I am dealing with some data from a household travel survey, and I have a question about how to best use the survey weights that are provided. The structure is that households are sampled, and all individuals in the household are asked to complete a travel diary for 1 day. Each individual records all trips during that 24 hour period. So in a basic sense, trips are nested within individuals, who are nested within households.The data contractor supplies three weights with the dataset: a household weight, a person weight, and a trip weight.
Now, I'd like to merge the household, person and trip files to run some analyses. My confusion stems from the fact that I want to include variables from each of these levels in my main model. For example, say I want to know the association between type of vehicle used for a given trip and the distance traveled on that trip, while adding a person's age and total household income as covariates, plus the interaction between age and vehicle used. So variables from all three levels are included. Without weights, this is clearly a 3-level model and I could run it as a multilevel model, but since there are weights, how should this be structured? Do I run as a one level model using the trip weight (since that is the lowest level of analysis)? Or does it have to be structured as a multilevel model while also including the survey weights at each level? I had originally figured the latter, but then read that there isn't really any method available to run weighted three level models with a categorical dependent variable, which I will be using in my analyses (end of 1st paragraph, Mplus User's Guide v7, pg 252).