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Abstract:
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Principal Components Analyses are typically conducted without taking into account the sampling design. Controlling for variables that are part of the sample design may affect the interrelationship of variables in a manner that is difficult to interpret. Controlling for clusters, strata or probabilities of selection may affect the substance or the stability of the results. To examine this issue, PCAs were conducted for several random, cluster, and stratified designs using a database of zip code areas. Clustering diminished the sample's ability to reproduce the population PCA, with adjustments producing mixed results. Stratification with a similar number of units selected per stratum and proper weighting led to results at times better than random sampling in spite of inequality of weights. Simulations also indicated that stability of results is in part a function of sample design.
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