Hi All,

I'm analysing some data that is conventionally modelled as log(Y) = a + bX + e.  However, using the boxcox function, it appears that the optimum value of lambda is approx 0.05.  I have 40 data sets of differing sizes and for about half of these, lambda is significantly non-zero.  So, it is worth looking into.

The alternative model, Y^lambda = a + bX + e, has been explored before by non-statistician colleagues.  But instead of using boxcox and maximising the profile likelihood, the model has been twisted, shuffled, differenced and logged, to get

ln(dY/dX) = A + B.ln(Y) + E

and lambda ( =f(B) ) estimated via LS regression.  Note: RHS contains Y, not X.  This relationship has some physical justification.


I assume that these two approaches are not equivalent, is this correct?  

I assume the Box Cox approach (profile likelihood) is better, is this correct and why?  


Any help would be greatly appreciated.

Thanks,
Paul.



Paul Livingstone
Statistical Analyst
AeroStructures®
Level 14, 222 Kings Way
South Melbourne, Vic, 3205
Phone: 03 9694 1083
Mobile: 0418 121 530
Fax: 03 9696 8195
Email: paul.livingstone@aerostructures.com.au
Web: www.aerostructures.com.au


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