Prediction approach in repeated measurement surveys: A methodological exploration

Abstract

In biological and life sciences, including fields like agriculture and medicine, we frequently encounter data with repeated measures. Repeated measures indicate that measurements have been taken on the same individual unit multiple times, either over time or across space. If a population contains repeated measures, there will necessarily be correlation within that population. Analyzing data with a repeated measures structure requires special consideration because it can invalidate standard analysis of variance techniques. This project investigates a prediction approach that has not been previously explored in the presence of intraclass correlation within the population. In this study, we attempt to predict the population total by drawing samples from a repeated measures population using Probability Proportional to Size with Replacement (PPSWR). The prediction approach outlined by Brewer (1963) and Royall (1970) is employed. The estimates of variance (σ²) and intraclass correlation coefficient (ρ) are obtained through analysis of variance (ANOVA) by fitting a one-way random effects model and equating the mean squares (MS) to the expected mean squares (EMS).