In many situations there is interest in parameters (e.g., mean) associated with the response distribution of individual clusters in a finite clustered population. We develop predictors of such parameters using a two-stage sampling probability model with response error. The probability model stems directly from finite population sampling without additional assumptions and thus is design-based. T...

SUMMARY The polya posterior gives a noninformative Bayesian justification for various single-stage sampling procedures. Here this type of reasoning is extended to two-stage cluster sampling problems. The frequency properties of the resulting procedures are studied.

Synthetic populations are used to study methods for adapting Efron’s bootstrap estimation technique to finite population sampling. Of particular interest is the extention of these methods to two-stage cluster sampling. Using simulations based on five artificial populations, two variations of bootstrap estimators and two Taylor series variance estimators for a ratio estimator are compared by mea...

The precision of parameters estimation are determined by the sample size and the sampling design used in a study. Due to such practical constraints as the budget and manpower, most large-scale educational studies would not adopt the simple random sampling design. TIMSS 2007 used a two-stage stratified cluster sampling design. In the first stage, about 150 schools were selected according to some...

To evaluate the performance of the empirical predictors presented in San Martino et al. (2005), we compute the cases where they are the best, “equivalent” to the best (tables 1) or poor (table2). We consider only the case of equal unknown within cluster variances. First, we consider the cases in which each of the proposed predictors has the best performance, i.e. we compute the percentage of ca...

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Best linear unbiased predictors developed from mixed models are widely used, but their development requires distributional assumptions or an infinite population frame...