Latent Growth Modeling: Orthogonal Polynomial vs. Raw Time Coding

[ahmad]

Hi,

I have a question regarding the interpretation of latent growth factors in a standard linear growth model (with raw time coding) versus an orthogonal polynomial growth model.

I understand that in the standard linear model, the intercept typically represents the expected value at the initial time point (when time is coded starting at zero). In contrast, in orthogonal polynomial models, the intercept represents the overall mean across time points.

However, I am less clear about the interpretation of the linear slope in these two approaches. What is the conceptual difference between the linear slope in the standard linear growth model and the linear component in an orthogonal polynomial model?

I would greatly appreciate your time and help.

Best,

A

[Terrence Jorgensen]

I am less clear about the interpretation of the linear slope in these two approaches. What is the conceptual difference between the linear slope in the standard linear growth model and the linear component in an orthogonal polynomial model?

You can interpret polynomial effects as a variable moderating its own effect (they are products of a variable with itself, rather than the product of a focal predictor and moderator).  So in either case, the linear simple-slope is the simple effect of X when X==0 (which is when its higher-order terms are also 0).  It is the slope of a tangent line just touching the curve, so you can interpret it as a local linear approximation of the amount of change in Y you expect when you "zoom in" on X around 0.  

• With raw time coding, X==0 (i.e., time == 0) is typically the initial time of measurement.
• With polynomial contrasts, X==0 is in the center of the schedule.

Terrence D. Jorgensen    (he, him, his)
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
http://www.uva.nl/profile/t.d.jorgensen