With the command fitstat, we can produce various types of model fit statistics. This command requires that you install a user-written package first. So, if you have not installed it already, type:

search spost13_ado

Click on the first link in the list, and then choose Click here to install.

More information help fitstat

Practical example

We perform this test for the full model, so let us go back to the example from the multiple regression analysis. The quietly option is included in the beginning of the command to suppress the output.

quietly mlogit marstat40 gpa sex ib1.educ if pop_multinom==1, rrr b(1)

And then we produce the statistics:

fitstat

This reports the log-likelihoods of the full (Model) and empty (Intercept-only) models, the deviance, the likelihood ratio test, Akaike’s Information Criterion (AIC), AIC/N, and the Bayesian Information Criterion (BIC). In addition, we obtain different types of R2 estimates (which are seldom used).

One very practical thing is that we can use these statistics to compare models. For example, we might want to see whether model fit improves if we include or exclude one or more x-variables, or if we make any transformations of the included x-variables.

Let us assume that we want to see here if our multiple regression model has a better fit if we exclude the variable gpa.

First, we run the original model. The quietly option is included in the beginning of the command to suppress the output.

quietly mlogit marstat40 gpa sex ib1.educ if pop_multinom==1, rrr b(1)

And then save the statistics:

fitstat, save

Then we run the alternative model (output suppressed here as well):

quietly mlogit marstat40 sex ib1.educ if pop_multinom==1, rrr b(1)

And then compare the statistics:

fitstat, dif

It seems as both the chi-square (as indicated by the significant LR test), and the AIC favours the original (saved) model with gpa, whereas the BIC favours the model without gpa. This is not surprising given that BIC tends to be lower for more parsimonious (simpler) models. Should we change our model based on these statistics by, in this case, excluding gpa? That is a difficult question that needs to be considered carefully (by reflecting upon theory, previous research, and other alternatives for estimation). 

Note When we compare BIC and/or AIC values, we prefer the model with the lowest values.