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### Degrees of NMAR

I've been working on a paper on nonresponse bias. As part of the setup, we describe the MAR and NMAR mechanisms first defined by Little and Rubin. In short, Missing-at-Random means we can fix the bias due to the missingness using the available data. While Not-Missing-at-Random means we can't repair the bias with the available data.

It can be hard to discuss the problem with this divide. We were looking at situations where the bias could be smaller and it could be bigger. The NMAR/MAR distinction doesn't capture that very well. There is another formulation that is actually pretty good for discussing different degrees of bias remaining after adjustment. It's due to the following article (I couldn't find it online):

Kalton, G. and D. Kasprzyk (1986). "Treatment of missing survey data." Survey Methodology 12: 1-16.

They define bias as having two components: A and B. One of the components is susceptible to adjustment and the other is not. In some situations, you can reduce the bias due to A and there will still be the bias due to B. In other situations, by adjusting for A you can actually increase the bias (i.e. when A and B are equal and in opposite directions).

In any event, I think this is useful for talking about bias as it gives us a way to talk about more or less biased that the NMAR/MAR distinction does not.

### Comments

1. This is a very interesting point, James. Kristen and Frauke's simulations in Sociological Methods & Research make a similar point. I wonder, however, about the implications. I think it would still be preferable to adjust for A even if it leads to greater bias, for at least three reasons. First, with respect to nonresponse variance, adjusting for A should decrease it. Especially if one considers a longitudinal survey where the key estimates of change. Second, adjusting for A may increase bias in estimates of one variable, but decrease it for estimates of other variables. Third, we rarely have much information for adjustments, so we try to use as much as we can. And seldom the ability to evaluate the impact on bias (i.e., a gold standard). Maybe the import of these findings is if there can be particular adjustment variables that can be identified to exacerbate bias in multiple surveys. I really look forward to seeing your article!

1. My main point was just as a way of thinking about the issue. In the real world, it's probably too simple to say it's either biased or it's not. Usually, it's more or less biased. We need a way to talk about the more or less part.

The simulations that I did were interesting and in a way comforting. These were done with real survey data. In most cases, the bias was either A or B. The two weren't mutually present. The end result was that you could either fix it almost completely, or you couldn't do anything about it. I didn't see any "pathological" situations where the adjustments made the bias worse.

2. Interesting! I really look forward to seeing what you found in more detail. I completely agree on talking about more or less bias in estimates, but still see statements like this one in a report I am reading right now: "To the extent that non-response is associated with age, sex and region, the adjustment will remove non-response bias."

2. Hi James,
I am a frequent reader of your blog, thanks for your posts! I think this is an interesting point in many ways. First, the missing data field seems to be dominated by "missing data people", who generally don't care about the extent of bias at all. So it's good if we, being "survey people" bring bias into the story. Second, I think that once you talk about bias, and missing data corrections, it is important to look at the effect of the corrections on both bias and variances. And I agree with Andy that it is usually better to correct, even if one knows that missingness is NMAR. In that case, missingness usually exists of multiple components. A MAR part and a NMAR part. And it is usually worthwhile to fix the bit you can fix, even if that appears to worsen your overall bias.

### "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…