The default approach to dealing with missing data in most statistical software packages is listwise deletion–dropping any case with data missing on any variable involved anywhere in the analysis. It also goes under the names case deletion and complete case analysis.
Although this approach can be really painful (you worked hard to collect those data, only to drop them!), it does work well in some situations. By works well, I mean it fits 3 criteria:
– gives unbiased parameter estimates
– gives accurate (or at least conservative) standard error estimates
– results in adequate power.
But not always. So over the years, a number of ad hoc approaches have been proposed to stop the bloodletting of so much data. Although each solved some problems of listwise deletion, they created others. All three have been discredited in recent years and should NOT be used. They are:
Pairwise Deletion: use the available data for each part of an analysis. This has been shown to result in correlations beyond the 0,1 range and other fun statistical impossibilities.
Mean Imputation: substitute the mean of the observed values for all missing data. There are so many problems, it’s difficult to list them all, but suffice it to say, this technique never meets the above 3 criteria.
Dummy Variable: create a dummy variable that indicates whether a data point is missing, then substitute any arbitrary value for the missing data in the original variable. Use both variables in the analysis. While it does help the loss of power, it usually leads to biased results.
There are a number of good techniques for dealing with missing data, some of which are not hard to use, and which are now available in all major stat software. There is no reason to continue to use ad hoc techniques that create more problems than they solve.
To increase power:
- Increase alpha
- Conduct a one-tailed test
- Increase the effect size
- Decrease random error
- Increase sample size
Sound so simple, right? The reality is that although these 5 ways all work (more…)
Some approaches to missing data work well in some situations, but perform very poorly in others. So it’s really important to get a good idea of the type and pattern of missingness in your data. You may even take different missing data approaches to different variables.
Matt Blackwell of the Harvard Social Science Statistics blog has come up with a nice way to visualize the missingness patterns in a data set. (I’m a big fan of graphing data to understand it). He calls it a Missingness Map.
The only drawback seems to be that it will be cumbersome for large data sets.
Most Multiple Imputation methods assume multivariate normality, so a common question is how to impute missing values from categorical variables.
Paul Allison, one of my favorite authors of statistical information for researchers, did a study that showed that the most common method actually gives worse results that listwise deletion. (Did I mention I’ve used it myself?) (more…)
I was recently asked about whether it’s okay to treat a likert scale as continuous as a predictor in a regression model. Here’s my reply. In the question, the researcher asked about logistic regression, but the same answer applies to all regression models.
1. There is a difference between a likert scale item (a single 1-7 scale, eg.) and a full likert scale , which is composed of multiple items. If it is a full likert scale, with a combination of multiple items, go ahead and treat it as numerical. (more…)
In choosing an approach to missing data, there are a number of things to consider. But you need to keep in mind what you’re aiming for before you can even consider which approach to take.
There are three criteria we’re aiming for with any missing data technique:
1. Unbiased parameter estimates: Whether you’re estimating means, regressions, or odds ratios, you want your parameter estimates to be accurate representations of the actual population parameters. In statistical terms, that means the estimates should be unbiased. If all the (more…)
