Logistic Regression

Question 1

Concept

Answer 1

Aim is to predict how likely it is that an event will occur that OV = 1 or how likely it is that OV = 0

Question 2

Why use logistic regression and not linear regression?

Answer 2

Many assumptions such as linear assumption will be violated

Question 3

Odds

Answer 3

Long run ratio of an event happening to an event not happening
Odds (wins) = n (wins) / n (losses) = p (win) / p (lose)

Question 4

What is chi square used for

Answer 4

To test significance of the model (bc categorical OV)

Question 5

3 values of model testing

Answer 5

Deviance (-2LL)
Pseudo R squared
Hit rate

Question 6

-2LL (log likelihood)

Answer 6

How much unexplained information after model has been fitted
(Big values, bad models)

Question 7

Pseudo R squared

Answer 7

Explanatory power of the model with PVs compared to null model without PVs
(Higher pseudo R squared the better)

Question 8

Hypotheses chi square

Answer 8

H0: newly added PVs, compared to null, have no difference on OV
- beta 1 = beta 2 = … = beta k = 0

H1: at least one beta does not equal 0

Question 9

Hit rate

Answer 9

Number of people in dataset we correctly predict the event to occur

Question 10

Effect of high cutoff rate

Answer 10

LESS 1s MORE 0s
Prediction of extra 0s are incorrect so correct estimates for 0s decrease and increase for 1s

Question 11

Effect of low cutoff rate

Answer 11

MORE 1s LESS 0s
Prediction of extra 1s are not correct so probability of correct estimates for 1s decrease and increase for 0s

Question 12

Exp(B) concept

Answer 12

When we increase PV by 1 unit, the odds of that event happening will change by exp(B) factor
Less than one: negative effect
More than one: positive effect
One: no effect

Question 13

Reporting chi square statistic

Answer 13

If p is less than 0.05 we reject H0 and conclude that at least one of the betas is not equal to 0, and at least one of the PVs is significant and has an effect on OV, so our model as a whole adds explanatory power compared to the null model

Reject? Equal to 0? Significant? Effect on OV? Adds explanatory power?

Question 14

Pseudo R squared interpretation

Answer 14

Explanatory power of the model with PVs compared to model without PVs
Gives an idea about “how well the PVs in the model fits into the data”
Higher they are more improvement

Question 15

Interpreting beta

Answer 15

Only see if the effect is positive or negative

Values above 0 have positive effect
Below 0 have negative effect

Question 16

Interpreting exp(B)

Answer 16

Exp(B) = odds ratio!
Interprets effect size
When we increase PV by 1 unit, the odds of that event happening (y=1) will change by factor exp (B)