In Stata, we use the ‘mlogit’ command to run a multinomial logistic regression. As with the logistic regression method, the command produces untransformed beta coefficients (in log-odd units) along with their confidence intervals. (These are often difficult to interpret, so are sometimes converted into relative risk ratios. If we wanted to get the relative risk ratios we could add the ‘rrr’ option (‘, rrr’) to the ‘mlogit’ example below). With the ‘mlogit’ command, we also include the option ‘base’ to specify which category is the reference group. For our analysis, we will use ‘normal or healthy’ weight as the reference category.
In the first regression we run, there will only be one predictor variable, ‘general ability at age 11’ (n920), which is a continuous variable.
The iterations 0 through 3 listed in the top left-hand corner of the output above are the log likelihoods at each iteration of the maximum likelihood estimation. Iteration 0 is the log likelihood of the model with no predictors. When the difference between successive iterations is very small, the model has ‘converged’. The final iteration is the log likelihood of the fitted model. The log likelihood of the fitted model is -4499.12. The number itself does not have much meaning, but is used to make comparisons across the models and to identify if the reduced model fits significantly better than the full model. The overall model is statistically significant (chi-square = 55.73, p=<.001), which means the model including ‘general ability at age 11’ fits the data statistically significantly better than the model without it, i.e. a model with no predictors. The ‘pseudo R-squared’ value (Pseudo R2) gives a very general idea of the proportion of variance accounted for by the model, but it is just an approximation and not very reliable which is why we call it ‘pseudo’.
In the output above, we also get a tabulation of the coefficient, standard error, the z statistic, associated p-values and the 95% confidence intervals of the coefficients. This table is in two parts, labelled with the categories of the outcome variable BMI42_C. In both outputs, ‘general ability at age 11’ (n920) is statistically significant. A 1 unit decrease in ‘general ability’ is associated with a 0.008 decrease in the relative log odds of being overweight compared to a normal/healthy weight, and a 0.022 decrease in the relative log odds of being obese compared to a normal/healthy weight.
In the next step, we will extend the model further to explore the influence of other variables on this association between general ability and the different categories of BMI.
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