Is it valid to use Anova (in R) to compare alternative multinomial log-linear models?

Question

I am familiar with the idea of comparing alternative linear regression models using anova(model1,model2), for models fitted using lm() in R. For example, I might use this function to test if it was worth adding an $X^2$ term to a linear model.

I am now interested in comparing two multinomial log-linear models (both fitted from the same dataset, using multinom from the nnet package in R):

Model 1: The intercept model, so essentially based only on the frequencies of each category.

Model 2: A more complex model, with an intercept term and some additional explanatory variables.

When I compare two multinomial log-linear models, Model 1 and Model 2 as specified above, R does run and produce output, including a Pr(Chi) value (note, in this example the Pr(Chi) value is not significant, but my questions are about the general principle rather than specific to these particular models):

  Model Resid. df Resid. Dev   Test    Df LR stat.   Pr(Chi)
1 Model1       471   218.4830           NA       NA        NA
2 Model2       465   215.2631 1 vs 2     6 3.219958 0.7807764

My questions are:

1. Is this a valid way to compare multinomial log-linear models, or is there some reason that it is not valid?

2. If it is not valid (or if there is potentially a better way), what are alternative ways to compare the models?

3. What exactly is anova comparing in this context? e.g. what are the values in the 'Resid. Dev' column of the output? Are these the log likelihoods or something else?

Answer 1

1. I think since the models are nested, your comparison makes sense.
2. Resid. Dev. is the residual deviance, which is given in comparison to the Null model. The lower number of your Model2 indicates that it was a better fit. If you are looking for the likelihoods, you do have this output under LR stat, it is the results from the likelihood ratio test.