We are going to train a multinomial logistic regression on 5,000 observations. The target field has five categories, namely, A, B, C, D, and E. The categorical feature has four categories, namely, I, II, III, and IV. Instead of a casewise dataset, the data have been aggregated and shown in the following table.

	Target Field
Feature	A	B	C	D	E
I	65	304	530	487	140
II	74	185	160	55	16
III	33	228	623	755	363
IV	90	290	349	213	40

We will use the Deviance Test to determine if the categorical feature is predictive for the categorical target. We will first train a model, say M0 , with only the Intercept terms. The log-likelihood value of the model M0 is -7249.5908 and the degree of freedom is 4. Next, we train another model M1 with the Intercept terms and the categorical feature.

What is the degree of freedom of the model M1 ?