Despite the widespread use of mixed-effects regression model, available methods for testing the covariance matrix of random effects are quite limited. In these cases, because of complexity and difficulties coming from an analysis of multiple variance components, inference based on testing the equality of two positive semi definite matrices seems most appropriate. We propose a test statistic based on a comparison between an estimate of a covariance matrix defined when data come from a linear regression model (covariance matrix zero) and an appropriate sample variance covariance matrix. We show that under the null hypothesis the test statistic is close to one and under the alternative it is expected to be larger than one. The objectives of the work are: a. To propose a test statistic with a finite sample distribution (under normality assumptions), whereas many existing tests have asymptotic distributions and require simulations to detect their performance in small samples, b. To make inference by defining and testing a parameter that equivalently reproduces the set of hypotheses on a covariance matrix. The defined parameter bypasses boundary value problem that typically precludes use of tests based on chi-square statistics, c. To avoid estimating and testing the covariance matrix. As known, the estimation problem is closely related to difficulties of determining how to deal with a non positive definite covariance matrix of random effects during numerical implementation, d. To define a test in unbalanced models.
A comparison of two matrices for testing Covariance Matrix in Unbalanced Linear Mixed Models / Barnabani, Marco. - In: BIOSTATISTICS AND BIOMETRICS OPEN ACCESS JOURNAL. - ISSN 2573-2633. - ELETTRONICO. - Vol 3 - issue 3:(2017), pp. 1-2. [10.19080/BBOAJ.2017.03.555611]
A comparison of two matrices for testing Covariance Matrix in Unbalanced Linear Mixed Models
Barnabani Marco
2017
Abstract
Despite the widespread use of mixed-effects regression model, available methods for testing the covariance matrix of random effects are quite limited. In these cases, because of complexity and difficulties coming from an analysis of multiple variance components, inference based on testing the equality of two positive semi definite matrices seems most appropriate. We propose a test statistic based on a comparison between an estimate of a covariance matrix defined when data come from a linear regression model (covariance matrix zero) and an appropriate sample variance covariance matrix. We show that under the null hypothesis the test statistic is close to one and under the alternative it is expected to be larger than one. The objectives of the work are: a. To propose a test statistic with a finite sample distribution (under normality assumptions), whereas many existing tests have asymptotic distributions and require simulations to detect their performance in small samples, b. To make inference by defining and testing a parameter that equivalently reproduces the set of hypotheses on a covariance matrix. The defined parameter bypasses boundary value problem that typically precludes use of tests based on chi-square statistics, c. To avoid estimating and testing the covariance matrix. As known, the estimation problem is closely related to difficulties of determining how to deal with a non positive definite covariance matrix of random effects during numerical implementation, d. To define a test in unbalanced models.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.