Tests of significance using regression models for ordered categorical data.
Regression models of the type proposed by McCullagh (1980, Journal of the Royal Statistical Society, Series B 42, 109-142) are a general and powerful method of analyzing ordered categorical responses, assuming categorization of an (unknown) continuous response of a specified distribution type. Tests of significance with these models are generally based on likelihood-ratio statistics that have asymptotic chi 2 distributions; therefore, investigators with small data sets may be concerned with the small-sample behavior of these tests. In a Monte Carlo sampling study, significance tests based on the ordinal model are found to be powerful, but a modified test procedure (using an F distribution with a finite number of degrees of freedom for the denominator) is suggested such that the empirical significance level agrees more closely with the nominal significance level in small-sample situations. We also discuss the parallels between an ordinal regression model assuming underlying normality and conventional multiple regression. We illustrate the model with two data sets: one from a study investigating the relationship between phosphorus in soil and plant-available phosphorus in corn grown in that soil, and the other from a clinical trial comparing analgesic drugs.
D000700:Analgesics / Q000627:therapeutic use; D000704:Analysis of Variance; D001699:Biometry; D002986:Clinical Trials as Topic / Q000379:methods*; D006261:Headache / Q000188:drug therapy*; D006801:Humans; D007484:Iowa; D008962:Models, Theoretical; D010710:Phosphates / Q000032:analysis; D011897:Random Allocation; D012044:Regression Analysis; D012987:Soil / Q000032:analysis
D000700:Analgesics; D010710:Phosphates; D012987:Soil