Theoretical examples

Example 1 Suppose we want to examine the association between gender (x) and political views (y). Gender has the values 0=Man and 1=Woman, whereas political views has the values 1=Conservative, 2=Centre, and 3=Liberal. We choose Centre as the base outcome. Now, we get an RRR of 0.82 for Conservative, which means that women are less likely to be conservative than centre compared to men. The RRR for Liberal is 1.39, suggesting that women are more likely to be liberal than centre compared to men.

Example 2 Here we want to examine the association between having young children (x) and the type of pet owned (y). Having young children is measured as either 0=No young children and 1=Young children. Type of pet owned has the values 1=No pet, 2=Cat, 3=Dog, and 4=Other type of pet. The category No pet is chosen as the base outcome. Let us say that we get an RRR for Cat that is 1.50. This means that those who have young children are more likely to own a cat than no pet at all, compared to those who do not have young children. The RRR for Dog is 1.75, suggesting that those who have young children are more likely to own a dog than no pet at all, compared to those who do not have young children. Moreover, the RRR for Other type of pet is 1.96, which tells us that those who have young children are more likely to own another type of pet than no pet at all, compared to those who do not have young children.

Practical example

Dataset

StataData1.dta

Variable name	marstat40
Variable label	Marital status (Age 40, Year 2010)
Value labels	1=Married 2=Unmarried 3=Divorced 4=Widowed

Variable name	sex
Variable label	Sex
Value labels	0=Man 1=Woman

sum marstat40 sex if pop_multinom==1

mlogit marstat40 sex if pop_multinom==1, rrr b(1)

When we look at the results for sex, we see that the relative risk ratio (RRR) is 0.76 for Unmarried, 1.24 for Divorced, and 3.48 for Widowed. This means that women (who are coded as 1 and thus compared to men who are coded as 0), have a lower risk of being unmarried, but a higher risk of being a divorced or widowed, as compared to being married/having a registered partner.

There are statistically significant differences between Married and Unmarried, Married and Divorced, as well as Married and Widowed, according to sex – as reflected in the p-values (0.000) and the 95% confidence intervals (0.69-0.84, 1.11-1.39, and 2.06-5.90, respectively).

Summary At age 40, women are less likely than men to be unmarried (RRR=0.76, 95% CI=0.69-0.84) but more likely to be divorced (RRR=1.24, 95% CI=1.11-1.39) or widowed (RRR=3.48, 95% CI=2.06-5.90), in comparison to being married.