### 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 assumed to have its own intercept which is from a $N(0,\sigma^{2}_{il})$ distribution. The model is estimated:

$Pr ( R_{ijl} = 1 ) = logit^{-1} ( \beta_{0l} + \beta_{0il} + \sum_{j=1}^{k} \beta_{jl} X_{ijl})$

The next step is to compare the estimated contact probabilities within a household and find the window with the highest probability of contact for that household. In that window, the case -- along with all other cases that meet this criterion -- will be sorted to the top of list by the call scheduling algorithm. Under this approach, a case with a low probability of contact could be sorted to the top of the list in any given call window, as long as the estimated probability of contact was highest for the case within that window.

The experimental design required frequent sorting of the list as the call windows were specific to the time zone. For example, on a Tuesday, the list was sorted first thing in the morning, at 5pm EST, 6pm EST, 7pm EST, and at 8pm EST as the various time zones crossed the call window boundary. The experimental design required that the experimental and control groups be sorted in an intervleaving fashion. The past practice had been to sort at the beginning of the day. The sort was based on sorting more promising cases to the top -- cases with more contacts, selected respondents, number of calls and so on.

So far, the experiment has been going well. In the first month, the contact rate for the experimental group had a 15% increase relative to the control group.

### 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…