Analyzing Multiple Imputation Data

Many procedures support pooling of results from analysis of multiply imputed datasets. When imputation markings are turned on, a special icon is displayed next to procedures that support pooling. On the Descriptive Statistics submenu of the Analyze menu, for example, Frequencies, Descriptives, Explore, and Crosstabs all support pooling, while Ratio, P-P Plots, and Q-Q Plots do not.

Both tabular output and model PMML can be pooled. There is no new procedure for requesting pooled output; instead, a new tab on the Options dialog gives you global control over multiple imputation output. See the topic Multiple imputations options for more information.

• Pooling of Tabular Output. By default, when you run a supported procedure on a multiple imputation (MI) dataset, results are automatically produced for each imputation, the original (unimputed) data, and pooled (final) results that take into account variation across imputations. The statistics that are pooled vary by procedure.
• Pooling of PMML. You can also obtain pooled PMML from supported procedures that export PMML. Pooled PMML is requested in the same way as, and is saved instead of, non-pooled PMML.

Unsupported procedures produce neither pooled output nor pooled PMML files.

Levels of Pooling

Output is pooled using one of two levels:

• Naïve combination. Only the pooled parameter is available.
• Univariate combination. The pooled parameter, its standard error, test statistic and effective degrees of freedom, p-value, confidence interval, and pooling diagnostics (fraction of missing information, relative efficiency, relative increase in variance) are shown when available.

Coefficients (regression and correlation), means (and mean differences), and counts are typically pooled. When the standard error of the statistic is available, then univariate pooling is used; otherwise naïve pooling is used.

Procedures That Support Pooling

The following procedures support MI datasets, at the levels of pooling specified for each piece of output.

Frequencies. The following features are supported:

• The Statistics table supports Means at Univariate pooling (if S.E. mean is also requested) and Valid N and Missing N at Naïve pooling.
• The Frequencies table supports Frequency at Naïve pooling.

Descriptives. The following features are supported:

• The Descriptive Statistics table supports Means at Univariate pooling (if S.E. mean is also requested) and N at Naïve pooling.

Crosstabs. The following features are supported:

• The Crosstabulation table supports Count at Naïve pooling.

Means. The following features are supported:

• The Report table supports Mean at Univariate pooling (if S.E. mean is also requested) and N at Naïve pooling.

One-Sample T Test. The following features are supported:

• The Statistics table supports Mean at Univariate pooling and N at Naïve pooling.
• The Test table supports Mean Difference at Univariate pooling.

Independent-Samples T Test. The following features are supported:

• The Group Statistics table supports Means at Univariate pooling and N at Naïve pooling.
• The Test table supports Mean Difference at Univariate pooling.

Paired-Samples T Test. The following features are supported:

• The Statistics table supports Means at Univariate pooling and N at Naïve pooling.
• The Correlations table supports Correlations and N at Naïve pooling.
• The Test table supports Mean at Univariate pooling.

One-Way ANOVA. The following features are supported:

• The Descriptive Statistics table supports Mean at Univariate pooling and N at Naïve pooling.
• The Contrast Tests table supports Value of Contrast at Univariate pooling.

GLM Univariate. The following features are supported:

• The Parameter Estimates table supports the coefficient, B, at Univariate pooling.

Linear Mixed Models. The following features are supported:

• The Descriptive Statistics table supports Mean and N at Naïve pooling.
• The Estimates of Fixed Effects table supports Estimate at Univariate pooling.
• The Estimates of Covariance Parameters table supports Estimate at Univariate pooling.
• The Estimated Marginal Means: Estimates table supports Mean at Univariate pooling.
• The Estimated Marginal Means: Pairwise Comparisons table supports Mean Difference at Univariate pooling.

Generalized Linear Models and Generalized Estimating Equations. These procedures support pooled PMML.

• The Categorical Variable Information table supports N and Percents at Naïve pooling.
• The Continuous Variable Information table supports N and Mean at Naïve pooling.
• The Parameter Estimates table supports the coefficient, B, at Univariate pooling.
• The Estimated Marginal Means: Estimation Coefficients table supports Mean at Naïve pooling.
• The Estimated Marginal Means: Estimates table supports Mean at Univariate pooling.
• The Estimated Marginal Means: Pairwise Comparisons table supports Mean Difference at Univariate pooling.

Bivariate Correlations. The following features are supported:

• The Descriptive Statistics table supports Mean and N at Naïve pooling.
• The Correlations table supports Correlations and N at Univariate pooling. Note that correlations are transformed using Fisher's z transformation before pooling, and then backtransformed after pooling.

Partial Correlations. The following features are supported:

• The Descriptive Statistics table supports Mean and N at Naïve pooling.
• The Correlations table supports Correlations at Naïve pooling.

Linear Regression. This procedure supports pooled PMML.

• The Descriptive Statistics table supports Mean and N at Naïve pooling.
• The Correlations table supports Correlations and N at Naïve pooling.
• The Coefficients table supports B at Univariate pooling and Correlations at Naïve pooling.
• The Correlation Coefficients table supports Correlations at Naïve pooling.
• The Residuals Statistics table supports Mean and N at Naïve pooling.

Binary Logistic Regression. This procedure supports pooled PMML.

• The Variables in the Equation table supports B at Univariate pooling.

Multinomial Logistic Regression. This procedure supports pooled PMML.

• The Parameter Estimates table supports the coefficient, B, at Univariate pooling.

Ordinal Regression. The following features are supported:

• The Parameter Estimates table supports the coefficient, B, at Univariate pooling.

Discriminant Analysis. This procedure supports pooled model XML.

• The Group Statistics table supports Mean and Valid N at Naïve pooling.
• The Pooled Within-Groups Matrices table supports Correlations at Naïve pooling.
• The Canonical Discriminant Function Coefficients table supports Unstandardized Coefficients at Naïve pooling.
• The Functions at Group Centroids table supports Unstandardized Coefficients at Naïve pooling.
• The Classification Function Coefficients table supports Coefficients at Naïve pooling.

Chi-Square Test. The following features are supported:

• The Descriptives table supports Mean and N at Naïve pooling.
• The Frequencies table supports Observed N at Naïve pooling.

Binomial Test. The following features are supported:

• The Descriptives table supports Means and N at Naïve pooling.
• The Test table supports N, Observed Proportion, and Test Proportion at Naïve pooling.

Runs Test. The following features are supported:

• The Descriptives table supports Means and N at Naïve pooling.

One-Sample Kolmogorov-Smirnov Test. The following features are supported:

• The Descriptives table supports Means and N at Naïve pooling.

Two-Independent-Samples Tests. The following features are supported:

• The Ranks table supports Mean Rank and N at Naïve pooling.
• The Frequencies table supports N at Naïve pooling.

Tests for Several Independent Samples. The following features are supported:

• The Ranks table supports Mean Rank and N at Naïve pooling.
• The Frequencies table supports Counts at Naïve pooling.

Two-Related-Samples Tests. The following features are supported:

• The Ranks table supports Mean Rank and N at Naïve pooling.
• The Frequencies table supports N at Naïve pooling.

Tests for Several Related Samples. The following features are supported:

• The Ranks table supports Mean Rank at Naïve pooling.

Cox Regression. This procedure supports pooled PMML.

• The Variables in the Equation table supports B at Univariate pooling.
• The Covariate Means table supports Mean at Naïve pooling.