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| From | Maarten Buis <maartenlbuis@gmail.com> |
| To | statalist@hsphsun2.harvard.edu |
| Subject | Re: st: Multicollinearity and Time Trends |
| Date | Wed, 11 Apr 2012 14:35:44 +0200 |
On Wed, Apr 11, 2012 at 1:31 PM, Stefan Pichler wrote: > I want to detrend time series data and allow not only for linear trends, but also for quadratic and cubic trends. Here is a minimalistic example of the data: > > Y...outcome variable (some randomly typed numbers) > year....the year of the observation > gen year2=year^2 > gen year3=year^3 > > gen year1=year-1950 (so that year starts from 1) > gen year12=year1^2 > gen year13=year1^3 > If I tell Stata: "reg Y year year2 year3", Stata omits year because of collinearity, however if I regress "Y year1 year12 year13" no variable is omitted. Think of this this way: Stata can distinguish between year12 and year1 because they are non-linearly related. This non-linearity is greatest near 0 (the minimum of the parabola). However, if you get further and further away from 0, it becomes almost linear. Consider these three graphs: twoway function y = x^2, range(1951 1960) twoway function y = x^2, range(1 10) twoway function y = x^2, range(-4.5 4.5) In the last graph it is easiest to distinguish x from its square. This is true for us when we look at the graph, but also for computers. 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/