Question: Logit model (6.1) multinomial variate y = (y1, ... ,Yc-1)T (with y; = 1 if outcome j occurred and 0 otherwise) for a single trial

Logit model (6.1) multinomial variate y = (y1, ... ,Yc-1)T (with y; = 1 if outcome j occurred and 0 otherwise) for a single trial with parameters (1+1, ... , IC-1) has distribution in the (c 1)-parameter exponential dispersion family, with baseline-category logits as natural parameters. Consider the baseline-category logit model (6.1). a. Suppose we impose the structure B; = j, for j = 1, ...,C 1. Does this model treat the response as ordinal or nominal? Explain. b. Show that the model in (a) has proportional odds structure when the c 1 logits are formed using pairs of adjacent categories. Logit model (6.1) multinomial variate y = (y1, ... ,Yc-1)T (with y; = 1 if outcome j occurred and 0 otherwise) for a single trial with parameters (1+1, ... , IC-1) has distribution in the (c 1)-parameter exponential dispersion family, with baseline-category logits as natural parameters. Consider the baseline-category logit model (6.1). a. Suppose we impose the structure B; = j, for j = 1, ...,C 1. Does this model treat the response as ordinal or nominal? Explain. b. Show that the model in (a) has proportional odds structure when the c 1 logits are formed using pairs of adjacent categories
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