Biomaterial Database

Likelihood ratio testing of variance components in the linear mixed-effects model using restricted maximum likelihood. 1998

C H Morrell

Mathematical Sciences Department, Loyola College, Maryland 21210-2699, USA. chm@Loyola.edu

This paper reports the results of an extensive Monte Carlo study of the distribution of the likelihood ratio test statistic using the value of the restricted likelihood for testing random components in the linear mixed-effects model when the number of fixed components remains constant. The distribution of this test statistic is considered when one additional random component is added. The distribution of the likelihood ratio test statistic computed using restricted maximum likelihood is compared to the likelihood ratio test statistic computed from the usual maximum likelihood. The rejection proportion is computed under the null hypothesis using a mixture of chi-square distributions. The restricted likelihood ratio statistic has a reasonable agreement with the maximum likelihood test statistic. For the parameter combinations considered, the rejection proportions are, in most cases, less than the nominal 5% level for both test statistics, though, on average, the rejection proportions for REML are closer to the nominal level than for ML.

UI	MeSH Term	Description	Entries
D009010	Monte Carlo Method	In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)	Method, Monte Carlo
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
D016014	Linear Models	Statistical models in which the value of a parameter for a given value of a factor is assumed to be equal to a + bx, where a and b are constants. The models predict a linear regression.	Linear Regression,Log-Linear Models,Models, Linear,Linear Model,Linear Regressions,Log Linear Models,Log-Linear Model,Model, Linear,Model, Log-Linear,Models, Log-Linear,Regression, Linear,Regressions, Linear