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I'm currently analysing an experiment where animals were presented with a stimulus under two different treatments (Po & Br) using a GLM. RespYN is a binary response variable showing whether the animal responded to the stimulus.

glm(RespYN ~ Treatment + Gender + Length_Diff + Cockroach_ID, data = data, family = binomial(link = "logit"))

I haven't really dealt with log odds at all before, so I'm asking for some clarification in interpreting the coefficient estimates

Coefficients:
         Estimate Std. Error z value Pr(>|z|)    

(Intercept)   1.74016    0.53317   3.264   0.0011 **
TreatmentPo  -4.40331    0.54346  -8.102 5.39e-16 ***

My understanding is that this means that Treatment having the value of Po is associated with a decrease in the log odds of observing a positive response of -4.40331 comapred to treatment having a value of Br.

However I'm a) not certain I've understood this correctly and b) not sure how to translate this into something meaningful i.e. what is the decrease in odds (not log odds) or probability.

Any help is greatly appreciated!

Toby Roberts
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  • Your understanding is spot on ! To get odds ratios, just exponentiate the estimated coefficients. – Robert Long Jan 27 '20 at 13:52
  • The question in the above link even seems to be using the same dataset! – Robert Long Jan 27 '20 at 13:55
  • Hi Robert! It is in fact the same dataset - that question was posted by my lab partner, but I wouldn't allow me to comment on it so I had to create a separate question. Thankyou for your help so far, I was just not sure I was understanding correctly. – Toby Roberts Jan 27 '20 at 16:40
  • In the previous question, you calculated that length was associated with a decrease of ~6% in likelihood of respYN being Y. I attempted to do the same for Treatment. Exponentiating -4.4 gives 0.0122. Taking that away from 1 gives 0.0122, does this therefore mean that treatmen = Po reduces the odds of obtaining a response by ~99%? – Toby Roberts Jan 27 '20 at 16:44
  • Or could I simply report that the odds ratio given is 0.0122 which is < 0 therefore treatment = Po lowers the odds of an outcome? Thanks again for all the help – Toby Roberts Jan 27 '20 at 16:45
  • You are correct except for the last comment. When the log-odds is negative, this means the odds ratio is less than 1 (an odds ratio cam never be negative). If the outcome is a disease then we say the exposure is protective when the odds ratio is below 1 and a risk factor if it is above 1. – Robert Long Jan 27 '20 at 17:17
  • Thankyou! sorry that was a typo, should have been '< 1' – Toby Roberts Jan 27 '20 at 18:24

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