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### Adaptive Design and Refusal Conversions

For me, the idea of adaptive design was influenced by work from the field of clinical trials on multi-stage treatments. Susan Murphy introduced me to adaptive treatment regimes as an approach to the problem. She points to methods developed in the field of reinforcement learning as useful approaches to problems of sequential decisionmaking.

Reinforcement learning describes some policies (i.e. a set of decision rules for a set of sequential decisions) as myopic. A policy is myopic if it only looks at the rewards available at the next step. I'm reading Decision Theory by John Bather right now. He uses an example similar to the following to demonstrate this issue. The following is a simple game. The goal is to get from the yellow square to the green square with the lowest cost. The number in each square is the cost of moving there.Diagonal moves are not allowed.

The myopic policy looks only at the next option and goes down a path that ends up with only expensive options to reach the target. The myopic policy is shown in the following picture:

The total cost is 7. The optimal policy looks for the sequence with the lowest cost (since the reward function in this game is to find the lowest cost path). The optimal policy starts out with a a more expensive move, but ends up overall less costly:

I find myself in a similar situation with the telephone experiment that I've been running. It is more efficient in the first step (before refusal conversions). But it is less efficient for refusal conversions. So much so that the overall efficiency is the same for the experimental and control groups.

On the other hand, maybe I can locate a policy for refusal conversions that will be better than either the current experimental or control methods. Even if I'm not able to find such a solution, I still think this is an interesting problem.

### "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…

### Goodhart's Law

I enjoy listening to the data skeptic podcast. It's a data science view of statistics, machine learning, etc. They recently discussed Goodhart's Law on the podcast. Goodhart's was an economist. The law that bears his name says that "when a measure becomes a target, then it ceases to be a good measure." People try and find a way to "game" the situation. They maximize the indicator but produce poor quality on other dimensions as a consequence. The classic example is a rat reduction program implemented by a government. They want to motivate the population to destroy rats, so they offer a fee for each rat that is killed. Rather than turn in the rat's body, they just ask for the tail. As a result, some persons decide to breed rats and cut off their tails. The end result... more rats.

I have some mixed feelings about this issue. There are many optimization procedures that require some single measure which can be either maximized or minimized. I think thes…