### What is a "response propensity"?

We talk a lot about response propensities. I'm starting to think we actually create a lot of confusion for ourselves by the way we sometimes have these discussions. First, there is a distinction between an actual and an estimated propensity. This distinction is important as our models are almost always misspecified. It is probably the case that important predictors are never observed -- for example, the mental state of the sampled person at the moment that we happen to contact them. So that the estimated propensity and true propensity are different things.

The model selection choices we make can, therefore, have something of an arbitrary flavor to them. I think the choices we make should depend on the purpose of the model. We examined in a recent paper on nonresponse weighting whether call record information, especially the number of calls and refusal indicators, were useful predictors of response propensities for this purpose. It turns out that these variables were strong predictors of response, but just added noise to the weights since they were unrelated to many of the survey variables. I think this reflects that the fact that the survey process is noisy -- lots of variation in recruitment strategies (e.g timing of calls varies across cases, interviewers vary), unobserved mental states of sampled persons, and possibly measurement error in the paradata.

Once considering the purpose, we might think of model selection very differently. I think this is true for adaptive designs that base design features upon these estimated response propensities. Here, I think it makes sense to identify predictors in these models that are also related to the survey outcome variables. Like the post-survey adjustment example, I think this gives us the best chance to control potential nonresponse biases.

Back to the original problem I raised, I think discussion of generic response propensities might lead us astray from this goal. It can be easy to forget that their are important modeling choices and the way we make those choices will impact our potential results.

### "Responsive Design" and "Adaptive Design"

My dissertation was entitled "Adaptive Survey Design to Reduce Nonresponse Bias." I had been working for several years on "responsive designs" before that. As I was preparing my dissertation, I really saw "adaptive" design as a subset of responsive design.

Since then, I've seen both terms used in different places. As both terms are relatively new, there is likely to be confusion about the meanings. I thought I might offer my understanding of the terms, for what it's worth.

The term "responsive design" was developed by Groves and Heeringa (2006). They coined the term, so I think their definition is the one that should be used. They defined "responsive design" in the following way:

1. Preidentify a set of design features that affect cost and error tradeoffs.
2. Identify indicators for these costs and errors. Monitor these during data collection.
3. Alter the design features based on pre-identified decision rules based on the indi…

### Future of Responsive and Adaptive Design

A special issue of the Journal of Official Statistics on responsive and adaptive design recently appeared. I was an associate editor for the issue and helped draft an editorial that raised issues for future research in this area. The last chapter of our book on Adaptive Survey Design also defines a set of questions that may be of issue.

I think one of the more important areas of research is to identify targeted design strategies. This differs from current procedures that often sequence the same protocol across all cases. For example, everyone gets web, then those who haven't responded to  web get mail. The targeted approach, on the other hand, would find a subgroup amenable to web and another amenable to mail.

This is a difficult task as most design features have been explored with respect to the entire population, but we know less about subgroups. Further, we often have very little information with which to define these groups. We may not even have basic household or person chara…

### An Experimental Adaptive Contact Strategy

I'm running an experiment on contact methods in a telephone survey. I'm going to present the results of the experiment at the FCSM conference in November. Here's the basic idea.

Multi-level models are fit daily with the household being a grouping factor. The models provide household-specific estimates of the probability of contact for each of four call windows. The predictor variables in this model are the geographic context variables available for an RDD sample.

Let $\mathbf{X_{ij}}$ denote a $k_j \times 1$ vector of demographic variables for the $i^{th}$ person and $j^{th}$ call. The data records are calls. There may be zero, one, or multiple calls to household in each window. The outcome variable is an indicator for whether contact was achieved on the call. This contact indicator is denoted $R_{ijl}$ for the $i^{th}$ person on the $j^{th}$ call to the $l^{th}$ window. Then for each of the four call windows denoted $l$, a separate model is fit where each household is assum…