# Survey weights at multiple levels

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).

The weights only need to be used when trying to generate population estimates from the survey data. If you're interested in running behavioral models - as you seem to be - just use the raw data without the weights. As long as you've got a reasonable cross section of survey respondents in the sample that cover the behavioral responses of interest, and you're only estimating a single coefficient on each variable, the models should work out just fine.

• This is the direction I am now leaning in, as I don't really care about generalizing to the particular state this data comes from anyway. As you said, the model of behavior is of greater interest than estimating a population mean or something similar. – Casey Sep 29 '14 at 13:07
• Define reasonable. Household travel surveys are not always collected according to probability sampling designs; oftentimes, unfortunately, they are a haphazard collection of convenience units. – StasK Aug 10 '16 at 15:08

i think you're over-thinking it, but i could be wrong so i hope others answer as well. i believe you want to simply aggregate or disaggregate to the levels you're ultimately making statements about (and solely use the weights for that specific level). this is certainly what's done for most household-level surveys run by the united states federal government when results are tabulated, summarized, or regressed at the person-level.

the replication script on this r-language national household travel survey step-by-step instructions page includes some estimates at the different levels and matches ornl's official publications.

• Thanks for the response. However, I'm not sure this actually addresses my issue. As far as I have seen, both in the R script and in the official NHTS documentation, there are no examples where data from multiple levels (households, persons, trips) are combined into a single analysis, save for a few ratio calculations. As for aggregating/disaggretating to the unit of analysis (in my case, the trip), my understanding is that this is generally an inappropriate way to handle a multilevel data structure. – Casey Sep 26 '14 at 15:52
• hi @Casey, do you know why nhts would be different from other household-level surveys that collect person-level data? the us census and cdc run a lot of household surveys, and i guess i've never come across a recommendation to make this sort of adjustment before.. :/ – Anthony Damico Sep 26 '14 at 16:10
• I think there are some distinctions to be made. For example, the BRFSS only samples one person per household, so there is no clustering at that level (even though they do provide household weights). Also, the NHANES, in which more than one person per household can participate, only provides weights at the individual level (the weights only differ depending on the measurements that person did), so this issue of weights at different levels doesn't occur. – Casey Sep 29 '14 at 13:12
• Another point is that household travel surveys essentially do repeated measures on each person (the multiple trips per travel day) that are weighted. I am not aware of another national survey that has that same structure of measures>persons>households, with weights at each level. Of course, there are many surveys I have no familiarity with, so I'd be very interested in finding a similarly structured, weighted survey. – Casey Sep 29 '14 at 13:15
• some PUF data sets and the weights they provide: ACS- household & person; CPS- householder & person; MEPS- family & person; HRS- household & person; PSID- family & person. while i don't know any other PUFs that have 3+ sets of weights, i also don't understand why a special accommodation made when there are three sets of weights can be ignored for PUFs with two sets of weights? – Anthony Damico Sep 29 '14 at 14:29

You need to think clearly about the particular population that you are analyzing. There are several populations involved in a typical travel survey:

1. Households (and families, although these are technically different): groups of people, usually living together under the same roof, that share income, expenditures, decision making, and sometimes vehicles.
2. Individuals, nested within households.
3. Travel days, which can be defined for households (all the trips that all members of a HH take on a given day) or within individuals (all the trips that a given individual undertakes in a given day).
4. Vehicles, nested within households.
5. Unlinked trips -- an individual segment with a single transportation mode.
6. Linked trips -- a trip with a specified purpose undertaken by an individual or a group of individuals. An example could be

I drove to the metro station, parked the car, walked to the train station, took the train, took the bus, and walked two blocks from the bus to work.

That is six unlinked trips in four modes.

A complicated example could be

My wife, our kid and I took off from our house with a bike on the rack. We dropped the kid off at school, my wife walked her for two blocks from where we could stop. Then I dropped my wife at her gym, and she unloaded the bike to ride home. I then drove to the metro station where I parked the car and took the train to work. My wife rode the bike back home after her workout at the gym.

This involves two vehicles, three people, and eight or so unlinked trips.

1. There may also be an interest in streets or blocks as analysis units. If these are not sampled explicitly, they will likely have to be treated as domains or subpopulations in analysis.

Each of these populations may require separate weights. Typically, in a HHTS, the household will be enumerated, and everybody would be asked to list all the trips on a given day, so the additional weighting factors going from HH (population 1) to individuals (population 2) and their trips (populations 5 and 6) would be 1.

Frankly, I don't see particular need to go with the multilevel models a la Mplus. First off, none of the variables that you have would be normal, even remotely (du-uh). Second, weighting at multiple levels in mixed models has its own set of perils (Pfeffermann et. al. 1998). There are just way too many moving pieces each threatening to ruin your analysis. I would just run this as a regression or a GLM model with the weights appropriate for the population of interest, and correcting the standard errors for clustering within HH (or any stages of selection prior to HH).

In a somewhat related note, I wrote about joint weighting for household and person characteristics here.