Regression Models for Categorical and Count Data by Martin Peter;

Author:Martin, Peter; [Martin, Peter]
Language: eng
Format: epub
Publisher: SAGE Publications
Published: 2021-05-12T08:29:45.571706+00:00

These models are nested, since I can turn Model 4.2 into Model 4.1 by setting β1,1 = β2,1 = β3,1 = 0. Now, we may be interested in investigating whether social status (z.ISEI) is associated with our outcome, cultural consumption, when adjusting for Rural. Then we can formulate the hypotheses of a likelihood ratio test of Model 4.2 versus Model 4.1 as follows:

Null hypothesis: Model 4.2 predicts cultural consumption no better than Model 4.1. Another way of stating this is that social status (z.ISEI) is hypothesised to have no relationship with the relative risk of any pair of outcome categories. Yet another way of stating this hypothesis is that all slope coefficients associated with z.ISEI are zero – that is H0 = β1,1 = β2,1 = β3,1 = 0.

Alternative hypothesis: Model 4.2 predicts cultural consumption better than Model 4.1. Another way of saying the same thing is that social status is related with the relative risk of at least one pair of outcome categories. In other words, the alternative hypothesis is that at least one slope coefficient associated with z.ISEI is not zero. In mathematical notation, we might write the alternative hypothesis as H1: βj,1 ≠ 0, for at least one j = {1,2,3}.

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