6. Multinomial Response Models

This section deals with regression models for discrete data with more than two response categories, where the assumption of a multinomial distribution is appropriate. We will consider multinomial logits for nominal data, and ordered logit models for ordinal data, with a brief mention of alternative-specific conditional logit models. We will also consider sequential logit models. (In line with the current syllabus we are skipping log-linear models for contingency tables, and thus their relationship with multinomial logit models.)

6.1 The Nature of Multinomial Data

We start by reading the data on contraceptive choice by age for currently married women in El Salvador, 1985, found in Table 6.1 of the lecture notes. The data are in “long” format with one row for each combination of predictor and response, showing the age group, method choice, and number of cases.

. use https://grodri.github.io/datasets/elsalvador1985, clear
(Contraceptive Use by Age. Currently Married Women. El Salvador, 1985)

. list, sep(3)

     ┌───────────────────────────────┐
     │  ageg            cuse   cases │
     ├───────────────────────────────┤
  1. │ 15-19   sterilization       3 │
  2. │ 15-19    other method      61 │
  3. │ 15-19       no method     232 │
     ├───────────────────────────────┤
  4. │ 20-24   sterilization      80 │
  5. │ 20-24    other method     137 │
  6. │ 20-24       no method     400 │
     ├───────────────────────────────┤
  7. │ 25-29   sterilization     216 │
  8. │ 25-29    other method     131 │
  9. │ 25-29       no method     301 │
     ├───────────────────────────────┤
 10. │ 30-34   sterilization     268 │
 11. │ 30-34    other method      76 │
 12. │ 30-34       no method     203 │
     ├───────────────────────────────┤
 13. │ 35-39   sterilization     197 │
 14. │ 35-39    other method      50 │
 15. │ 35-39       no method     188 │
     ├───────────────────────────────┤
 16. │ 40-44   sterilization     150 │
 17. │ 40-44    other method      24 │
 18. │ 40-44       no method     164 │
     ├───────────────────────────────┤
 19. │ 45-49   sterilization      91 │
 20. │ 45-49    other method      10 │
 21. │ 45-49       no method     183 │
     └───────────────────────────────┘

With only one predictor, this example affords limited opportunities for interpreting coefficients, but will allow us to focus on the outcome and the comparisons underlying each type of model.

Updated fall 2022