### Reflecting the Uncertainty in Design Parameters

I've been thinking about responsive design and uncertainty. I know that when we teach sample design, we often treat design parameters as if they were known. For example, if I do an optimal allocation for a stratified estimate, I assume that I know the population element variances for each stratum. The same thing could be said about response rates, which relate to the expected final sample size.

Many years ago, the uncertainty might have been small about many of these parameters. But responsive design became a "thing" largely because this uncertainty seemed to be growing. The question then becomes, how do we acknowledge and even incorporate this uncertainty into our designs? Especially responsive designs.

It seems that the Bayesian approach is a natural fit for this kind of problem. Although I can't find a copy online, I recall a paper that Kristen Olson and Trivellore Raghunathan presented at JSM in 2005. They suggested using a Bayesian approach to update estimates of the required sample size to reach a targeted number of interviews when you are uncertain about layers of response and eligibility rates.

This is a really nifty idea. I think it has broader application than just setting the sample size. There are a lot of parameters, even cost parameters, about which we lack certainty. The approach might be vary helpful in even thinking about the consequences of this uncertainty (e.g. worst case scenarios, best case scenarios, etc.)

### "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…

### 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…

### 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…