Theoretical examples

Example 1 Suppose we want to examine the association between unemployment days (x) and type of health care visit (y). Unemployment days are measured as the total number of days in unemployment during a year, and ranges from 0 to 365. Type of health care visit has the values 1=No health care visit, 2=Out-patient care, and 3=In-patient care. We choose No health care visit as our base outcome. Let us say that we get an RRR for unemployment days and Out-patient care that is 2.88. That would mean that for every unit increase of employment days, the risk of experiencing out-patient care compared to having had no health care visit increases. Moreover, we get an RRR for unemployment days and In-patient care that is 4.02. This would suggest that for every unit increase of employment days, the risk of experiencing in-patient care compared to having had no health care visit increases.

Example 2 In another example, we examine the association between intelligence scores (x) and the preferred type of books (y). Intelligence scores are measured by a series of tests that render various amounts of points, and ranges between 20 and 160 points. Preferred type of books has the values 1=Fiction, 2=Non-fiction, 3=Comic books. We choose Fiction as our base outcome. Here, we get an RRR of 1.40 for intelligence scores and Non-fiction, meaning that for every unit increase of intelligence, the likelihood of preferring non-fiction books over fiction books increases. For intelligence scores and Comic books, the RRR is 0.92. This suggests that for every unit increase of intelligence, the likelihood of preferring comic books over fiction books decreases.

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	gpa
Variable label	Grade point average (Age 15, Year 1985)
Value labels	N/A

sum marstat40 gpa if pop_multinom==1

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

When we look at the results for gpa, we see that the relative risk ratio (RRR) is 0.72 for Unmarried, 0.72 for Divorced, and 1.19 for Widowed. This means that the higher the gpa, the lower the risk of being unmarried or divorced, but the higher the risk of being widowed, as compared to being married.

There are statistically significant differences between Married and Unmarried, and between Married and Divorced, according to gpa – as reflected in the p-values (0.000) and the 95% confidence intervals (0.67-0.78 and 0.66-0.78, respectively). The difference between Married and widowed is not statistically significant (p=0.29 and 95% CI=0.86-1.64).

Summary At age 40, individuals who had higher grade point average at age 15 are less likely to be unmarried (RRR=0.72, 95% CI=0.67-0.78) or divorced (RRR=0.72, 95% CI=0.66-0.78), in comparison to being married. No significant differences in being widowed versus married according to grade point average, were found (RRR=1.19, 95% CI=0.86-1.64).