LOGISTIC REGRESSION

Question 1

What is the distribution of a logistic regression?

Answer 1

Bernouilli

Question 2

What’s the formula that is the essence of logistic regression?

Answer 2

log[p/(1-p)]

also, odds = p/(1-p)

Question 3

What is the range of odds?

Answer 3

0 to infinity

Question 4

What is the range of log(odds)?

Answer 4

• infinity to + infinity

Question 5

So why do we use logit?

Answer 5

Because it enables to go from probabilities (0,1) to the range of log, that are infinite both ways, making this a more natural space for a linear model
(we’re not transforming the outcome, but the probability)

Question 6

Key assumptions of logistic model (2)

Answer 6

• Outcome is binary

- Observations are independent

Question 7

Probability =

Answer 7

exp(b0+bx)/[1+exp(b0+bx)]

Question 8

How do we estimate the coefficients?

Answer 8

With a maximum likelihood function, which looks the set of coefficients that make the observed responses maximally likely

Unlike least squares, no closed-form solution to problem, so it’s found by trial and error

Question 9

When does the explanatory variable as a significant effect?

Answer 9

When the beta is more than 2 standard errors away from 0
- but since p is not linear with X, the same change has a more drastic impact on p towards the center of the p-range than in the extremes

Question 10

The deviance of a model is…

Answer 10

-2*loglikelihood of the data under the model considered

• the smaller the deviance, the better the fit
• decreases when we add parameters

Question 11

We can get the RR by…

Answer 11

Predicting the risk of the outcome