Joint Analysis Of Longitudinal And Cross-Sectional Data Based On Functional Mixed Effects Model

In many fields such as biomedicine,for the same problem,sometimes there are several different types of datasets from different sources that can be used for study.For example,in the study of influencing factors of infant growth,researchers will collect both small-scale longitudinal data and large-scale cross-sectional data based on sampling survey.Because of the different types of data,researchers usually model and analyze them separately.However,since these two types of data can be used for studying the same problem and the collected variables are similar,if these two types of data can be appropriately combined for joint modeling,it will significantly increase the total sample size and greatly improve the research results.At present,there are few researches in this field.This paper will focus on the joint modeling method of longitudinal data and cross-sectional data,and apply this method to the analysis of influencing factors of infant growth.This paper first introduces the k-means clustering algorithm,and how to use the k-means clustering algorithm to cluster the cross-sectional data into pseudo-longitudinal data with multiple observations for each individual.Then,this paper introduces an existing functional mixed effect model,and focuses on how to develop an extended functional mixed effect model based on this model.When the original model is used to analyze the longitudinal data,the random effects of all individuals correspond to the same covariance function?(t,s),and the measurement errors of all individuals correspond to the same time-varying variance function?~2(t).In the expanded model,different covariance functions and error variance functions are introduced for different groups of longitudinal data.In the joint analysis of real longitudinal data and pseudo longitudinal data,this paper sets that real longitudinal data and pseudo longitudinal data have different covariance functions in the model?_k(t,s),k=1,2 and different error variance function?_k~2(t),k=1,2,and a specific estimation method is given.A thorough simulation study is carried out in this paper,and the effects of the method JFMM proposed in this paper and the method CW proposed in the existing literature on the simulation data analysis are compared.It can be found that when the covariance of individual random effect and the variance of measurement error of the two groups of data in the simulation are expanding,the method JFMM is better than method CW in terms of both the width of confidence band and the mean square error.In the real data analysis,we collected cross-sectional data and lon-gitudinal data on infant growth and its influencing factors.First,the k-means clustering method is used to cluster the cross-sectional data with only one observation for each individual,individuals of the same cluster have high similarity,thus each class can be regarded as a”pseudo-individual”with multiple observations.A large number of pseudo-individuals constitute pseudo-longitudinal data,which transforms the cross-sectional data into the form of longitudinal data.Then the method proposed in this paper is used to analyze the joint data composed of the real longitudinal data and the pseudo longitudinal data obtained by clustering,and the results of the analysis of the two types of data are compared.