Large-scale surveys using complex sample designs are frequently carried out by government agencies. The statistical analysis technology available for such data is, however, limited in scope. This study investigates and further develops statistical methods that could be used in software for the analysis of data collected under complex sample designs. First, it identifies several recent methodological lines of inquiry which taken together provide a powerful and general statistical basis for a complex sample, structural equation modeling analysis. Second, it extends some of this research to new situations of interest. A Monte Carlo study that empirically evaluates these techniques on simulated data comparable to those in large-scale complex surveys demonstrates that they work well in practice. Due to the generality of the approaches, the methods cover not only continuous normal variables but also continuous nonnormal variables and dichotomous variables. Two methods designed to take into account the complex sample structure were investigated in the Monte Carlo study. One method, termed aggregated analysis, computes the usual parameter estimates but adjusts standard errors and goodness-of-fit model testing. The other method, termed disaggregated analysis, includes a new set of parameters reflecting the complex sample structure. Both of the methods worked very well. The conventional method that ignores complex sampling worked poorly, supporting the need for development of special methods for complex survey data.

* University of California, Los Angeles
** Universitat Pompeu Fabra, Barcelona