Modeling longitudinal INMA(1) with COM–Poisson innovation under non-stationarity: application to medical data

Improved mixed model for longitudinal data analysis using shrinkage method

“…In our simulation scheme, we fix n i = 4 measurements for each subject i and generate data according to the model of (2) where = (0.0, 0.1, 0.2, 0.4, 0.8) , b ijk ∼ N(0, 0.6) and ijk ∼ N(0, 1) . To generate multicollinear data, using the "EnvStats" package in R, each predictor variable is assumed to arise from N (5,1), and the correlation between predictor variables is taken from the set {0.0, 0.2, 0.5, 0.7, 0.9} . Initial values of the variance components are set to be the estimates obtained from fitting a mixed model with no ridge component.…”

“…In longitudinal data setup, repeated measures of some variables of interest are collected over a specified time period for different independent subjects or individuals. Such types of data are commonly encountered in medical research where the responses are subject to various time-dependent and time-constant effects such as pre-and post-treatment types, gender effect, baseline measures and among others (see Mamode Khan et al [1], Yuan et al [2], Verbeke et al [3], Temesgen and Kebede [4], Seyoum et al [5] and the references therein). It is quite natural, in the above examples, the repeated measures shall exhibit some forms of dependence that may be resulted from some serial or random effects as outlined by Zeger and Liang [6], Thall and Vail [7], Laird and Ware [8], Sutradhar [9] and Sutradhar and Jowaheer [10].…”

Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data

“…In time series settings, Zhu () proposed an integer‐valued generalized autoregressive conditional heteroscedastic model with CMP distribution. Mamode Khan et al () introduced an observation‐driven integer‐valued moving average model of order 1 (INMA(1)) with CMP innovations under non‐stationary moment conditions. Despite this last model includes the thinning operator considering the serial correlation, it is more appropriate for low counts.…”

“…Although the models proposed by Zhu () and MacDonald and Bhamani () are able to model underdispersion and overdispersion, they do not include covariates. The model proposed by Mamode Khan et al () includes regressors, but the mean is not directly modeled, leading to a complicate interpretation of parameters. For the proposed model in this article, the mean of the conditional distribution is directly modeled, making the model parameters easily interpretable.…”