Single Trajectory Examples:     

 

Three-group CNORM model with risk factors.

 

Three-group ZIP model with zero-inflation.    

 

Two-group LOGIT model with risk factors.

 

About Start Values:  PROC TRAJ fits a non-linear model that does not have a closed form solution for maximum likelihood estimates. The alternative to closed form solutions is to iteratively search the parameter space of the likelihood for the maximum likelihood solution. There are many iterative methods but they all share a common requirement. They must be told where to start the search.

 

Default Start Values: If start values are not specified in the SAS program, the TRAJ procedure provides default start values by calculating group intercepts spaced based on the range or standard deviation of the dependent variables. Starting group sizes are assumed to be equal be default. Due to model complexity and possible data oddities, some trajectory models are difficult to fit. There is no guarantee that the procedure will be able to fit a model successfully beginning at the default starting point that the procedure provides. The procedure may fail to find a solution or find only a local maximum instead of the required global maximum. For these reasons it is important that the process of specifying start values is understood.

 

Start Value Examples:

 

Adjusting group trajectories

Joint trajectory model

Adding risk factors

Adding time-varying covariates.