Generalized Quasi-Likelihood Ratio Tests for Semiparametric Analysis of Covariance Models in Longitudinal Data

Abstract

We model generalized longitudinal data from multiple treatment groups by a class of semiparametric analysis of covariance models, which take into account the parametric effects of time dependent covariates and the nonparametric time effects. In these models, the treatment effects are represented by nonparametric functions of time and we propose a generalized quasi-likelihood ratio test procedure to test if these functions are identical. Our estimation procedure is based on profile estimating equations combined with local linear smoothers. We find that the much celebrated Wilks phenomenon which is well established for independent data still holds for longitudinal data if a working independence correlation structure is assumed in the test statistic. However, this property does not hold in general, especially when the working variance function is mis-specified. Our empirical study also shows that incorporating correlation into the test statistic does not necessarily improve the power of the test. The proposed methods are illustrated with simulation studies and a real application from opioid dependence treatments.

Nested Hierarchical Functional Data Modeling and Inference for the Analysis of Functional Plant Phenotypes

“…The approach has also recently extended to uni-level sparse functional data by Tang et al (2016), who build a GLR test based on working independence estimators. In our setting, we introduce three versions of GLR tests based on marginal likelihood, conditional likelihood and working independence (WI), respectively.…”

“…For comparison, we also define a test based on working independence which totally ignores the covariance structure among the response observations. In general, WI is a simple strategy in longitudinal data analysis that results in consistent estimation (Lin and Carroll, 2001) and legitimate test procedures (Tang et al, 2016). In fact, our initial mean estimators in Section 3.1, which we now denote as µ µ µ W g and α α α W , are WI estimators.…”

Selected topics in measurement error and functional data analysis

“…Some recent reviews on this test include Fan and Jiang (2007), and González-Manteiga and Crujeiras (2013). It is also recently extended to uni-level sparse functional data by Tang, Li, and Guan (2016), who build a GLR test based on working independent estimators.…”

“…For comparison, we also define a test based on working independence which totally ignores the covariance structure among the response variables. In general, WI is a simple strategy in longitudinal data analysis that results in consistent estimation (Lin and Carroll, 2001) and legitimate test procedures (Tang, Li, and Guan, 2016). In fact, our initial mean estimators in Section 4.3.1, now denote as µ µ µ W g and α α α W , are WI estimators.…”

“…First, the asymptotic distributions of the GLR tests on bivariate alternatives verses univariate null have not been investigated in the literature. Second, as pointed out by many authors (Mammen, 1993;Fan and Jiang, 2007;Tang, Li, and Guan, 2016), the asymptotic distribution of a nonparametric test statistic usually performs poorly under finite samples because of the slow convergence rate in nonparametric settings. Even for the cases where the asymptotic distribution of the test statistic is available, these authors favor resampling methods.…”