Hi
I am carrying out growth curve modeling in AMOS and am incorporating a quadratic effect (i.e. adding another latent variable which is the same as the slope latent variable). I can do this no problem, and the fit improves in my model (which I'd expect given the descriptive stats).
My question is - does anyone know of books or websites that cover quadratic effects and their interpretation in any detail? All I can find are very brief mentions of this in books/websites dealing with LCGM models - i.e. they tend to say "it's easy to add a quadratic term, here's how" but don't go into much detail on interpretation.
Oh, also, is it necessary to mean center all of the indicators? I've read conflicting advice about this - some very good sources don't even mention it but other sources suggest it is always something to do.
Thanks in advance
Simon
Dear Simon,
This can be a very challenging work. Jeffrey R. Edwards (professor at University of North Carolina-Chapel Hill) and I wrote a conference paper, "Inevitable Data Redundancies in Moderated and Curvilinear Structural Equation Models. Paper presented as part of a symposium entitled: “Let the Wicked Fall, While I Escape Safely: Avoiding Methodological Pitfalls in I-O”. Unfortunately, we did not publish this work at a journal. You can contact Jeff (who is very nice) for this issue.
Dear Simon,
This can be a very challenging work. Jeffrey R. Edwards (professor at University of North Carolina-Chapel Hill) and I wrote a conference paper, "Inevitable Data Redundancies in Moderated and Curvilinear Structural Equation Models. Paper presented as part of a symposium entitled: “Let the Wicked Fall, While I Escape Safely: Avoiding Methodological Pitfalls in I-O”. Unfortunately, we did not publish this work at a journal. You can contact Jeff (who is very nice) for this issue.
You may read Robert Ping's blog on these issues, the link is attached.
Hope it would be helpful.
http://www.wright.edu/~robert.ping/research1.htm
Generally I would centre both linear and quadratic - to help estimation and easier interpretation - you are not then talking about impossible values -eg a smoker who is aged zero
This site has huge resources
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html
and here is a specific straightforward paper
http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/repeated-measures.pdf
Hi Everyone
Many thanks for directing me towards these resources. I'll read these with interest.
Kelvyn - is centering necessary in the statistical sense? For example, I center when creating cross-products in linear regression in order to reduce multicollinearity. Or, is centering simply to help with interpretation? If the latter, then I may not need to do this as I am dealing with reports of how much time people spent looking at a screen and so have a ratio scale where 0 is meaningful already.
Thanks again!
Simon
Centering is mainly used for interpretation - predicted response for meaningful values of the X predictors ; it can also help with estimation and ease the passage to convergence- particularly with random slopes models. And just to add - the random effects approach is more flexible than the structural equation approach eg you can have continuous time in the fixed part and allow the effect of this to vary at higher levels. This usually gives you more power to detect effects than using integer time. MLwin is free to UK academics as we have been supported for a long time by UK ESRC.
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