Snapinn S M, Small R D
Biometrics. 1986 Sep;42(3):583-92.
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.
麦卡拉（1980年，《皇家统计学会学报》，B辑第42卷，第109 - 142页）提出的这类回归模型是分析有序分类响应的一种通用且强大的方法，它假定对具有特定分布类型的（未知）连续响应进行分类。使用这些模型进行显著性检验通常基于具有渐近卡方分布的似然比统计量；因此，数据集较小的研究者可能会关注这些检验在小样本情况下的表现。在一项蒙特卡罗抽样研究中，发现基于序数模型的显著性检验功效强大，但建议采用一种修正的检验程序（使用分母自由度有限的F分布），以便在小样本情况下，经验显著性水平更接近名义显著性水平。我们还讨论了假定潜在正态性的序数回归模型与传统多元回归之间的相似之处。我们用两个数据集来说明该模型：一个来自一项研究，该研究调查土壤中的磷与在该土壤中种植的玉米中植物可利用磷之间的关系；另一个来自一项比较镇痛药的临床试验。
