Model based graphs: Level-1 equation modeling

WHLM will also let us examine plots for individual level-2 units by just using the level-1 equation instead of the entire model. For this example, we will be using the vocabulary data, vocab.mdm, and have run the following model:

To perform level-1 equation graphing

After the model is run, select Graph Equations...Level-1 equation graphing from the File menu, which will give us the following dialog box.

There are three options for the number of groups: (a) First ten groups; (b) Random sample of spec'd prob (specified probability) and (c) All groups (n = total number of groups) for users to choose from in the Number of groups drop-down list box. The selection of option (b) requires the user to specify the proportion or percent of the level-2 units to be included.

Select an X focus variable. In our example, we want the age of the child in months minus 12 to be the X focus. Choose AGE12 from the X focus drop-down list box.

Select the number of groups. We will include all the children. Choose All groups (n=22) in the Number of groups drop-down list box.

Specify the relationship between the transformed and the original variable. The transformed variable is AGE12S and the original variable is AGE12. Click 1 in the Categories/ transforms/interactions section and select power of x/z for polynomial relationships. A Equation Graphing - power dialog box will open. Select AGE12S from the drop-down list box to the left of the equal sign. AGE12 will appear in the drop-down list box as it is the only level-1 variable left. Enter 2 in the text box for the power to be raised. Click OK.

The ranges for x- and y-axis (the default values are those computed from the data), legend and graph titles, and selection of screen color can be changed by clicking Range/Legend/Color to obtain the Range/Legend/Color dialog box.

Click the Other settings button and click the selection button for Smooth in For continuous x section to display a set of smooth curves. Click OK.

Click OK and we get the following figure that shows vocabulary size accelerates during the second year of life. Note that the individual trajectories, as expected, are “smoother” than in  comparable data-based graphs.

To include a level-2 classification variable

Click Graph Settings on the menu bar to open the Level-1 equation Graphing dialog box. Choose MALE from the Z-focus drop-down list box as the level-2 classification variable and click OK.

A colored version of the graph indicates that girls on average have a greater acceleration rate in vocabulary growth over the course of the study.