Groupe d’études et de recherche en analyse des décisions

Using Tests of Homoscedasticity to Test Missing Completely at Random

Mori Jamshidian

Test of homogeneity of covariances (or homoscedasticity) among several groups has many applications in statistical analysis. In the context of incomplete data analysis, tests of homoscedasticity among groups of cases with identical missing data patterns have been proposed to test whether data are missing completely at random (MCAR). The proposed tests of MCAR often require large sample sizes $$n$$ and/or large group sample sizes ni, and they usually fail when applied to non-normal data. Hawkins (1981) proposed a test of multivariate normality and homoscedasticity that is an exact test for complete data when ni are small. In this talk we present a modification of the Hawkins test for complete data to improve its performance, and extends its application to test of homoscedasticity and MCAR when data are multivariate normal and incomplete. Moreover, we will show that the statistic used in the Hawkins test in conjunction with a nonparametric $$k$$-sample test can be used to obtain a nonparametric test of MCAR that works well for both normal and non-normal data. It will be explained how a combination of the proposed normal-theory Hawkins test and the nonparametric test can be employed to test for homoscedasticity, MCAR, and multivariate normality. We will present simulation studies that indicate the newly proposed tests generally outperform their existing competitors in terms of Type I error rejection rates. Also, a power study of the proposed tests indicates good power. The newly proposed methods use appropriate methods of imputations to impute missing data. As such, multiple imputation is employed to assess the performance of our tests in light of imputation variability. Moreover, examples will be presented where multiple imputation enables one to identify a group or groups whose covariance matrices differ from the majority of other groups. Finally, an $$R$$-package that implements these new tests, called MissMech, will be briefly presented.