0

I have a multivariate linear regression model where the predictors are concentrations of different drugs, of the same units, and the responses are the survival percentages of each different kind of bacteria within a bacteria community, which are also of the same unit in the sense that these are percentages.

My questions are:

1) For a single bacteria (the same response), can I compare the regression coefficients across the predictors so that I can say one drug is more correlated with the response than another drug?

2) For a single predictor (the same predictor), can I compare the regression coefficient across the responses (different bacteria) so that I can say the drug is more correlated with one bacteria (response) than another bacteria?

S.Wang
  • 65

1 Answers1

2

Ill start from the end - having compared the coefficients, one would not talk of correlation (that is a different test - $Pearson's\ r$) since normally correlation is bivariate, meaning that no controls are affecting the relationship. One could say that drug A is more influential on the mortality of the bacteria, while controlling for drug B (or that it has a larger affect size).

Generally, when you wish to compare coefficients in a single model, than compare the $beta$ - or the standardized coefficients. In effect, if two coefficients have the same meaning and unit of measurement, that a direct comparison is possible.

Regarding comparison between models (with different bacteria mortality as your $\hat{Y}$, I would be more careful with the phrasing, because the situations are potentially different. Example: Say model 1 has $bacteria_1$ and model 2 has $Bacteria_2$ - both with survival percentage as the dependent variable, and both models have a $drugA$ coefficient. The models are:

$Bacteria_1=\beta_0+5X_{DrugA}$

$Bacteria_2=\beta_0+10X_{DrugA}$

You could say that every increase in 1% in the concentration of DrugA increases the death of Bacteria 1 by 5 percent, and that it increases the death of Bacteria 2 by 10 percent. But saying that it has twice the efficacy might be misleading. Perhaps Bacteria 1 is much more resistant to drugs than bacteria 2. If Bacteria 2 can be easily killed by drugs, than comparing efficiencies is difficult. You can say, however, that Drug A kills more of Bacteria 2 than Bacteria 1.

Yuval Spiegler
  • 2,091
  • 1
  • 17
  • 33
  • Thank you for your answer. So for my case, my conclusion is not about whether Drug A is more effective for Bacteria 2 than 1, but something like Drug A is more negatively correlated with Bacteria 2 than 1. Does this sounds like a fair conclusion? – S.Wang Apr 06 '17 at 15:17
  • I wouldn't use the term 'correlation' for the reasoning in my answer. You might say that it has a stronger negative effect in absolute terms on bacteria 2 than on bacteria 1. – Yuval Spiegler Apr 06 '17 at 22:25