Creating the Diagnostic Scatterplot

1. To create a scatterplot of the partial residuals by time, from the menus choose:

   Graphs > Chart Builder...

   

2. In the Chart Builder, select the Scatter/Dot gallery and choose Simple Scatter.
3. Select Partial residual for AGE as the y variable and Time to second arrest as the x variable.
4. Click OK.

   These selections produce the scatterplot.

5. To see a best-fit line overlaid on the points in the scatterplot, activate the graph by double-clicking on it.
6. Select a point in the Chart Editor.
7. Click the Add fit line tool, then close the Chart Editor.

The resulting scatterplot can be used to assess the proportional hazards assumption. The horizontal axis shows the times until the second arrest. The vertical axis shows the partial residuals for Age in years. The partial residuals for a covariate are the differences between the observed and expected (given the model is correct) values of the covariate for each case. The partial residuals, and thus the points on the plot, are only produced for uncensored cases.

If the proportial hazards assumption is correct with respect to the offender's age, then there should be no patterns in this plot. However, there is a clear negative correlation between the partial residuals and time, which suggests that the effect of Age in years is dependent on time. Add a time-dependent covariate to the model to see if this is the case.

Next