Calculating odds ratio from glm output

Question

It is my first time doing logistic regressions and I am currently trying to teach myself how to find the odds ratio. I got my coefficients from r as shown below.

    (Intercept)   totalmins 
       0.2239254    1.2424020

To exponentiate the regression coefficient I did the following:

exp1.242/exp1.242+1   = 0.77

Really not sure if this is the correct process or not.

Any advice on how I would go about calculating odds ratio would be greatly appreciated

detection- 1/0 data if animal was detected at site
total mins- time animal spent at site

here's the output

    glm(formula = detection ~ totalmins, family = binomial(link = "logit"), 
    data = data)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.81040  -0.63571   0.00972   0.37355   1.16771  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)  
(Intercept)  -1.49644    0.81818  -1.829   0.0674 .
totalmins  0.21705    0.08565   2.534   0.0113 
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 41.194  on 33  degrees of freedom
Residual deviance: 21.831  on 32  degrees of freedom
  (1 observation deleted due to missingness)
AIC: 25.831

Number of Fisher Scoring iterations: 8

If you have an example data set it might be easier to help. Let's say you build a logistic regression model called "model1". To obtain the odds ratios and 95% confidence intervals for your model you could type: exp(cbind(OR = coef(model1), confint(model1, level = 0.95))) — user3585829, Jan 07 '18 at 18:59
The above code should still work for you to get your odds ratios. Did you try it? — user3585829, Jan 07 '18 at 19:08
Some more useful info here: https://stats.stackexchange.com/questions/8661/logistic-regression-in-r-odds-ratio — AntoniosK, Jan 07 '18 at 19:31

Len Greski · Answer 1 · 2018-01-07T21:41:22.750

This model evaluates the log odds of detecting an animal at the site based on the time in minutes that the animal spent on the site. The model output indicates:

log odds(animal detected | time on site) = -1.49644 + 0.21705 * minutes animal on site

To convert to odds ratios, we exponentiate the coefficients:

odds(animal detected) = exp(-1.49644) * exp(0.21705 * minutes animal on site)

Therefore, the odds and probability of detection if the animal spends 0 minutes on site is e(-1.49644) or 0.2239. The odds ratio of detection if an animal is on site for X minutes is calculated as follows. We'll model odds ratios for minutes 0 through 10, and calculate the associated probability of detection.

# odds of detection if animal on site for X minutes
coef_df <- data.frame(intercept=rep(-1.49644,11),
                   slopeMinutes=rep(0.21705,11),
                   minutesOnSite=0:10)
coef_df$minuteValue <- coef_df$minutesOnSite * coef_df$slopeMinutes
coef_df$intercept_exp <- exp(coef_df$intercept)
coef_df$slope_exp <- exp(coef_df$minuteValue)
coef_df$odds <- coef_df$intercept_exp * coef_df$slope_exp
coef_df$probability <- coef_df$odds / (1 + coef_df$odds)

...and the output:

> coef_df[,c(3:4,6:8)]
   minutesOnSite intercept_exp slope_exp   odds probability
1              0        0.2239     1.000 0.2239      0.1830
2              1        0.2239     1.242 0.2782      0.2177
3              2        0.2239     1.544 0.3456      0.2569
4              3        0.2239     1.918 0.4294      0.3004
5              4        0.2239     2.383 0.5335      0.3479
6              5        0.2239     2.960 0.6629      0.3986
7              6        0.2239     3.678 0.8235      0.4516
8              7        0.2239     4.569 1.0232      0.5057
9              8        0.2239     5.677 1.2712      0.5597
10             9        0.2239     7.053 1.5793      0.6123
11            10        0.2239     8.763 1.9622      0.6624
>

See also How to get probability from GLM output for another example using space shuttle autolander data from the MASS package.

Calculating odds ratio from glm output

1 Answers1