Sample size estimation for HB CBC

Question

Hi
Is there any rule of thumb for minimum sample size for CBC/HB like the one Johnson gave for aggregate full profile CBC?

Thanks

Answer 1

Robin,

Not really.  We typically use rules of thumb that were developed for aggregate logit modeling:  the one you mention or the rule where we want to limit the standard errors of main effects to 0.05 and of interactions to 0.10.  

We recognize that both of these were written for a different model than HB, but they seem to work well in that new context.  

Another criterion I like to think about is the effect of my sample size on my simulations.  Simulated shares are (approximately) proportions, so from sampling theory we know that sample sizes of 100 have margins of error of about 9.8 percentage points, while samples of 400 have margins of error of about 4.9 percentage points and so on.  Then I work back from what kind of accuracy I need to have in my simulator to come up with a sample size.

If you want to get really complicated there are formulas you can use to estimate your sample size but they require that you have estimates of what the utilities are before you can use them.

Comments

Hello Keith,

Is below formula also valid for fixed design?
(p(1-p)/n)^0.5

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Is below formula also valid for fixed design?
(p(1-p)/n)^0.5

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Robin,

Yes, this formula for the precision of simulations would work as well for a fixed design as for any other.

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How do you use 0.05 and 0.1 standard error to calculate estimated sample size?

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Robin, we create an artificial data set of random responders to complete the survey, then we run the analysis and check the size of the standard errors.  This is built in to our software, but it's something you can do on your own, too.  Then you can use a sample size with the size of your standard errors in mind.