6 Multinomial Response Models in Stata

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 fill focus on three Stata commands, mlogit for multinomial logits, ologit for ordered logits, and oprobit for ordered probit models, with a brief mention of asclogit for alternative-specific conditional logit models. We will also have occassion to use an old friend, logit, for fitting 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, found in Table 6.1 of the lecture notes. We will read the 7 by 3 table as 21 observations and treat the counts as frequency weights:

. clear
 
. input ageg cuse cases
 
          ageg       cuse      cases
  1.     1   1     3
  2.     1   2    61
  3.     1   3   232
  4.     2   1    80
  5.     2   2   137
  6.     2   3   400
  7.     3   1   216
  8.     3   2   131
  9.     3   3   301
 10.     4   1   268
 11.     4   2    76
 12.     4   3   203
 13.     5   1   197
 14.     5   2    50
 15.     5   3   188
 16.     6   1   150
 17.     6   2    24
 18.     6   3   164
 19.     7   1    91
 20.     7   2    10
 21.     7   3   183
 22. end
 
. label define cuse 1 "sterilization" 2 "other method" 3 "no method"
 
. label values cuse cuse
 
. label define ageg 1 "15-19" 2 "20-24" 3 "25-29" 4 "30-34" 5 "35-39" ///
>         6 "40-44" 7 "45-49"
 
. label values ageg ageg

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.

Continue with The Multinomial Logit Model