Study Of Latent Trait For Longitudinal Data

Longitudinal data are widely applied in many studies such as medicine, biol-ogy, economics and psychology. Analysis of longitudinal data has become one of hotresearch fields in Statistics. Longitudinal data could always, from deferent aspects,reflect a latent trait of an unit, which is usually potential and might not be directlyobserved. However, the interest is aroused by the latent trait and the correlations withcovariates. The motivation of this paper is a dataset from a test of the children’s psy-chological measurement center of Northeast Normal University in2009. This test ismainly about children’s information processing efciency research for children aged4-7. Study of latent trait for longitudinal data is introduced. The statistics analysis underthe latent trait follows normal distribution is considered. At the same time, the statis-tics analysis under the random efects of longitudinal data in GLMM with unspecifieddistribution is also carefully considered.Since the latent trait follows normal distribution, this paper focuses on the esti-mator of the individual latent trait and its correlations with covariates. Based on theideal of latent variable model, a latent processing ability model is developed. Theapproach adopted can not only efectively evaluate the efects of covariates on the la-tent processing ability, but also estimate the latent trait of each child by calculatingits posterior mean. In addition, the correlations structure of latent processing abilityamong diferent age groups is derived. EM algorithm is used to obtain the estimatesof model parameters. Simulations and real data analysis are conducted to evaluate theperformance of the proposed model.If the random efects of longitudinal data in GLMM are unspecified distributed,given the random efects and the data are measured from the same machine, the corre-lations may exist between them. If the correlations structure is mis-specified, it couldafect the efciency of the fixed-efects estimator. Based on the advantages of mix GEEand conditional quadratic inference functions, this paper proposes a new approach de-fined as conditional mix GEE method. The merit of conditional mix GEE method is that it does not require the normality assumption for the latent trait and could con-sider the serial correlations given the latent trait. At the same time, it could identifythe true correlations structure of data. The estimates of model parameters can be ob-tained using iterative algorithm. Under the regularity conditions, the conditional mixGEE estimator is consistent and asymptotically normal. Simulation study and real dataanalysis reflect efciency of the method.