Re: different result in two nb reg and Poisson reg

Posted by Jon K Peck on Sep 16, 2014; 5:23pm
URL: http://spssx-discussion.165.s1.nabble.com/different-result-in-two-nb-reg-and-pisson-reg-tp5727252p5727277.html

aka Tukey Ladder of Powers for transforming a distribution to normality (not always possible).  Googling for this turns up many references.

In Statistics, the ADP procedure will calculate the optimal power for you using the Box-Cox transformation (Transform > Prepare Data for Modeling > Interactive (or Automatic) then Rescale Fields

Jon Peck (no "h") aka Kim
Senior Software Engineer, IBM
[hidden email]
phone: [phone]


The Box-Cox transformation exploits this to find a normality-inducing power on the ladder (not always possible).
 

From:        Rich Ulrich <[hidden email]>
To:        [hidden email]
Date:        09/16/2014 10:45 AM
Subject:        Re: [SPSSX-L] different result in two nb reg and pisson reg
Sent by:        "SPSSX(r) Discussion" <[hidden email]>

---

Oh - I think everyone concerned with power transformations should have a
proper orientation to the notion of "strength".  Look at the transformation of
  x' = x**k        (New) x' is equal to x raised to the k.

For k=1, this is the identity "transformation": no transformation at all.
The stronger transformation is whatever is further from 1.0.  For social
sciences, the transformations are usually less than 1.  
 k= 0.5  is taking the square root, which normalizes a Poisson.
 k= 0.0  is (asymptotically) taking the log, which normalizes log-normal.
 k= -1   is taking the reciprocal, which is equivalent to flipping a ratio a/b  to b/a;
that is the simplest justification.  It also seems to work fairly often for distances.

Thus: If taking the log isn't strong enough to bring in the stretched-out tail, you can
try the reciprocal as a stronger option.  You can also use log-log plots of two variables
in order to estimate the power needed for a linear relation between quantities, but I
think of that as more common in physics than in the social sciences.

For any power transformation, it is important that the zero is functioning as "zero",
so it is sometimes important to start by subtracting x  from the maximum value of x,
or otherwise re-center it.  If that is not problematic, is usually pretty easy to see (from
plots) which of those three transformations gives most symmetry.  

--
Rich Ulrich




> Date: Tue, 16 Sep 2014 05:26:50 -0700
> From: [hidden email]
> Subject: Re: different result in two nb reg and pisson reg
> To: [hidden email]
>
> I'm not quite sure what "The reciprocal will be a bit stronger than taking
> the log" means.
...

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===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD