December 16, 2011

Chapter 13


Page 374, Figure 13.4: It should read in the figure title "and Amplitude (R) of 2".

On the top of page 358: In the SAS code, the command NOINT should be added:



Page 348: If OBS_ID were to be computed using the formula given in SAS or SPSS, you would need to have an asterisk or * between NT and (DYAD_ID - 1).


Piecewise or Bilinear Growth

For growth-curve modeling, another way to model nonlinearities is to use what is called a "piecewise" or "bilinear" growth-curve 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: {-2,-1,0,0,0} 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 these two slopes may vary across persons or dyads and may be correlated.  Alternatively, the deflection in slopes can be measured by using {-2,-1,0, 1, 2} and {0,0,0,1,2}.  The first variable would model the linear slope for waves 1 to 5 and second the change in the slope that occurs at wave 3.

Convergence Issues

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.

For growth-curve modeling, convergence can be aided by changing the units of measurement of time, i.e., by having "longer" periods of time.  For instance, instead of months, use years or instead of days use weeks.  However, in some instances, we have found that shorter periods improves convergence.

Programs vary considerable in convergence.  In our limited experience, SPSS performs the worst and HLM the best.  Convergence in SPSS can be improved by changing UNR to UN, by using REML as opposed to ML, and adding a statement of /MXSTEP(50) where other numbers besides 50 might be used.

A series of multi-modeling PowerPoints are available for download.  The plan is to turn these into webinars eventually.  There is a small charge for these PowerPoints.

Data and Files

The Leonard data:
Data (SPSS)
    Data (SAS)
    Syntax (SAS)

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