Biomaterial Database

Generalized linear models with ordinally-observed covariates. 2006

Timothy R Johnson

Department of Statistics, University of Idaho, Moscow 83844-1104, USA. trjohns@uidaho.edu

An ordinally-observed variable is a variable that is only partially observed through an ordinal surrogate. Although statistical models for ordinally-observed response variables are well known, relatively little attention has been given to the problem of ordinally-observed regressors. In this paper I show that if surrogates to ordinally-observed covariates are used as regressors in a generalized linear model then the resulting measurement error in the covariates can compromise the consistency of point estimators and standard errors for the effects of fully-observed regressors. To properly account for this measurement error when making inferences concerning the fully-observed regressors, I propose a general modelling framework for generalized linear models with ordinally-observed covariates. I discuss issues of model specification, identification, and estimation, and illustrate these with examples.

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
D003625	Data Collection	Systematic gathering of data for a particular purpose from various sources, including questionnaires, interviews, observation, existing records, and electronic devices. The process is usually preliminary to statistical analysis of the data.	Data Collection Methods,Dual Data Collection,Collection Method, Data,Collection Methods, Data,Collection, Data,Collection, Dual Data,Data Collection Method,Method, Data Collection,Methods, Data Collection
D003627	Data Interpretation, Statistical	Application of statistical procedures to analyze specific observed or assumed facts from a particular study.	Data Analysis, Statistical,Data Interpretations, Statistical,Interpretation, Statistical Data,Statistical Data Analysis,Statistical Data Interpretation,Analyses, Statistical Data,Analysis, Statistical Data,Data Analyses, Statistical,Interpretations, Statistical Data,Statistical Data Analyses,Statistical Data Interpretations
D006306	Health Surveys	A systematic collection of factual data pertaining to health and disease in a human population within a given geographic area.	Abortion Surveys,Abortion Survey,Health Survey,Survey, Abortion,Survey, Health,Surveys, Abortion,Surveys, Health
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
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
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
D015982	Bias	Any deviation of results or inferences from the truth, or processes leading to such deviation. Bias can result from several sources: one-sided or systematic variations in measurement from the true value (systematic error); flaws in study design; deviation of inferences, interpretations, or analyses based on flawed data or data collection; etc. There is no sense of prejudice or subjectivity implied in the assessment of bias under these conditions.	Aggregation Bias,Bias, Aggregation,Bias, Ecological,Bias, Statistical,Bias, Systematic,Ecological Bias,Outcome Measurement Errors,Statistical Bias,Systematic Bias,Bias, Epidemiologic,Biases,Biases, Ecological,Biases, Statistical,Ecological Biases,Ecological Fallacies,Ecological Fallacy,Epidemiologic Biases,Experimental Bias,Fallacies, Ecological,Fallacy, Ecological,Scientific Bias,Statistical Biases,Truncation Bias,Truncation Biases,Bias, Experimental,Bias, Scientific,Bias, Truncation,Biase, Epidemiologic,Biases, Epidemiologic,Biases, Truncation,Epidemiologic Biase,Error, Outcome Measurement,Errors, Outcome Measurement,Outcome Measurement Error
D016012	Poisson Distribution	A distribution function used to describe the occurrence of rare events or to describe the sampling distribution of isolated counts in a continuum of time or space.	Distribution, Poisson
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