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# st: interprating orthogonal polynomial regression

 From jl591164@albany.edu To statalist@hsphsun2.harvard.edu Subject st: interprating orthogonal polynomial regression Date Thu, 22 Jul 2010 16:33:26 -0400 (EDT)

```Hi All,
I fitted a three level logistic regression of y on the first, second, and
third order of orthogonal polynomials of time to examine the trend of y.
Coefficients of the three orthogonal polynomials are significant. The
signs of linear and cubic trend are negative and the quadratic term is
positive.

I conclude that y has a cubic trend. The interpretation is that As time
increases, the probability of y first decrease. With a further increase in
time y appeared to increase. Then at about 51 months(based on the graph of
the sample mean of y), y decreases again.

What else should i interpret about the cubic trend? Do I have to calculate
the time points when the sings change? If so, i probably need to transform
the coefficients of orthogonal polynomials into coefficients for the
original time scale. I do not know how stata does this transform after
fitting a -mim:gllamm- model.

Then I need to think about why y has a cubic trend. One possible
explanation is age. With the increase in time, the age of participants
increase as well. The cubic trend may because different age intervals have
different trends. Does this mean i need to use age as the time variable
instead? However, the longitudinal data is collected at each "time" point,
but not at each age.

Just to check how age may influence the trend of y, I ran a multilevel
logistic regression with the three orthogonal polynomials of time and the
three orthogonal polynomials of age. The are all significant. So what
should be my final model of the trend of Y, just use the polynomials of
time, or also the polynomials of age? Thanks a lot.

Junqing

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