Confidence interval of parameters in multiresponse multipredictor semiparametric regression model for longitudinal data based on truncated spline estimator

Abstract

In this paper, we provide a theoretical discussion on estimating confidence interval of parameters in a multiresponse multipredictor semiparametric regression (MMSR) model for longitudinal data. The MMSR model consists of two components namely a parametric component and a nonparametric component. In consequently, estimating the MMSR model is equivalent to estimating the parametric and nonparametric components. Estimating the parametric component is equivalent to estimating parameters of the model, while estimating the nonparametric component is estimating unknown smooth function. In this paper, we estimate the parametric and nonparametric components using a weighted least square method and a smoothing technique namely truncated spline, respectively. Next, we estimate the confidence interval of parameters in the MMSR model using pivotal quantity and Lagrange multiplier functions. The results of this study can be applied to the Covid-19 data that is to model the case growth rate (CGR) and case fatality rate (CFR) of Covid-19 which are influenced by many variables including comorbid, age, gender, temperature, self-isolation, isolation in hospital, and others.