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Thread: -->(BOX-COX) Transformation breaks down for large (positive) coefficient values <--

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    -->(BOX-COX) Transformation breaks down for large (positive) coefficient values <--




    Hi,

    I have done a box-cox transformation of my response variable, using the following formula: (Y^lambda - 1)/lambda
    Previously, I have got some excellent help in understanding the way interpretation works for different levels of Y (q1,median,q3). My formula for inverse transformation is:

    x=(lambda*z + 1)^(1/lamda)

    In my analysis, lambda= -1

    My interpretation of this formula is that z=y+x (the response times the specific coefficient value). Or just z=y which would return the original values if the response variable.
    In short, this works very well. When z=y the back-transformation produces almost the same values as the original.

    But a problem arises with one of the beta-coefficients. It is to large, so that z>1 (or, y+x>1 in the transformed scale).
    That returns negative values for the back-transformed value of y with respect to x. Does anyone knows how to deal with this problem?

    As an example:
    Back-transformed values of Y (very close to the real data):
    Q1: Q2: Q3:
    353,04077 403,8761 496,2258
    After the effect of X1, holding the other variables constant (producing plausible results):
    Q1: Q2: Q3:
    331,2585 373,374179 450,9129
    After the effect of X2 (inplausible results):
    Q1: Q2: Q3:
    -428,079 -373,61786 -318,767

    Another question I am searching an answer to, is how to correctly describe the change process?
    If the beta-value is -0,00019481 (in transformed scale), and its effect to y varies between 6-9% with different values of y (quantile 1-3 in back-transformed, original scale), how do I describe the change process with respect to a change in x?
    Is it correct to describe the change in Y as an interval of 6-9% depending on the value of Y, with respect to a unit change in X? It is this last part of the sentence that I is still not certain about..

    Any input is much appreciated! I have searched the webb for any material to read about interpreting back-transformed boc-cox transformation, but although there is plenty to read about the method of transforming, interpretation and inverse transformation is rarely mentioned.

    Best regards,
    Hank
    Last edited by hanke83; 06-07-2013 at 04:15 AM.

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