I am developing a Growth model using either GEE (gamma) or generalized mixed effect model(gamma) for psychiatric symptoms in Alzheimer with 6 measurments over 6 consecutive years. There are linear, quadratic and cubic growth terms. My statistical abilities are limited to SPSS. I want to use orthogonal polynomials and have copied in the same values for each subject from a calculator for Chebyshev and Legendres polynomials which improve model fit and pred/observed. I suspect this is wrong and that I should generate different values for each subject and create a Matrix. Does anyone know how to do this (and maybe miraculousley in SPSS, I guess by syntax)?
Orthogonal polynomials are available in spss
see http://www.ats.ucla.edu/stat/spss/webbooks/reg/chapter5/spssreg5.htm
and for how to use OPs in random effects growth models see
https://www.researchgate.net/publication/234015221_Manual_supplement_for_MLwiN_Version_214
for a practical example
Don Hedeker's book uses the approach - it is very useful for fitting random slopes for time as the discreet time dummies will be orthogonal and parsimonious
http://hedeker.people.uic.edu/ml.html
Hedeker, D., and R. D. Gibbons. 2006. Longitudinal Data Analysis. Wiley-Interscience.
Data Manual supplement for MLwiN Version 2.14
Thank you so much. I did implement the orthogonal polynomials and divided them by SS/root N for scale.
I want to model predictors for neuropsychiatric symptoms as measured by the neuropsychiatric inventory (n=91 patients) and 10 scores (calculated as the frequency (1-3) times intensity (1 to 4), scale 0-12 for all scores and they follow a gamma distribution. I have reduced them to 3 (or 4) factors by CAT-PCA (non-linear) using numbers and discretization by ranks in SPSS CAT-REG procedure and saved the scores where 1 have problems with a leptokyrotic distribution.
The patients have had 5 year follow up and thus 6 measurements.
There is 23% missing data, 8% from loss to follow up (which is MCAR) and the remaining are MAR by death which the predictors predict positively (also on cox.reg. for same paper).
There are enormous amounts of individual changes in growth, where individual curve-fit of each patient (by inverse normal transforming the outcomes, which cannot be used in a complex model) show dominance of cubic growth (average R squared for individuals where cubic is allowed is 0.6)
Most importantly, there is on _average_, no overall change. The line is close to flat, but I can get something out of a GEE where time-terms are insignificant but interactions are. Even so, the distribution is not strictly gamma and the errors also form a leptokyrotic distribution. This is without addressing missingness.
Being within the limitations of SPSS, do you have any input for the following:
- SPSS gen.lim does not implement missing data analysis by imputation. Is imputing the grand mean of imputations for all missing and the first measurement after death (leaving the rest missing) a terrible way to go?
- When setting up a random-effects model (have never done this) do you implement it as time in fixed with intercept (grand mean) and then subjects+intercept+ random effects (time, quad time, cubic time + predictors and interactions) or is it without subjects? Intercept?
- How do you evaluate the effect within gen.lim setup?
- If imputing befor factoring does not solve the leptokyrosis issue, does it increase type I and type II error rates? I run it robust.
I completely understand if you cannot take the time to answer all this. Thank you still for the above. Growth modeling makes desperate men (at least newcomers).
Lasse
... and some years later. Perhaps, considering mixed models, one can transform time, as categories, using SPSS transform into different variabel, and a table adapted from http://users.stat.ufl.edu/~winner/tables/orthpol.pdf to generate orthogonal polynomial contrast for time (up till cubic).
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