# 5 Discrete Response Models

This section is based on (Agresti 2018) and (Afifi, May, and Clark 2011).

In the previous chapters we have primarily focused on econometric models for continuous data, like price, output, wage, expenditure and other quantities. However, microeconometrics also encompass a general theory of choice, where choices cannot be measured by a continuous response variable:

• If a choice is between two outcomes - it can be expressed as a binary variable, with value “1” usually indicating one choice and “0” - indicating the alternative choice. The choices can either be an active choice, when a person can control the outcome themselves (i.e. choose one of the outcomes), or a consequence, which is a result of various factors (which we may be interested in determining). Examples include: - Buying a product (action) or not buying (inaction); - Smoking (action) or nonsmoking (inaction); - Defaulting on a loan or not defaulting on a loan (consequence); - Having cancer or not having cancer (consequence);

• If a choice is between multiple outcomes - each outcome can be assigned a number. Examples include: - Choosing from multiple brands of milk; - Choosing a career; - Rating a movie/hotel/shop/etc.;

• Finally, discrete response models also encompass count data response variables, these include: - the number of children at a school; - the number of insurance claims in a construction company; - the number of car accidents; - the number of crimes, committed in a city;

We note that the aforementioned cases with two or more outcomes are usually referred to as classification models/algorithms. In this chapter, we will be focusing on estimation and inference for these discrete response models.

### References

Afifi, A., S. May, and V. A. Clark. 2011. Practical Multivariate Analysis, Fifth Edition. Chapman & Hall/Crc Texts in Statistical Science. Taylor & Francis. https://books.google.lt/books?id=W95M2rT31VUC.

Agresti, A. 2018. An Introduction to Categorical Data Analysis. Wiley Series in Probability and Statistics. Wiley. https://books.google.lt/books?id=onZyDwAAQBAJ.