#StackBounty: #regression #logistic #standard-error #logit Calculating confidence intervals for a logistic regression

Bounty: 50

I’m using a binomial logistic regression to identify if exposure to has_x or has_y impacts the likelihood that a user will click on something. My model is the following:

fit = glm(formula = has_clicked ~ has_x + has_y, 
          family = binomial())

This the output from my model:

glm(formula = has_clicked ~ has_x + has_y, 
    family = binomial(), data = active_domains)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.9869  -0.9719  -0.9500   1.3979   1.4233  

                      Estimate Std. Error z value Pr(>|z|)    
(Intercept)          -0.504737   0.008847 -57.050  < 2e-16 ***
has_xTRUE -0.056986   0.010201  -5.586 2.32e-08 ***
has_yTRUE  0.038579   0.010202   3.781 0.000156 ***
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 217119  on 164182  degrees of freedom
Residual deviance: 217074  on 164180  degrees of freedom
AIC: 217080

Number of Fisher Scoring iterations: 4

As each coefficient is significant, using this model I’m able to tell what the value of any of these combinations is using the following approach:

predict(fit, data.frame(has_x = T, has_y=T), type = "response")

I don’t understand how I can report on the Std. Error of the prediction.

  1. Do I just need to use $1.96*SE$? Or do I need to convert the
    $SE$ using an approach described here?

  2. If I want to understand the standard-error for both variables
    how would I consider that?

Unlike this question, I am interested in understanding what the upper and lower bounds of the error are in a percentage. For example, of my prediction shows a value of 37% for True,True can I calculate that this is $+/- 0.3%$ for a $95% CI$? (0.3% chosen to illustrate my point)

Get this bounty!!!

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