7.

Question 1

How categorical dependent variable regression can be described?

Answer 1

Categorical dependent variable regressions means we are trying to see how different factors affect if an observation belongs to a particular group.

Question 2

Where categorical dependent variable regression could be used for?

Answer 2

Create a model that predicts if a company will, or will not, go bankrupt.
Identify which factors increase / decrease the probability that a political party will or not will be elected.
Create a filter that classifies emails into spam and non-spam.

Question 3

What are different types of caregorical dependent variable regressions?

Answer 3

The linear probability model
The binomial logit model

Question 4

Problems with the linear probability model

Answer 4

R-squared is innacurate messure
The left side of equation could only be between 0 and 100%

Question 5

What is the binomial logit model?

Answer 5

The binomial logit model – a regression equation model with a binary dependent variable that uses logs and exponents.

Question 6

What are advantages of binomial logit model?

Answer 6

Easy to understand
It indicates by how much a change in the independent variables affects the dependent variable

Question 7

How the binomial logit model works?

Answer 7

The binomial logit model models the probability of the default situation (i.e., 𝐷_𝑖=1).
The output / prediction of the regression equation ranges from 0 to 1.
Given the specific of this approach it does not estimate the regression line using OLS. Instead it uses something called Maximum Likelihood (ML). Because of this, the only thing you should check is collinearity
Decisions to which group an observation should be classified are made based on some decision threshold. For example, if the probability of a default is > 0.5 for an individual, we can say he/she will default, while if it is below, we can say he/she will not.

Question 8

What are different strategies of interpreting results of binomial logit model?

Answer 8

1. Changing an average observation. Create an average observation by plugging the means of all independent variables. Then change one independent variable and calculate how the dependent variable probabilities change.
2. Calculating the odds ratio. Odds ratio – compares the probability of 𝐷_𝑖=1 to 𝐷_𝑖=0. It is calculated as follows: 𝑒^(𝛽_𝑘 )=(P(𝐷_𝑖=1))/(P(𝐷_𝑖=0))
3. Partial derivative. The expected value of (𝐷_𝑖 )̂ that is associated with one unit increase in 𝑋_1𝑖 is equal to 𝛽_1 (𝐷_𝑖 )̂ (1−(𝐷_𝑖 )̂)
4. Dividing coefficient by 4. Dividing the coefficient by 4 provides the upper bound marginal effect of an independent variable

Question 9

What is a confusion matrix?

Answer 9

Confusion matrix – a table indicating correct and incorrect predictions. Accuracy of it’s prediction is calculated by 1 + 4 / 1 + 2 + 3 + 4

Question 10

Whatare different alternatives of models?

Answer 10

Probit – uses the standard normal distribution to derive similar predictions as the logit model.
Tobit – used when there are variables that are censored – we only have partial information.
Ordered logit/probit models – a logit/probit model that can be used with an ordered dependent variable.
Multinomial logit model – a logit model that can be used with a categorical variable with many categories.