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Multiple Imputation

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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Member Training: Missing Data

by TAF Support 

Missing data causes a lot of problems in data analysis. Unfortunately, some of the “solutions” for missing data cause more problems than they solve.

[Read more…] about Member Training: Missing Data

Tagged With: data issues, listwise deletion, mean imputation, Missing Data, Multiple Imputation

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Member Training: Multiple Imputation for Missing Data

by Jeff Meyer 

There are a number of simplistic methods available for tackling the problem of missing data. Unfortunately there is a very high likelihood that each of these simplistic methods introduces bias into our model results.

Multiple imputation is considered to be the superior method of working with missing data. It eliminates the bias introduced by the simplistic methods in many missing data situations.
[Read more…] about Member Training: Multiple Imputation for Missing Data

Tagged With: data issues, Missing Data, Monotone missing data, Multiple Imputation

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Multiple Imputation for Missing Data: Indicator Variables versus Categorical Variables

by Jeff Meyer  Leave a Comment

A data set can contain indicator (dummy) variables, categorical variables and/or both. Initially, it all depends upon how the data is coded as to which variable type it is.

For example, a categorical variable like marital status could be coded in the data set as a single variable with 5 values: [Read more…] about Multiple Imputation for Missing Data: Indicator Variables versus Categorical Variables

Tagged With: categorical variable, dummy variable, indicator, Missing Data, Multiple Imputation

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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

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Two Recommended Solutions for Missing Data: Multiple Imputation and Maximum Likelihood

by Karen Grace-Martin  16 Comments

Two methods for dealing with missing data, vast improvements over traditional approaches, have become available in mainstream statistical software in the last few years.

Both of the methods discussed here require that the data are missing at random–not related to the missing values. If this assumption holds, resulting estimates (i.e., regression coefficients and standard errors) will be unbiased with no loss of power.

The first method is Multiple Imputation (MI). Just like the old-fashioned imputation [Read more…] about Two Recommended Solutions for Missing Data: Multiple Imputation and Maximum Likelihood

Tagged With: maximum likelihood, Missing Data, Multiple Imputation, R, SAS, SPSS

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