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I am running some logistic regressions in R. I need some help with interpreting coefficients.

So, if my DV is 1 = yes and 0 = no, and I have five groups (a, b, c, d, e) and I make a the reference group (dummy coding), and the coefficient for b is significant and positive:

  • does this mean the odds of b saying yes compared to the odds of a saying yes is greater?
  • Or is there a greater odds of saying yes for group a compared to b?
luchonacho
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gui_gui
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  • We have lots of questions and answers about interpretation of logistic regression in our archives: http://stats.stackexchange.com/search?q=interpret+logistic+regression – Sycorax Sep 18 '16 at 21:51

1 Answers1

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Denote the coefficient for $b$ by $\beta$ and the model's intercept by $\alpha$. We let group $a$ be the reference level.

Logistic regression fits the model:

$logit(\pi(x)) = \alpha + \beta_1 x_1 + ... + \beta_p x_p$

Where $logit(\pi(x)) = log(\frac{\pi(x)}{1-\pi(x)}) = log(odds(\pi(x)))$

Our reference group $a$ has the fit:

$logit(\pi(a)) = \alpha$

Hence, the odds of success for an individual from group $a$ is given by

$odds(\pi(a)) = e^\alpha$

While our group $b$ with coefficient $\beta$ has the fit:

$logit(\pi(b)) =\alpha + \beta$

and so in the same way as above, we find the odds for group $b$ by taking the exponential of both sides:

$odds(\pi(b)) = e^{\alpha + \beta} = e^\alpha \times e^\beta = odds(\pi(a))\times e^\beta$

Hence, under your model, the odds for group $b$ are $e^\beta$ times the odds for group $a$. It follows that if $\beta$ is positive, then $e^\beta>1$ and so the odds for group $b$ will be larger than group $a$. On the other hand, if $\beta$ is negative, then $e^\beta<1$ and so the odds of group $b$ will be smaller than that of group $a$.

Patty
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