Notice: On March 31, it was announced that Statalist is moving from an email list to a forum. The old list will shut down on April 23, and its replacement, statalist.org is already up and running.

# Re: st: interprating orthogonal polynomial regression

 From jl591164@albany.edu To statalist@hsphsun2.harvard.edu Subject Re: st: interprating orthogonal polynomial regression Date Fri, 23 Jul 2010 13:34:54 -0400 (EDT)

```Thanks, Maarten. This is very helpful. I have additional question on the
age-period-cohort effects.

The study that i am working on interviewed the same individuals at five
waves(wave is my time variable) over 8 years. So the cohorts(subjects) are
the same through the five interviews. I fitted a random intercept model
and i believe that the cohort effects(between-subject effects) should be
captured by the variance of the random intercept.

I included the three orthogonal polynomials of age(continuous variable)
and the three orthogonal polynomials of time as fixed effects in the three
level random intercept model and found the six fixed coefficients are all
significant. This means that age is not the only factor that contribute to
the cubic trend of Y.

Then what i should do to possibly explain why y(mental health service
access) has a cubic trend. No much theory as I am aware of talks about the
curvilinear trend of Y.

Thanks a lot for any advice.

Junqing

> --- On Thu, 22/7/10, jl591164@albany.edu wrote:
>> 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
>>
>> 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?
>
> It is your argument, so you decide what you think is
> confincing or illuminating evidence and what is not. We
> can only make suggestions. Finding these points can be sorta
> nice, but they should not be taken too literaly, as they
> are to a large extend influenced by the functional form you
> assumed.
>
>> 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.
>
> *--------------- begin example ----------------
> sysuse auto, clear
> orthpoly weight, deg(3) generate(pw*)
> logit foreign mpg pw1-pw3 rep78
> orthpoly weight, deg(3) poly(P)
> matrix b = e(b)
> // extract the polynomials and the constant
> matrix b = b[1, "foreign:pw1".."foreign:pw3"], b[1,"foreign:_cons"]
> matrix b = b*P
> matlist b
>
> // check
> gen w1 = weight
> gen w2 = weight^2
> gen w3 = weight^3
>
> logit foreign mpg w1-w3 rep78
> *---------------- end example -----------------------
>
> Personaly, I like linear splines better, as they often provide
> a better balance between allowing for non-linear effects and
> giving directly interpretable coefficients. See -help mkspline-.
>
>> 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.
>
> Assuming that participants aren't all born in the same year,
> you can add time and age, or time and year of birth, or age
> and year of birth, but not all three, as time - age = year of
> birth.
>
> There is a large literature on still trying to estimate
> these "age-period-cohort effects" which basically consists of
> proposing different constraints on one or more of these
> variables. Assuming that this constraint is true you can
> estimate all three, but you cannot test whether the constraint
> is true, so...
>
>> Does this mean i need to use age as the time variable
>
> There is only one person who can decide that, and that is you.
>
> Hope this helps,
> Maarten
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
> http://www.maartenbuis.nl
> --------------------------
>
>
>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```