# Re: st: tobit?

 From Steven Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: tobit? Date Wed, 13 Aug 2008 07:54:35 -0400

I agree with Kieran. There was a thread about using ratios as dependent or predictor variables in June, 2007, "dependent as denominator on the RHS". Here is part of my response, which is missing from the archive.

Dick Kronmal (RA Kronmal, 1993. Spurious Correlation and the Fallacy of the Ratio Standard Revisited. Journal of the Royal Statistical Society A, 156, 379-392) treated different problems from the one asked about. The following is my intepretation of his article. He considred three cases.

1) Y/Z is regressed against W/Z
This is the classic Neyman example of storks bringing babies: Neyman, J. (1952). Lectures and conferences on mathematical statistics and probability (2nd ed.; pp. 143-154). Washington, DC: U.S. Department of Agriculture. In applications, the same applies when per-capita measures appear on both sides of a model equation.

2) Y is regressed against W/Z
3) Y/Z is regressed against W.

A common example of a single ratio in cases 2 & 3 is the analysis of Body Mass Index (BMI) = Weight/Height^2 (units of Kg/M^2).

Kronmal observes that "W/Z" on the RHS of the model equation in cases 1 & 3 is an interaction term: W x (1/Z). He cites the general principle that one should not include an interaction term without including the main effects (W & Z, or W and 1/Z).

More basically, use of a ratio with Z in the denominator is an attempt to "control" for Z. However control via a ratio will always be incomplete. The question being asked in all three cases is, "If Z is held constant, what is the relation between Y & W?" When the question is put this way, one would control for Z by stratification or by putting some form of Z on the RHS of the model. Another approach would take logs of Y,W, & Z.

-Steve

On Aug 12, 2008, at 8:50 PM, Kieran McCaul wrote:

Since BMI is weight divided by height squared, why not regress weight on
SES while adjusting for height squared?

______________________________________________
Kieran McCaul MPH PhD
WA Centre for Health & Ageing (M573)
University of Western Australia
Level 6, Ainslie House
48 Murray St
Perth 6000
Phone: (08) 9224-2140
Phone: -61-8-9224-2140
email: kamccaul@meddent.uwa.edu.au
http://myprofile.cos.com/mccaul
_______________________________________________

--- Mona Mowafi <mmowafi@hsph.harvard.edu> wrote:

```I have a dataset in which I am evaluating the effect of SES on BMI
and BMI is heavily skewed toward obesity (i.e. over 50% of the sample
```
```30 BMI).  I preferred to run a linear regression so as to use the
```
```full range of data, but the outcome distribution violates normality
assumption and I've tried ln, log10, and sqrt transformations, none
of which work.

Is it appropriate to use tobit for modeling BMI in this instance?  If
not, any suggestions?
```
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