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Im working on a panel data set and have difficulties to understand the odds ratio of a fixed effect logit model. I prepared an cross sectional exapmle. I suppose the interpretation is identical:

 data(cars)
 attach(cars)

 fit<-glm(Sound ~ Mileage+Price, family=binomial(link="logit"))

 summary(fit)


  Coefficients:
                Estimate Std. Error z value Pr(>|z|)    
  (Intercept)  1.581e+00  2.811e-01   5.623 1.88e-08 ***
  Mileage     -1.189e-05  9.428e-06  -1.261 0.207205    
  Price       -2.734e-05  7.564e-06  -3.614 0.000301 ***


  require(MASS)

  exp(cbind(coef(fit), confint(fit))) ## for odds ratios

                             2.5 %    97.5 %
    (Intercept) 4.8578575 2.8174158 8.4927615
    Mileage     0.9999881 0.9999695 1.0000065
    Price       0.9999727 0.9999577 0.9999874

How can I interpret odds ratios as an increase/decrease in chance or probability?

Googme
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  • You can interpret the odds ratios as ratios of odds not as an increase or decrease in probability. – Maarten Buis Jul 17 '15 at 08:04
  • @ Maarten Buis. Thank you for the asnwer. In terms of the example. That means that the odds of having a load car decreases by `(0.9999881/0.9999727)` ? – Googme Jul 17 '15 at 08:14
  • No, the odds of getting a loud car decreases by a factor .9999727 for every dollar/euro/yen/pound/... increase in price (which is why you probably want to measure price in 1000s of dollars/euros/yen/pounds/...). It is a decrease because if you multiply a number with a number less than 1 the outcome will be less than the original number. – Maarten Buis Jul 17 '15 at 10:20

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