Model based graphs: Level-1 residual vs predicted value

Users can graphically assess the assumptions of constant error variance and linearity and probe for outlying cases by examining a scatter plot of level-1 residuals and predicted values. Using the same data and model of the previous two sections, we now plot the level-1 residual against its predicted value.

After the model is run, select Graph Equations...Level-1 residual vs predicted value from the File menu, which will give us the following dialog box.

Note that the X-axis variable, Pred. val. and Y-axis variable, Level-1 residuals have been pre-selected.

Select All groups (n=22) in the Number of groups to include all the 22 children in the display. Click the selection button for Scatter plot in the Type of plot section to request a scatter plot of the predicted values by level-1 residuals. Select All groups on same graph in the Pagination section to display all the residuals pooled across the level-2 units. To examine the residuals for individual children, choose either of the other pagination options. Click OK.

The plot suggests that there is a tendency for the residual scatter to get narrower at the smallest predicted values and to get wider around the interval between 150 and 170. The residuals seem to follow a slightly curvilinear trend as well.  They may suggest that there is a specification error in the model.

Users can also choose to include a level-2 classification variable when examining the level-1 residuals.