Pooled Parameter Estimates

This table is rather large, but pivoting will give us a couple of different useful views of the output.

1. Activate (double-click) the table, then select Pivoting Trays from the context menu.

   

2. Move Imputation Number from the Row into the Layer.
3. Select Pooled from the Imputation Number dropdown list.

   

   This view shows all the statistics for the pooled results. You can use and interpret these coefficients in the same way you would use this table for a dataset with no missing values.

   The parameter estimates table summarizes the effect of each predictor. The ratio of the coefficient to its standard error, squared, equals the Wald statistic. If the significance level of the Wald statistic is small (less than 0.05) then the parameter is different from 0.

   • Parameters with significant negative coefficients decrease the likelihood of that response category with respect to the reference category.
   • Parameters with positive coefficients increase the likelihood of that response category.
   • The parameters associated with the last category of each factor is redundant given the intercept term.

   There are three additional columns in the table that provide more information about the pooled output. The fraction of missing information is an estimate of the ratio of missing information to "complete" information, based on the relative increase in variance due to non-response, which in turn is a (modified) ratio of the between-imputation and average within-imputation variance of the regression coefficient. The relative efficiency is a comparison of this estimate to a (theoretical) estimate computed using an infinite number of imputations. The relative efficiency is determined by the fraction of missing information and the number of imputations used to obtain the pooled result; when the faction of missing information is large, a greater number of imputations are necessary to bring the relative efficiency closer to 1 and the pooled estimate closer to the idealized estimate.

   

4. Now reactivate (double-click) the table, then select Pivoting Trays from the context menu.
5. Move Imputation Number from the Layer into the Column.
6. Move Statistics from the Column into the Layer.
7. Select B from the Statistics dropdown list.

This view of the table is useful for comparing values across imputations, to get a quick visual check of the variation in the regression coefficient estimates from imputation to imputation, and even against the original data. In particular, switching the statistic in the layer to Std. Error allows you to see how multiple imputation has reduced the variability in the coefficient estimates versus listwise deletion (original data).

However, in this example, the original dataset actually causes an error, which explains the very large parameter estimates for the Plus service intercept and non-redundant levels of ed (Level of education) in the original data column of the table.

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