A quasiF‐test for functional linear models with functional covariates and its application to longitudinal data

Abstract

Functional linear models are useful in analyzing data from designed experiments and observational studies with functional responses, as well as longitudinal data with a large number of repeated measures on each subject. We propose a quasi F-test for functional linear models with functional covariates and outcomes. We develop a numerical procedure and an efficient approximation for computing p-values, and present a simple way to test individual predictors. For illustration, we apply the proposed procedure to a longitudinal depression data set with repeatedly measured methamphetamine use as a predictor. We conduct a simulation study to assess the size and the power of the test.

Additive nonlinear functional concurrent model

“…We discuss two particular testing problems: 1) testing the global effect of the functional covariate against a model involving a single functional covariate, and 2) testing the null hypothesis of no association between the response and a particular covariate against a model involving two functional covariates. We consider an F-ratio type test statistic (see, e.g., [32]; [42]) and propose a resampling based algorithm to construct the null distribution of the test statistics. Our resampling procedure takes into account the correlated error structure and thus maintains the correct nominal size.…”

A test of linearity in partial functional linear regression

“…Cardot et al (2003) considered the problem of testing a simple hypothesis in the case where the response is scalar and the predictor is a random function, while Mas (2007) investigated a test for the mean of random curves. Recently, Xu et al (2011) discussed an F-test in a linear longitudinal data model, and Kokoszka et al (2008) tested for lack of dependence in a functional linear model where both the response and the predictor are curves. Delsol et al (2011) proposed a theoretical framework for structural testing procedures adapted to functional regression.…”