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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
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César Capinha
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1 Answers1

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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
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  • 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