M12 - Logistic Regression

Question 1

Whats the idea of log regression?

Answer 1

When the dv is discrete (ctegorial, nominal, ordinal)

Question 2

Types of discrete variables?

Answer 2

Dichotomous
–> binary log. regr

Ordinal
–> ordinal log. regre

Nominal
–> multinominal log. regr

Question 3

Why does OLS make little sense for binary variables?

Answer 3

The dv is dichotomous

Classical OLS does not produce sensible values of the dv, which only takes on 0/1

Question 4

What does logistic regression do?

Models the …. of y= … ( … ) and y = … ( …… ) for theory testing and forecasting

Answer 4

What does logistic regression do?

Models the % of y= 1 ( EVENT ) and y = 0 ( NO EVENT ) for theory testing and forecasting

Question 5

1st step in log regr: logit coeff

Assumption

Answer 5

An unobservable / latent variable z generates the discrete values for the dv =’logit coeff’

• -> z depends on the iv
• -> the sum of the iv loads to y=1

Question 6

2nd step in log regr: link function

Answer 6

Logit coeff gives no statement about %

• -> function is required that generates from z the probability od y=1
• -> generates p(y=1) from z

Assumption:

• non linear relship between % of y=1 and iv
• linear relship between z and iv

Question 7

Whats saturation!

Answer 7

When z takes on extreme values, changes in x have littlfe effect

Question 8

Horizontal shifts?

Answer 8

Beta0 only affects horizontal shifts

Beta0 > 0 –> to the left
Beta0 < 0 –> to the right

Question 9

Stepness

Answer 9

A large beta1 implies, that with a variation in xj, extreme probability values are reached quickly

–> steep

Question 10

Problem with maximum likelihood?

Maximum-Likelihood estimation

• corresponding to … in linear regression
• how?

Answer 10

Effect od changing x sepends on where you are
Annoying!

–> odds ratio
Not dependent on wheerw you are

• corresponding to OLS to estimate regression parameters (but does not aim at minimizing variance)
• selects coefficients that make the observed values most likely to occur

Question 11

Interpretation of Metric Variables

• odds
• odds ratio

label in SPSS

Answer 11

• odds: the likelihood of an event occuring relative to the likelihood of an event not occuring
• odds ratio: “effect size” : how much do the odds (event occuring) increase/decrease when there is a unit change in the associated IV (OR = Odds after 1unit change/ original odds)
  –> if >1, than as IV increases, th odds of the outcome occuring increases
  –> if < 1, than as the predictor increases, the odds of the outcome occuring decreases
  “the higher blabla, the lower the probability of blabla to occur”

–> statement about how many percentages can only marginal effects give

• SPSS: odds ratio : Exp(B)

Question 12

When is the odds ratio equal to the ratio of the odds?

Answer 12

• xj has its original value + 1

- xj has its original value

Question 13

Likelihood Ratio test

• alternative to…
• based on …
• the resulting statistic is based on …
• interpretation

Answer 13

• alternative to chi²
• based on maximum-likelihood test
• based on comparing observed frequencies with those predicted by the model
• also has a chi² distribution: look up critical values for the df: it is significant if the value is bigger than the critical value

Compare the full model with a null model (contains only const term)

–> chi^2 distributed

Question 14

Marginal effects

• how?
• difference between …
• Obacht!

Answer 14

• set all variables equal to the mean and consider the marginal effects of xi on y
• difference between the p-values of Y=1 and Y=0
• Obacht: marginal value dpeends on the considered variable and on the values of other IV