An Adaptive Test for a Subset of Coefficients in a Multivariate Regression Model

Abstract

An adaptive multivariate test is proposed for a subset of regression coefficients in a linear model. This adaptive method uses the studentized deleted residuals to calculate an appropriate weight for each observation. The weights are then used to compute Wilk's lambda for the weighted model. The adaptive test is performed by permuting the independent variables corresponding to those parameters that are assumed to equal zero in the null hypothesis. The permuted variables are then weighted to obtain a permutation test statistic that is used to estimate the p-value. An example is presented of a multivariate regression that uses systolic and diastolic blood pressure as dependent variables with age and body mass index as independent variables. The simulation results show that the adaptive test maintains its size for the three multivariate error distributions that were used in the study. For normal error models the power of the adaptive test nearly equaled that of the non-adaptive test. For models that used non-normal errors the adaptive test was considerably more powerful than the traditional non-adaptive test.