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Re: st: Interpretation of Curvilinear Effects

From   John Antonakis <>
Subject   Re: st: Interpretation of Curvilinear Effects
Date   Tue, 09 Jun 2009 20:42:43 +0200


First, don't use stepwise regression--it is the plague; no worse. Many journals simply won't even review manuscript with such data-driven methods (unless used for a particular goal--ridge, least-angular regression). For instance, see:

Thompson, B. (1995). Stepwise Regression and Stepwise Discriminant-Analysis Need Not Apply Here - a Guidelines Editorial. Educational and Psychological Measurement, 55(4), 525-534.

The best way to get a feel for the shape of the interaction is to plot it; i.e., fit the model, and then plug the numbers across your x-values and plot the predicted value. In the case of a positive x and positive x^2 the line should be relatively flat and positive and the shoot up like a "J" shape.

Or try this after you fit the model:

predictnl y_hat= 1.89 + _b[x]*x + _b[x^2]*x^2 , ci(yhat_left yhat_right)
twoway (connect y_hat  yhat_left yhat_right x, sort)

Instead of 1.89 above, put in the estimate of your intercept.



Prof. John Antonakis
Associate Dean Faculty of Business and Economics
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny

Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305

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Personal page:

On 09.06.2009 20:31, Christian Weiss wrote:
Dear Statalisters,

I am currently evaluating curvilinear effects of the variable X on Y
by standard OLS. To asses the curvilinearity I generated X^2 and X^3
and included these variables stepwise in the regressions. Looking at
the significance levels and the signs of the coefficients I concluded
the following:

if X and X^2 is significant:
-> X has a positive sign and X^2 has a negative sign: Bell Shaped
-> X has a negative sign and X^2 has a positive sign: U Shaped

However, the last regression analysis yielded significant X and X^2,
but both with the same sign. I am struggling how to interpret this
effect. Any help is highly appreciated! :)

Best regards
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