4

I wonder if someone could give me some advice on using ratios as a dependent variable in a Generalized Linear Model.

I have a variable referring to the increase of "size at Time 1" to "size at Time 2" for $n=37$ individuals. I want my dependent variable to be percentage increase from Time 1 to Time 2. Because "size at Time 2" is equal to or greater than "size at Time 1" my dependent may range from 0 to +infinity.

I'm interested in testing a number of potential explanatory variables for this percent increase while also taking into account a potential confounding factor (that will be represented as a continuous variable).

I've read that I might log-transform my dependent variable and use a GLM to conduct the analysis. This would allow me to include my confounding factor as a covariate in the analysis in order to measure its effect.

My question is can I also test the influence of "size at Time 1" as an explanatory variable? What are the implications of using as predictor a variable previously used for calculating the dependent?

Nick Cox
  • 48,377
  • 8
  • 110
  • 156
César Capinha
  • 41
  • 1
  • 2
    [Here](http://stats.stackexchange.com/questions/47222/techniques-for-analyzing-ratios/) might help. – Scortchi - Reinstate Monica Jan 30 '13 at 11:32
  • Hi Scortchi, I also read here [link](http://www.jerrydallal.com/LHSP/logs.htm) and in couple of reviewed papers that log transformation solve the lack of symmetry problem. What is not clear to me is if it is correct to use as predictor the variable that was used to 'weight' the dependent. Thanks – César Capinha Jan 30 '13 at 12:25

1 Answers1

3

There aren't a priori correct & incorrect models - it depends what you're modelling. If your dependent variable is $Y=\log \frac{Q}{R}$ & you don't include $R$ as a dependent variable, you're saying you know the relation between $Q$ & $R$, effectively bundling $-\log R$ into the intercept term of the model for $\log Q$. If you're not so sure, then by all means include it - perhaps as a $\beta_r \log R$ term.

Scortchi - Reinstate Monica
  • 27,560
  • 8
  • 81
  • 248
  • Many thanks Scortchi. I do not know the relation between Q & R. You suggest that I include log(R) as a dependent? Your "βrlogR term" is not clear to me. – César Capinha Jan 31 '13 at 10:41
  • Yes that's what I meant (using $\beta_r$ for the coefficient you're going to estimate). So you'd be saying that, other things being equal, $\frac{Q}{R^{\beta_r}}$ was constant, where $\beta_r$ might turn out to be 1, but might not. Just a consideration though - has to look plausible to you. – Scortchi - Reinstate Monica Jan 31 '13 at 11:11