Interactive Linear Models in Survey Sampling

Considered is a linear 'interactive' model in the context of survey sampling. This situation arises when investi- gator and/or supervisor interventions are contemplated in the responses. An appropriate linear model is intro- duced to represent the response profile(s) arising out of each respondent-cum-investigator-cum-supervisor com- bination as per the planned 'design layout'. Two situations (blinded and unblinded submission of responses) are differentiated and corresponding data analysis techniques are discussed. Variance components are assumed to be known in this study. 1. Introduction to Survey Design and Interactive Linear Model Considered is the set-up of simple i.e., direct response on a quantitative response variable Y in the context of a finite labeled population of size N. It so happens that in actual surveys, we need investi- gators and often some supervisors as well. The instruction manuals are prepared for the investigators to maintain uniformity in data collection. The field level data are collected by the investigators. The scrutiny manual is prepared for scrutiny of the filled-in schedules by the supervisors. This is accom- plished independently of the investigators. We depict a situation wherein there are possibilities of investigator intervention effect and/or supervisor intervention effect on the response profiles before the same are finally received by the data collection agency. Of course, these intervention effects may be assumed to be random, having mean zero, non-interactive within and between the two sets of 'people'. The problem is to unbiasedly estimate the finite population total of the response vari- able Y by incorporating a fixed size (n) sampling design and by administering the sampling design in a situation wherein the above two types of random effects are likely to be present. Denote by i a respondent unit in the sample of size n and by S(i) the number of schedule-based observations collected on this particular unit. It is quite possible that a respondent unit is composed of more than one individual. In this article, we will deal with fixed-size non-overlapping clusters of individuals to represent such respondent units. These clusters are formed before the sampling