Biomaterial Database

Tests of significance using regression models for ordered categorical data. 1986

S M Snapinn, and R D Small

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.

UI	MeSH Term	Description	Entries
D007484	Iowa	State bounded on the north by Minnesota, on the east by Wisconsin and Illinois, on the south by Missouri, and on the west by Nebraska and South Dakota.
D008962	Models, Theoretical	Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.	Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D010710	Phosphates	Inorganic salts of phosphoric acid.	Inorganic Phosphate,Phosphates, Inorganic,Inorganic Phosphates,Orthophosphate,Phosphate,Phosphate, Inorganic
D011897	Random Allocation	A process involving chance used in therapeutic trials or other research endeavor for allocating experimental subjects, human or animal, between treatment and control groups, or among treatment groups. It may also apply to experiments on inanimate objects.	Randomization,Allocation, Random
D012044	Regression Analysis	Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.	Regression Diagnostics,Statistical Regression,Analysis, Regression,Analyses, Regression,Diagnostics, Regression,Regression Analyses,Regression, Statistical,Regressions, Statistical,Statistical Regressions
D002986	Clinical Trials as Topic	Works about pre-planned studies of the safety, efficacy, or optimum dosage schedule (if appropriate) of one or more diagnostic, therapeutic, or prophylactic drugs, devices, or techniques selected according to predetermined criteria of eligibility and observed for predefined evidence of favorable and unfavorable effects. This concept includes clinical trials conducted both in the U.S. and in other countries.	Clinical Trial as Topic
D006261	Headache	The symptom of PAIN in the cranial region. It may be an isolated benign occurrence or manifestation of a wide variety of HEADACHE DISORDERS.	Cephalgia,Hemicrania,Bilateral Headache,Cephalalgia,Cephalodynia,Cranial Pain,Generalized Headache,Head Pain,Ocular Headache,Orthostatic Headache,Periorbital Headache,Retro-Ocular Headache,Sharp Headache,Throbbing Headache,Unilateral Headache,Vertex Headache,Bilateral Headaches,Cephalalgias,Cephalgias,Cephalodynias,Cranial Pains,Generalized Headaches,Head Pains,Headache, Bilateral,Headache, Generalized,Headache, Ocular,Headache, Orthostatic,Headache, Periorbital,Headache, Retro-Ocular,Headache, Sharp,Headache, Throbbing,Headache, Unilateral,Headache, Vertex,Headaches,Headaches, Bilateral,Headaches, Generalized,Headaches, Ocular,Headaches, Orthostatic,Headaches, Periorbital,Headaches, Retro-Ocular,Headaches, Sharp,Headaches, Throbbing,Headaches, Unilateral,Headaches, Vertex,Ocular Headaches,Orthostatic Headaches,Pain, Cranial,Pain, Head,Pains, Cranial,Pains, Head,Periorbital Headaches,Retro Ocular Headache,Retro-Ocular Headaches,Sharp Headaches,Throbbing Headaches,Unilateral Headaches,Vertex Headaches
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000700	Analgesics	Compounds capable of relieving pain without the loss of CONSCIOUSNESS.	Analgesic,Anodynes,Antinociceptive Agents,Analgesic Agents,Analgesic Drugs,Agents, Analgesic,Agents, Antinociceptive,Drugs, Analgesic
D000704	Analysis of Variance	A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable.	ANOVA,Analysis, Variance,Variance Analysis,Analyses, Variance,Variance Analyses