Skip to main content

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.
Labels:

Comments

  1. Andy PeytchevJanuary 13, 2013 at 7:43 AM

    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!

    ReplyDelete
    Replies
    1. James WagnerJanuary 14, 2013 at 1:20 PM

      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.

      Delete
    2. Andy PeytchevJanuary 15, 2013 at 11:29 AM

      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."

      Delete
  2. www.peterlugtig.comJanuary 22, 2013 at 4:01 PM

    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.

    ReplyDelete

Post a Comment

Popular posts from this blog

Tailoring vs. Targeting

One of the chapters in a recent book on surveying hard-to-reach populations looks at "targeting and tailoring" survey designs. The chapter references this paper on the use of the terms among those who design health communication. I thought the article was an interesting one. They start by saying that "one way to classify message strategies like tailoring is by the level of specificity with which characteristics of the target audience are reflected in the the communication." That made sense. There is likely a continuum of specificity ranging from complete non-differentiation across units to nearly individualized. But then the authors break that continuum and try to define a "fundamental" difference between tailoring and targeting. They say targeting is for some subgroup while tailoring is to the characteristics of the individual. That sounds good, but at least for surveys, I'm not sure the distinction holds. In survey design, what would constitute
36 comments
Read more

What is Data Quality, and How to Enhance it in Research

  We often talk about “data quality” or “data integrity” when we are discussing the collection or analysis of one type of data or another. Yet, the definition of these terms might be unclear, or they may vary across different contexts. In any event, the terms are somewhat abstract -- which can make it difficult, in practice, to improve. That is, we need to know what we are describing with those terms, before we can improve them. Over the last two years, we have been developing a course on   Total Data Quality , soon to be available on Coursera. We start from an error classification scheme adopted by survey methodology many years ago. Known as the “Total Survey Error” perspective, it focuses on the classification of errors into measurement and representation dimensions. One goal of our course is to expand this classification scheme from survey data to other types of data. The figure shows the classification scheme as we have modified it to include both survey data and organic forms of d
Post a Comment
Read more

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 assu
4 comments
Read more