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How can we estimate "e"?

AAPOR defines response rates that include an adjustment factor for cases that have unknown eligibility at the end of the survey. They call the factor "e". Typically, people use the eligibility rate from the part of the sample where this variable (eligible=yes/no) is observed. This estimate is sometimes called the CASRO estimate of e.

But in a telephone survey, this estimate of "e" is likely to be biased upwards for the unknown part of the sample. Many of the cases that are never contacted are not households. They are simply numbers that will ring when dialed, but are not assigned to a household. These cases are never involved in estimates of "e".

A paper in POQ (Brick and Montaquila, 2002) described an alternative method of estimating e. They use a survival model. This lowers estimates of e relative to the CASRO method. But it's still upwardly biased since many of the noncontacts could never be contacted.

I like the survival method since it's closer to reality. But, for other reasons, I started imputing eligibility. I like this approach as it develops a nice range of estimates. And it allows great flexibility. It's very easy to include covariates in the model. It's not as easy to include covariates in the survival model.
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  1. Andy PeytchevOctober 29, 2009 at 2:05 PM

    I like this, James, and may even try it too. I am wary of how it can be used, as simple model misspecification can lead to more bias in "e" that through the biased estimation using those for whom eligibility is established. Maybe I am wrong, but I have not thought about how to specify such a model enough. I guess I suspect that using number of calls, for example, may lead to a downward bias in "e".

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  2. JamesOctober 31, 2009 at 2:22 PM

    I would argue that these sorts of models always overestimate "e". The problem is the set of numbers that will ring, but are not in fact assigned to households. Since none of these are ever resolved (even as nonsample), we apply the e from the other part of the sample to these cases.

    I think using the number of calls is similar to Brick and Montquilla's survival model, but you can also add covariates.

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