Interpretation of MXL Standard Errors using weighting

[mweir]

Hi,
I am exploring the use of sample weights so that the results of a current study may be interpreted as more generalizable. The study uses a DCE to measure seafood preferences. I used CDC NHANES data to calculate appropriate sample weights using equivalent data. There are two questions I have which may be more general but hopefully someone can point me in the right direction.

1) The sample weights are very large which caused issues with convergence. I rescaled the weights (dividing by powers of 10) until the models converged. This doesn't feel right to me and I'm concerned the weights may not be doing there job correctly. The weights still have the same relative relationship to one another but is that enough to achieve the goal of a "representative" result?

2) Within this line of thought, can the standard errors be interpreted as usual when using weights in MXL estimation? From what I've read so far about use of sample weights, the standard errors from conventional estimation seem useless for direct interpretation. If this is the same for MXL is there a recommendation for obtaining correct standard errors within Apollo's framework?

Thanks for your input.

Mike

[stephanehess]

Hi Mike

in general, I am not a fan of using weights in estimation. It implies that some choices are more important than others. It's much better to use interactions with socio-demographics that relate to the variables along which the data is not representative, and then to reweight your results.

Re standard errors, weighted estimation indeed affects your standard errors, and there is no correction implemented for that

Stephane

[mweir]

Thank you for the reply! This is a curiosity more than anything, but I'm wondering if the following procedure makes sense and also might result in consistent standard errors. Admittedly, this is more of an intuitive exercise that may not hold any water.

1) Estimate/obtain sample weights using typical methods
2) Calculate the following proportion : weight_i/sum(weight_i)
- As I interpret this, this would be an individuals "unique contribution" to the representativeness of the sample
3) Scale the proportion obtained above by the final sample size, N
4) use values calculated in step 3 as the sample weights
- Again based on my interpretation of how weights enter the likelihood function in Apollo, this should still achieve the affect of giving more (less)representative data more (less) weight without artificially inflating sample size.

In my test of this, the standard errors are all very similar (even identical in some cases) to the unweighted model though with different point estimates of the mean of random parameters.

This may be a fluke that the standard errors were similar but wondering if there is something to this process. Apologies if I'm way off base. I appreciate your input.

Mike

[stephanehess]

That's simply ensuring that the weights sum to N, but the same issues remain. It's much better to just incorporate interactions, and then reweight your results