Tie Turning Box-Cox including Quadratic Forms in Regression
In a regression model where a Box-Cox transformation is used on a positive independent variable X which appears only once in the equation, the effect of X on the dependent variable Y is either strictly increasing or decreasing over the whole range of X , since the transformation is a monotonic function of X , increasing or decreasing depending on the Box-Cox parameter ë. This paper considers the case where the variable X appears twice in the regression with two different Box-Cox parameters 1 ë and 2 ë , to allow a turning point in Y which can be a maximum or minimum. First and second-order conditions for the critical point are derived. This general specification includes as a special case the quadratic form in X where 1 ë and 2 ë are set equal to 1 and 2, respectively. If, instead of using the Box-Cox transformations, one uses simple powers of X , this form is equivalent to the Box-Cox form except that neither 1 ë nor 2 ë can be equal to zero, since in this case 1 ë X or 2 ë X reduces to a constant of value 1.
|Date of creation:||2000|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +33 3 68 85 20 69
Fax: +33 3 68 85 20 70
Web page: http://www.beta-umr7522.fr/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gaudry, Marc & Laferriere, Richard, 1989. "The box-cox transformation : Power invariance and a new interpretation," Economics Letters, Elsevier, vol. 30(1), pages 27-29.
When requesting a correction, please mention this item's handle: RePEc:ulp:sbbeta:2000-13. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.