jmcm: An R Package for Joint Mean-Covariance Modeling of Longitudinal Data

Abstract

Longitudinal studies commonly arise in various fields such as psychology, social science, economics and medical research, etc. It is of great importance to understand the dynamics in the mean function, covariance and/or correlation matrices of repeated measurements. However, high-dimensionality (HD) and positive-definiteness (PD) constraints are two major stumbling blocks in modeling of covariance and correlation matrices. It is evident that Cholesky-type decomposition based methods are effective in dealing with HD and PD problems, but those methods were not implemented in statistical software yet, causing a difficulty for practitioners to use. In this paper, we first introduce recently developed Cholesky decomposition based methods for joint modeling of mean and covariance structures, namely modified Cholesky decomposition (MCD), alternative Cholesky decomposition (ACD) and hyperspherical parameterization of Cholesky factor (HPC). We then introduce our newly developed R package jmcm which is currently able to handle longitudinal data that follows a Gaussian distribution using the MCD, ACD and HPC methods. The use of package jmcm is illustrated and a comparison of those methods is made through the analysis of two real datasets.

Nonparametric covariance estimation with shrinkage toward stationary models

“…Analyzing the sample regressogram and sample innovation variogram, Pourahmadi () suggested that both sample generalized autoregressive parameters and the logarithms of the innovation variances can be characterized in terms of low degree polynomials of the lag only and time, respectively. Pan and Pan () had the same observation that the regressogram of empirical estimates of ϕ t , s shows consistent behavior over l = t − s for each value of t , indicating a lack of a strong functional component of m . They used the BIC to choose the order of the polynomials for the generalized autoregressive parameters and innovation variances.…”

“…The analysis of the same dataset provided by Zimmerman and Núñez-Antón (1997) rejected equality of the two covariance matrices corresponding to treatment group using the classical likelihood ratio test, making it reasonable to study each treatment group's covariance matrix separately. Following Pourahmadi (1999), Zhang, Leng, and Tang (2015), and Pan and Pan, (2017), we analyze the data from the cattle assigned to treatment Group A (N = 30). Given that the animals belong to the same treatment group and share a common set of observation times, we posit common covariance matrix Σ for each subject.…”

Robust and Adaptive Anticoagulant Control

“…For example we removed the discrete time assumption and considered modelling in realtime with a point process of clinic visits. We included gender, age and time intervals between visits as covariates, and we used mean–covariance modelling (Pourahmadi, ; Liu et al ., ) as implemented in the jmcm R package of Pan and Pan () to allow previous responses, doses and covariates to affect not just the mean, but also (via a Cholesky decomposition) the variance of responses. None of these more involved models brought a substantial improvement over the simple model (1) with patient‐specific coefficients.…”

Double Machine Learning for Partially Linear Mixed-Effects Models with Repeated Measurements

“…Subsequently, we apply our method to longitudinal CD4 cell counts data collected from human immunodeficiency virus (HIV) seroconverters. This data has previously been analyzed by Zeger and Diggle (1994) and is available in the R-package jmcm (Pan and Pan, 2017) as aids. The dataset contains 2376 observations of CD4 cell counts measured on 369 subjects, which were collected during a period ranging from 3 years before to 6 years after seroconversion.…”