Effects of covariance model assumptions on hypothesis tests for repeated measurements: analysis of ovarian hormone data and pituitary‐pteryomaxillary distance data

Abstract

In the analysis of repeated measurements, multivariate methods which account for the correlations among the observations from the same experimental unit are widely used. Two commonly-used multivariate methods are the unstructured multivariate approach and the mixed model approach. The unstructured multivariate approach uses MANOVA types of models and does not require assumptions on the covariance structure. The mixed model approach uses multivariate linear models with random effects and requires covariance structure assumptions. In this paper, we describe the characteristics of tests based on these two methods of analysis and investigate the performance of these tests. We focus particularly on tests for group effects and parallelism of response profiles.

Comparison of Some Multivariate Nonparametric Tests in Profile Analysis to Repeated Measurements

“…Therefore it is implied the nonparametric alternatives can be confidently applied in place of MANOVA tests in profile analysis regardless of the nature of underlying distribution. Park et al (2001) investigated the performance of profile analysis using Hotelling's T 2 and mixed model approach to test group and interaction effects. Also, Vossoughi et al (2012) compared the performance of profile analysis, linear mixed model and summary measure approach in repeated measurements generated from a linear mixed model setting.…”

“…The linear mixed model to repeated measurements (Laird & Ware, 1982;Ware, 1985) was developed to analyze incomplete and unbalanced data. However, the performance of this complex approach is highly sensitive to the choice of model for mean function and correlation structure for errors (Littell, Pendergast, & Natarajan, 2000;Park, Park, & Davis, 2001;Vossoughi, Ayatollahi, Towhidi, & Ketabchi, 2012). Although several nonparametric methods have been developed for non-normal responses (Azzalini & Bowman, 1991;Singer, Poleto, & Rosa, 2004;Wernecke & Kalb, 1999;Wernecke & Kaufmann, 2000), model building and software implementation of these methods are extremely complicated.…”

“…Although the Monte Carlo comparison of methods for the analysis of repeated measurements has been an active area of research (Bhapkar & Patterson, 1978;Marcucci, 1986;Mendoza, Toothaker, & Nicewander, 1974;Park et al, 2001;Schwertman, Flynn, Stein, & Schenk, 1985;Schwertman, Fridshal, & Magrey, 1981), this study has been designed to examine some different aspects. First, the performances of recent nonparametric tests based on spatial signs and ranks considered here have not yet been studied in the area of profile analysis.…”

Using Adaptive Tests for the Analysis of Repeated Measurements

“…The MIXED procedure also allows the user to specify a method for computing the denominator degrees of freedom for tests of fixed effects. Overall et al (1999) and Park et al (2001), reported that the mixed procedure often failed to maintain its size when the default methods were used in tests of parallelism and group effects. Kowalchuk (2004) reported that a modification to the testing method that was proposed by Kenward and Roger (1997) had adequate control of Type I error rates for small sample size configurations.…”

“…In our simulations we have used the REML method because several authors, including Park et al (2001) have shown that it produces better control over the Type I error. The MIXED procedure also allows the user to specify a method for computing the denominator degrees of freedom for tests of fixed effects.…”