Elaborations
For growth-curve modeling, another way to model nonlinearities is to use what is called a "piecewise growth model." For instance if there were five waves which were centered the linear time variable would be {-1,-2,0,1,2}. Say we want the slope to change after wave 3, we would add to the model two time variables: {-1,-2,0,0,0} and {0,0,0,1,2}. The first variable would model the linear slope for waves 1 to 3 and second for waves 3 to 5. Note these two slopes may vary.
On pages 349 and 353, we discuss how multilevel models will sometimes not run when a variance component in the model is small or non-existent. Besides small variances, convergence problems will also occur when two or more random effects are highly correlated (i.e., problems of multicollinearity). This problem can occur in dyadic models, when there is a couple-level effect. As an example, consider a growth curve model where the two members share the same growth curve which would make the correlation of the two slopes and the two intercepts one. To diagnose the problem, from the output determine the correlation between the two random effects. If the correlation is large, then the two random effects can be collapsed into one effect. The same would occur if the correlation between the two intercepts was perfect.
