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Suppose that the model had the following output:

                        Estimate Std. Error z value Pr(>|z|)   
(Intercept)              0.07       0.33      0.21   0.829     
x0_low                   0.44       0.22      1.96   0.049   * 
x1_m                    -0.51       0.25     -1.98   0.047   * 
x1_l                    -0.05       0.22     -0.24   0.809     
x2_no                    0.51       0.26      1.94   0.051   .

where

  • x0 has levels hi, low
  • x1 has levels s, m, l
  • x2 has levels yes, no

I'm wondering what an interpretation for the coefficient x1_m would be.

It seems as though it could be:

x1_m reduces the log(odds) by roughly 40% having adjusted for x0 and x2

But what I'm a bit confused about is whether this is actually what it's saying, because x1_m is simply a level within the factor x1, so does that change its meaning?

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1 Answer 1

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x0, x1 and x2 are factors. So, so called 'reference levels' are chosen for them (by default these wolud be their first levels: hi, s and yes respectively).

All the coefficients of the model can be interpreted as a difference between 'modelled' and 'reference' level.

So, in you case, x1=m reduces the log(odds) by roughly 0.51, as comapred to x1=s and having adjusted for x0 and x2.

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  • $\begingroup$ I didn't realise that the interpretation of a beta coefficient for log odds could be considered as a percentage, for some reason i thought that was just when the exponential was taken, thanks $\endgroup$
    – baxx
    Commented Apr 4, 2019 at 8:40
  • $\begingroup$ You're right. Answer edited $\endgroup$
    – Łukasz Deryło
    Commented Apr 4, 2019 at 9:06

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