In the research of scientific field, it is often necessary to continuously observe different indicators of individuals at different times and analyze the observed results. Among them, variables are mainly of two types...In the research of scientific field, it is often necessary to continuously observe different indicators of individuals at different times and analyze the observed results. Among them, variables are mainly of two types: ordered variables and continuous variables. When analyzing data for different types of variables, it is necessary to consider the correlation between multiple indicators of an individual, and often perform joint analysis on variable observation data of multiple indicators of an individual at different times, in order to achieve more accurate and true analysis results. Joint analysis often yields more information than separate analysis of various variables. In this paper, the ordered variable and the continuous variable are numerically modeled. Based on the potential variable model, the multivariate longitudinal data containing the ordered variable and the continuous variable are jointly analyzed, and the approximate value of the edge likelihood can be obtained by using the method of numerical integration.展开更多
Multivariate longitudinal data arise frequently in a variety of applications,where multiple outcomes are measured repeatedly from the same subject.In this paper,we first propose a two-stage weighted least square estim...Multivariate longitudinal data arise frequently in a variety of applications,where multiple outcomes are measured repeatedly from the same subject.In this paper,we first propose a two-stage weighted least square estimation procedure for the regression coefficients when the random error follows an irregular autoregressive(AR)process,and establish asymptotic normality properties for the resulting estimators.We then apply the smoothly clipped absolute deviation(SCAD)variable selection approach to determine the order of the AR error process.We further propose a test statistic to check whether multiple responses are correlated at the same observation time,and derive the asymptotic distribution of the proposed test statistic.Several simulated examples and real data analysis are presented to illustrate the finite-sample performance of the proposed method.展开更多
文摘In the research of scientific field, it is often necessary to continuously observe different indicators of individuals at different times and analyze the observed results. Among them, variables are mainly of two types: ordered variables and continuous variables. When analyzing data for different types of variables, it is necessary to consider the correlation between multiple indicators of an individual, and often perform joint analysis on variable observation data of multiple indicators of an individual at different times, in order to achieve more accurate and true analysis results. Joint analysis often yields more information than separate analysis of various variables. In this paper, the ordered variable and the continuous variable are numerically modeled. Based on the potential variable model, the multivariate longitudinal data containing the ordered variable and the continuous variable are jointly analyzed, and the approximate value of the edge likelihood can be obtained by using the method of numerical integration.
基金supported by the Fundamental Research Funds of Shandong University(Grant No.2018GN050)the Academic Prosperity Program provided by School of Economics,Shandong University and the Taishan Scholar Program of Shandong Province+2 种基金supported by National Natural Science Foundation of China(Grant No.11871323)the State Key Program in the Major Research Plan of National Natural Science Foundation of China(Grant No.91546202)Program for Innovative Research Team of Shanghai University of Finance and Economics。
文摘Multivariate longitudinal data arise frequently in a variety of applications,where multiple outcomes are measured repeatedly from the same subject.In this paper,we first propose a two-stage weighted least square estimation procedure for the regression coefficients when the random error follows an irregular autoregressive(AR)process,and establish asymptotic normality properties for the resulting estimators.We then apply the smoothly clipped absolute deviation(SCAD)variable selection approach to determine the order of the AR error process.We further propose a test statistic to check whether multiple responses are correlated at the same observation time,and derive the asymptotic distribution of the proposed test statistic.Several simulated examples and real data analysis are presented to illustrate the finite-sample performance of the proposed method.
