Skip to main content

Imputation and the Impact of Nonresponse


I've been thinking about the evaluation of the risk of nonresponse bias a bit lately. Imputation seems to be a natural way to evaluate those risks. In my setup, I impute the unit nonresponders. Then I can use imputation to evaluate the value of the data that I observed (a retrospective view) and to predict the value of different parts of the data that I did not/have not yet observed (a prospective view).

Allow me to use a little notation. Y_a is a matrix of observed data collected under protocol a. Y_b is a matrix of observed data collected under protocol b. Y_m is the matrix of data for the nonresponders. It's missing. I could break Y_m into two pieces: Y_m1 and Y_m2.


1) Retrospective. I can delete data that I observed and impute the values plus all the other missing values (i.e. the unit nonresponse). I can impute Y_b and Y_m conditional on Y_a. I can also impute Y_m conditional on Y_b and Y_a. It might be interesting to compare the estimates from these two procedures to see if protocol b has added much.

2) Prospective. In this case I can use a nested imputation procedure to predict the impact of each piece on the fraction of missing information (see Harel and Stratton, 2009). If I impute Y_m1 conditional on Y_a and Y_b, and then Y_m2 conditional on Y_a, Y_b, and Y_m1, I can then break the estimated FMI into components due to Y_m1 and Y_m2. In this way I can predict which cases are more valuable in the sense of contributing more to the information.
Labels:

Comments

Post a Comment

Popular posts from this blog

Assessment of Maching Learning Classifiers

I heard another interesting episode of the Data Skeptic podcast . They were discussing how a classifier could be assessed (episode 121). Many machine learning models are so complex that a human being can't really interpret the meaning of the model. This can lead to problems. They gave an example of a problem where they had a bunch of posts from two discussion boards. One was atheist and the other board was composed of Christians. They tried to classify each post as being from one or the other board. There was one poster who posted heavily on the Christian board. His name was Keith. Sadly, the model learned that if the person who was posting was named Keith, then they were Christian. The problem is that this isn't very useful for prediction. It's an artifact of the input data. Even cross-validation would eliminate this problem. A human being can see the issue, but a model can't. In any event, the proposed solution was to build interpretable models in local areas of t...
3 comments
Read more

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 f...
1 comment
Read more