Sutradhar, Brajendra C.; Warriyar, K. V. Vineetha; Zheng, Nan Inference in semi-parametric dynamic models for repeated count data. (English) Zbl 1373.62162 Aust. N. Z. J. Stat. 58, No. 3, 397-434 (2016). Summary: This paper deals with a longitudinal semi-parametric regression model in a generalised linear model setup for repeated count data collected from a large number of independent individuals. To accommodate the longitudinal correlations, we consider a dynamic model for repeated counts which has decaying auto-correlations as the time lag increases between the repeated responses. The semi-parametric regression function involved in the model contains a specified regression function in some suitable time-dependent covariates and a non-parametric function in some other time-dependent covariates. As far as the inference is concerned, because the non-parametric function is of secondary interest, we estimate this function consistently using the independence assumption-based well-known quasi-likelihood approach. Next, the proposed longitudinal correlation structure and the estimate of the non-parametric function are used to develop a semi-parametric generalised quasi-likelihood approach for consistent and efficient estimation of the regression effects in the parametric regression function. The finite sample performance of the proposed estimation approach is examined through an intensive simulation study based on both large and small samples. Both balanced and unbalanced cluster sizes are incorporated in the simulation study. The asymptotic performances of the estimators are given. The estimation methodology is illustrated by reanalysing the well-known health care utilisation data consisting of counts of yearly visits to a physician by 180 individuals for four years and several important primary and secondary covariates. Cited in 6 Documents MSC: 62G08 Nonparametric regression and quantile regression 62G20 Asymptotic properties of nonparametric inference 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62P10 Applications of statistics to biology and medical sciences; meta analysis Keywords:consistency of the estimators; dynamic model for repeated counts; improved efficiency; mean squared error consistency and efficiency; nonparametric function; non-stationary correlations; semiparametric generalised quasi-likelihood estimation; semiparametric regression model PDFBibTeX XMLCite \textit{B. C. Sutradhar} et al., Aust. N. Z. J. Stat. 58, No. 3, 397--434 (2016; Zbl 1373.62162) Full Text: DOI