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This example illustrates the use of PROC TRAJ to fit a trajectory model for a dual set of dependent variables.

In this example, oppositional  and hyperactivity behavior scale data on 138 subjects from the Montreal Longitudinal Study data are analyzed. Teachers assessed the students annually at ages 6 and ages 10-15 on an opposition scale ranging from 0 to 10 and a hyperactivity scale ranging from 0 to 4.

The statements to fit the model appear first followed by the corresponding output pages and graphs.  First, the basic statements used to fit the censored normal / censored normal model are shown.

The following statements create the data set and perform the first PROC TRAJ  analysis, producing OUTPUT 1, OUTPUT 2, and GRAPH 1.

 

 

Output 1: Four-group x four-group CNORM-CNORM model results.

The output lists the results for the first model and second model as in a single trajectory case. The difference in the second set is the reporting of conditional probabilities of group membership in the second trajectory model given group membership in the first.

Now the model is modified by considering the significance results. Order and order2 statements are added.

 

 

Output 2: Final four-group x four-group CNORM-CNORM model results.

 

 

Graph 1: Hyperactivity and oppositional behavior average and predicted trajectories.

 

The resulting model appears satisfactory. The difference in the second set of group membership results is the reporting of conditional probabilities of group membership in the second trajectory model given group membership in the first as well as other joint, conditional and unconditional probabilities. These results express the relationship between membership in one behavior group to the membership in the other behavior group.

For instance, of subjects classified as following trajectory three in hyperactivity; 0.2%, 10.4%, 72.2%, and 17.2% of subjects are predicted to fall in classes one to four of oppositional behavior.

Note: missing standard errors on group membership probabilities can be obtained by switching models one and two and refitting.

Detailed explanations of all PROC TRAJ statements are located in the Documentation section.

The data and SAS statements used to generate this example are here: cnorm_cnorm.sas.

Modified 09/20/05 Bobby L. Jones
Contact: Bob by Email