Testing linearity and relevance of ordinal predictors

Abstract

In a linear model relevance of a categorical predictor with ordered levels is typically tested by use of the standard F-test (known from statistical textbooks). Such a test can also be applied for testing whether the regression function is linear in the ordinal predictor's class labels. In this paper we propose an alternative (restricted) likelihood ratio test for these hypotheses which is especially suited for ordinal predictors and is based on the mixed model formulation of penalized dummy coefficients. We show in simulation studies that the new test is more powerful than the standard F-test in many situations. The advantage of the new test is especially striking when the number of ordered levels is moderate or large. Using the relationship to mixed effect models and robust existent fitting software obtaining the test and its null distribution is very fast; a fast R implementation is provided.