I'll try to be concise and up to the point:
Problem: estimate income elasticities for various products from household survey data.
Given: I have to big complex household survey datasets that uses two stage stratified sampling. However, I have the design specified (strata variable) for only one, and replicate weights for the other data set.
The idea: is to estimate some for of a regression
expenditure_for_product ~ household's income and then use the coefficients to estimate it's elasticity
What is unclear: To estimate simple statistics as mean expenditure for a product or its S.E. one has to properly account for the survey design (especially for variance estimation). But I am not sure how if at all I need to adjust it in my regression case because the literature survey in fact does not provide a clear answer ( whether the weights (and correspondingly the survey design) should be used in my regression case)
Software: there is in fact R package
survey which is capable of incorporating (not sure exactly how, as help files does not specify or I can't locate it) the survey design into regressions but this of course does not mean I actually need to do it in my case.
A small digression: For example, say that
log(expenditure_for_product) ~ log(household's income) captures the relationship nicely. In that case, the regression coefficient would be all that I need. However, as there are many zero purchases reported by households for goods, I cannot model it in logs. I had an idea of aggregating the data into percentiles so that there would be 100 points with
(average income of x percentile, average expenditure for some product of x percentile). But how can if at all should adjust this idea for survey design to get correct estimates?
In essence: In essence I am looking for a theoretically correct* way to calculate income elasticities given complex household survey data and thus references on this matter or suggestions would be very helpful.
*Note, I cannot incorporate price effects because I do not have price information available, so I realize that it will not be too precise.