Tests For Random Effects In Single-index Models With Random Effects

For a given longitudinal data set,if we do not know whether it contains random effects,we use the model with random effects to analyze the data directly,which will lead to large deviations or even invalid results when the data does not contain random effects.In order to prevent the occurrence of specifying model incorrectly,at the same time to address two issues of whether a single-index models with random effects can be reduced to a single-index models and whether a varying coefficient mixed model can be reduced to a simpler varying coefficient model,in this paper,respectively for the null hypothesis that all variance components of the random effects of single-index models with random effects and varying coefficient mixed model are zero,there is no need to assume the distribution of random effects and random errors,using the idea of extended quasi-likelihood,the Score test is proposed and it is proved that the asymptotic distribution of the score test statistic is a chi-squared distribution withdegrees of freedom under mild regularity conditions.About random effect test of single-index models with random effects,through simulation studies,in that case where the random effects which come from the mixed normal distribution are univariate and bivariate respectively and the random errors are subject to the multivariate normal distribution and (?) distribution,we compare the test statistics given in this paper with the the test statistics obtained by assuming that the random errors are subject to the normal distribution.The simulation results show that the Score test statistic constructed in this paper has better finite sample properties.Finally,the validity of the test method proposed in this paper are illustrated by an example analysis.