Biomaterial Database

Regression with bivariate grouped data. 1991

D F Heitjan

Center for Biostatistics and Epidemiology, Pennsylvania State University College of Medicine, Hershey 17033.

The problem of accounting for the grouping of continuous, bivariate data in regression analyses is considered. Reasons why grouping must be taken seriously are advanced, and a strategy for accounting for grouping is demonstrated. The specific model asserts that, in the absence of grouping, the data would be bivariate normal. This model is used to adjust estimates of parameters in a regression relating disease severity to a grouped exposure variable, using data on pneumoconiosis in English coal miners (Ashford, 1959, Biometrics 15, 573-581). The choice of computing methods is discussed and likelihood formulas are presented.

UI	MeSH Term	Description	Entries
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
D000465	Algorithms	A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.	Algorithm
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
D001699	Biometry	The use of statistical and mathematical methods to analyze biological observations and phenomena.	Biometric Analysis,Biometrics,Analyses, Biometric,Analysis, Biometric,Biometric Analyses
D015233	Models, Statistical	Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.	Probabilistic Models,Statistical Models,Two-Parameter Models,Model, Statistical,Models, Binomial,Models, Polynomial,Statistical Model,Binomial Model,Binomial Models,Model, Binomial,Model, Polynomial,Model, Probabilistic,Model, Two-Parameter,Models, Probabilistic,Models, Two-Parameter,Polynomial Model,Polynomial Models,Probabilistic Model,Two Parameter Models,Two-Parameter Model
D016013	Likelihood Functions	Functions constructed from a statistical model and a set of observed data which give the probability of that data for various values of the unknown model parameters. Those parameter values that maximize the probability are the maximum likelihood estimates of the parameters.	Likelihood Ratio Test,Maximum Likelihood Estimates,Estimate, Maximum Likelihood,Estimates, Maximum Likelihood,Function, Likelihood,Functions, Likelihood,Likelihood Function,Maximum Likelihood Estimate,Test, Likelihood Ratio