Complex survey data is that typically found produced by the National Center for Health Statistics (NCHS) or the NSLY; it typically contains information on PSU, strata, and weights. To make nationally representative samples, one would traditionally perform a weighted regression that accounts for the sampling design by Taylor linearization (i.e. the survey analog to Huber-White errors).
I'm interested in matched analyses (e.g., King's MatchIt program) as a manner in which to improve causal inference. What remains unclear from a first look is: (1) what criteria should be used to determine when matched analyses are appropriate with complex survey data; and (2) how such matched analyses ought to account for weights and/or survey sampling.
My understanding of (1) is that there is nothing different about these analyses than any other, but that it might/must improve inference and efficiency when the number of matched cases is small. As regards (2), my understanding is that common recommendations suggest including weights, and not the sampling design, in the matching (e.g., a weighted logistic regression to develop propensity scores) and not the later causal inference.
Should the sampling structure (e.g., PSU, strata) not be taken into account? Any references, suggestions, confirmations, or contradictions of what is above would be welcomed.
