Al Quds university
"Fitting Variance Components Model and Fixed Effects Model for One-Way Analysis of Variance to Complex Survey Data"
This talk is concerned with fitting the statistical models: variance components model (two-stage model) and fixed effects model (one-stage model) for one-way analysis of variance under complex surveys (two-stage sampling, stratification, and unequal probability of selection, etc.). Classical theory underlying the use of two-stage model involves simple random sampling for each of the two stages. In such cases the model in the sample is the same as modeled for the population. When the selection probabilities are related to the values of the response variable, the sample design is defined as informative. This may result in selection bias and, consequently, the model holding for the sample is then different from the model holding in the population. Thus standard estimates of the population model parameters may be severely biased, leading possibly to false inference. The idea behind the proposed approach is to extract the model holding for the sample data as a function of the model in the population and the first order inclusion probabilities, and then fit the sample model using analysis of variance, maximum likelihood, and pseudo maximum likelihood approaches. The main feature of the proposed techniques is related to their behaviour in terms of the informativeness parameter. We also show that the use of the population model, that ignores the informative sampling design, yields biased fitting.