Small area estimation under a multivariate linear model for repeated measures data

Abstract

In this article, Small Area Estimation under a Multivariate Linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points and per group units are derived. A parametric bootstrap method is proposed for estimating the mean-squared errors of the predicted small area means. Results are supported by a simulation study.

Small-area estimation with missing data using a multivariate linear random effects model

“….I k Þ : k  mk captures all k group units by stacking as column blocks the m data matrices of model (1) together in a new matrix and is included in the model for technical issues of estimation. More details about model formulation and estimation of model parameters can be found in Ngaruye et al (2017).…”

“…We will in this section consider the multivariate linear regression model for repeated measurements with covariates at p timepoints suitable for discussing the SAE problem, which was defined by Ngaruye et al (2017), when data are complete. It is supposed that the target population of size N, whose characteristic of interest y is divided into m subpopulations called small areas of sizes N d , d ¼ 1; .…”

“…Most surveys are conducted continuously in time based on cross-sectional repeated measures data. There are also some works related to time series and longitudinal surveys in small-area estimation, for example, one can refer to Consortium (2004), Ferrante and Pacei (2004), Nissinen (2009), Singh and Sisodia (2011) and Ngaruye et al (2017). In Ngaruye et al (2017), the authors have proposed a multivariate linear model for repeated measures data in a SAE context.…”

“…There are also some works related to time series and longitudinal surveys in small-area estimation, for example, one can refer to Consortium (2004), Ferrante and Pacei (2004), Nissinen (2009), Singh and Sisodia (2011) and Ngaruye et al (2017). In Ngaruye et al (2017), the authors have proposed a multivariate linear model for repeated measures data in a SAE context. The model is a combination of the classical growth curve model (Potthoff and Roy 1964) and a random effects model.…”

Contributions to Small Area Estimation: Using Random Eects Growth Curve Model

“…For estimation and prediction of model parameters in model (2.12), we may refer to Ngaruye et al (2016).…”