I've been worrying about how to use information about the number of calls in propensity models for a while. To me, it seems that you shouldn't expect simple, linear relationships between the number of calls and the propensity of response. The distance between 1 and 2 calls, is greater than the distance between 12 and 13 calls. Maybe some kind of transformation (natural logarithm) can patch that up.
But I recently saw a presentation (at the International Statistical Institute conference in Dublin) by Paul Biemer, Patrick Chen, and Kevin Wang from RTI. They found that there were reporting errors in the call records. Interviewers didn't record when they drove by housing units and saw that no one was home. They also sometimes didn't record calls since they had limits on the number of calls they could place on any housing unit. I'm sure these errors are endemic in many/all face-to-face surveys. Biemer and his colleagues also demonstrated how these errors can bias results that use the call records for adjustment purposes. Ouch.
This is very useful to know. But it also opens up another can of worms. My first question is, what's going to be easier? Improving call records, or developing more complex models involving call records that account for measurement error?