Pooling and Selection Methods Sample Clauses

Pooling and Selection Methods. Suppose data on the vector of predictors (X) has been collected on N subjects, but that the budget permits only n lab assays (n < N ) for assessment of the response Y . The simplest way to reduce the number of assays is to randomly select n specimens for inclusion in the analysis. Another strategy is to randomly allocate each of the N specimens into one of n equal-sized pools, so that all (or essentially all) specimens are included in the analysis. Given that the predictor (X) data are available on each subject prior to pooling, however, substantial gains in efficiency relative to these random strategies are possible when this information is applied to the selection or pooling process. Based on the WLS models presented in Section 2.2, an optimal pooling or selection strat- egy with respect to efficient estimates of the coefficient vector β would minimize V ar(βˆp) for all p = (1, . . . , P ), where P is the total number of predictors. In the case of SLR, P = 1, so this simplifies to minimizing ΣV ar(β ) =1 i=1 σ2 wi(xi — x¯w )2 , (2.1) Σ Σ where wi is the weight corresponding to observation i and x¯w = ( wi)−1( wixi) is the weighted mean. 2.3.1 “Smart” Selection 2.3.2 “Smart” Pooling j=1 size), and the components in the denominator of (2.1) are defined as xi = 1 Σki xij and i=1 N i=1 j=1