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missing data mechanism

Multiple Imputation in a Nutshell

by Karen Grace-Martin  1 Comment

Updated 9/20/2021

Imputation as an approach to missing data has been around for decades.

You probably learned about mean imputation in methods classes, only to be told to never do it for a variety of very good reasons. Mean imputation, in which each missing value is replaced, or imputed, with the mean of observed values of that variable, is not the only type of imputation, however.

Two Criteria for Better Imputations

Better, although still problematic, imputation methods have two qualities. They use other variables in the data set to predict the missing value, and they contain a random component.

Using other variables preserves the relationships among variables in the imputations. It feels like cheating, but it isn’t. It ensures that any estimates of relationships using the imputed variable are not too low. Sure, underestimates are conservatively biased, but they’re still biased.

The random component is important so that all missing values of a single variable are not exactly equal. Why is that important? If all imputed values are equal, standard errors for statistics using that variable will be artificially low.

There are a few different ways to meet these criteria. One example would be to use a regression equation to predict missing values, then add a random error term.

Although this approach solves many of the problems inherent in mean imputation, one problem remains. Because the imputed value is an estimate–a predicted value–there is uncertainty about its true value. Every statistic has uncertainty, measured by its standard error. Statistics computed using imputed data have even more uncertainty than their standard errors measure.

Your statistical package cannot distinguish between an imputed value and a real value.

Since the standard errors of statistics based on imputed values are too small, corresponding p-values are also too small. P-values that are reported as smaller than they actually are? Those lead to Type I errors.

How Multiple Imputation Works

Multiple imputation solves this problem by incorporating the uncertainty inherent in imputation. It has four steps:

  1. Create m sets of imputations for the missing values using a good imputation process. This means it uses information from other variables and has a random component.
  2. The result is m full data sets. Each data set will have slightly different values for the imputed data because of the random component.
  3. Analyze each completed data set. Each set of parameter estimates will differ slightly because the data differs slightly.
  4. Combine results, calculating the variation in parameter estimates.

Remarkably, m, the number of sufficient imputations, can be only 5 to 10 imputations, although it depends on the percentage of data that are missing. A good multiple imputation model results in unbiased parameter estimates and a full sample size.

Doing multiple imputation well, however, is not always quick or easy. First, it requires that the missing data be missing at random. Second, it requires a very good imputation model. Creating a good imputation model requires knowing your data very well and having variables that will predict missing values.

Tagged With: mean imputation, Missing Data, missing data mechanism, Multiple Imputation, S-Plus, SAS, SPSS

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  • Statistical Software Access From Home

When Listwise Deletion works for Missing Data

by Karen Grace-Martin  1 Comment

You may have never heard of listwise deletion for missing data, but you’ve probably used it.

Listwise deletion means that any individual in a data set is deleted from an analysis if they’re missing data on any variable in the analysis.

It’s the default in most software packages.

Although the simplicity of it is a major advantage, it causes big problems in many missing data situations.

But not always.  If you happen to have one of the uncommon missing data situations in which [Read more…] about When Listwise Deletion works for Missing Data

Tagged With: listwise deletion, MCAR, Missing Data, missing data mechanism, Statistical power

Related Posts

  • Missing Data Mechanisms: A Primer
  • Confusing Statistical Term #13: Missing at Random and Missing Completely at Random
  • Multiple Imputation in a Nutshell
  • How to Diagnose the Missing Data Mechanism

How to Diagnose the Missing Data Mechanism

by Karen Grace-Martin  11 Comments

One important consideration in choosing a missing data approach is the missing data mechanism—different approaches have different assumptions about the mechanism.

Each of the three mechanisms describes one possible relationship between the propensity of data to be missing and values of the data, both missing and observed.

The Missing Data Mechanisms

Missing Completely at Random, MCAR, means there is no relationship between [Read more…] about How to Diagnose the Missing Data Mechanism

Tagged With: MAR, maximum likelihood, MCAR, missing data mechanism, Multiple Imputation

Related Posts

  • Confusing Statistical Term #13: Missing at Random and Missing Completely at Random
  • Multiple Imputation in a Nutshell
  • Missing Data Mechanisms: A Primer
  • When Listwise Deletion works for Missing Data

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