical variables measure qualitative traits; in other words, they evaluate concepts that can be expressed in words. Table 3.1 presents examples of variables that are measured in a categorical scale and are often found in insurance companies databases. These variables are also called risk factors when they denote characteristics that are associated with losses.

Categorical variables must have mutually exclusive outcomes. The number of categories is the number of possible response levels. For example, if we focus on insurance policies, we can have a variable such as TYPE OF POLICY CHOSEN with as many categories as the number of possible choices for the contracts offered to the customer.

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Predictive Modeling Applications in Actuarial Science , pp. 65 - 86
Publisher: Cambridge University Press
Print publication year: 2014

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References

Artis, M., Ayuso, M., and Guillén, M. (1999). Modelling Different Types of Automobile Insurance Fraud Behaviour in the Spanish Market, 24(1), 67–81.
Cameron, A. C. and P. K., Trivedi (2005). Microeconometrics: Methods and Applications. Cambridge University Press, New York.CrossRefGoogle Scholar
Frees, E. W. (2010). Regression Modeling with Actuarial and Financial Applications. Cambridge University Press, New York.Google Scholar
Greene, W. H. (2011). Econometric Analysis (7th ed.). Prentice Hall, New York.Google Scholar
Hilbe, J. M. (2009). Logistic Regression Models. CRC Press, Chapman & Hall. Boca Raton, FL.Google Scholar
Hosmer, D. W. and S., Lemeshow (2000). Applied Logistic Regression (2nd ed.). John Wiley & Sons, New York.CrossRefGoogle Scholar
Long, J. S. (1997). Regression Models of Categorical and Limited Dependent Variables. Sage, Thousand Oaks, CA.Google Scholar
McFadden, D. (1974). The Measurement of Urban Travel Demand. Journal of Public Economics, 3(4), 303–328.

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