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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: interprating orthogonal polynomial regression |

Date |
Fri, 23 Jul 2010 07:16:31 +0000 (GMT) |

--- 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 > 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? 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 > instead? 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/

**References**:**st: interprating orthogonal polynomial regression***From:*jl591164@albany.edu

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