Binary Dep for kids

Question 1

What three models do we have?

Answer 1

Logit, Probit, LPM

Question 2

How do we interpret Binary dependent variable regression

Answer 2

interpreted as a conditional probability function

Question 3

What is conditional probability

Answer 3

Conditional probability is the probability of one thing being true given that another thing is true

Question 4

Difference between Probit & Logit and LPM

Answer 4

• Probit, Logit allows for non-linear relationship between dependent and regressors
• Probit, Logit will be between 0 to 1

Question 5

-

Answer 5

•

Question 6

R2 Interpretation

Answer 6

No meaningful interpretation

- regression line never able to fit the data perfectly because y is binary and regressors are continious

Question 7

R2 relies on ___ which make it unusable

Answer 7

linear relationshipt between X and Y

Question 8

What measures the fit of the model

Answer 8

PseudoR2 measureas the fit using the likelihood function

Question 9

What is a good PseudoR2 value

Answer 9

Rule of thumb is between 0,2 and 0,4

Question 10

PsuedoR2 is also called

Answer 10

McFadden

Question 11

Standard errors in LPM are always

Answer 11

Heteroscedastic, so we use robust standard errors

Question 12

.

Answer 12

.

Question 13

When Y is the binary variable -> explain the regression

Answer 13

The population regression function shows the probability that Y = 1 given the value of the regressors

Question 14

Why is it called LPM

Answer 14

Because the probability that Y = 1 is a linear function of the regressors

Question 15

What is Probit and Logit regressions

Answer 15

They are regression models that are nonlinear when Y is used as a binary variable

Question 16

Difference between LPM and Probit & Logit

Answer 16

Probit & Logit regressions ensure that the predicted probability will be between 0 and 1

Question 17

Probit Regression uses …..

Answer 17

Cumulative Distribution function

Question 18

What is cumulative distribution function

Answer 18

It is the probability that the variable takes a value less than or equal to X

Question 19

What does Probit and Logit regression allow for that LPM doesnt

Answer 19

Probit and Logit models allows for non-linear relationship between regressors and dependent variable.

Question 20

Logit Model uses _________

Answer 20

Logistic cumulative distribution function

Question 21

Logit and Probit Models are appropriate when attempting to model ___

Answer 21

a dichotomus dependent variable, e.g. yes/no, agree/disagree, like/dislike.

Question 22

How does the Probit and Logit model look like? Shape

Answer 22

S-Shape, y is between 0 and 1

Question 23

Y axis shows

Answer 23

We can think of the y-axis as originally having a value 0 to 1. But this value get transformed into the value of log(p/(1.p)). So if p (or y) was 0,5, the new value on this axis is log(0,5/(1-0,5))=0.

when p = 1, we get log(1) - log(0). This equals positive infinity, we now got both positive and negative infinity

Question 24

where infinity come from

Answer 24

when p = 1, we get log(1) - log(0). This equals positive infinity, we now got both positive and negative infinity

Question 25

.

Answer 25

.

Question 26

What is the z value

Answer 26

Rule of thumb: Z should be over 2 and p under 0,05 for H0 to be rejected

estimated intercept divided by the standard error

• the number of standard deviations the estimated intercept is away from 0 on a standard normal curve (Wald test)

Question 27

Why cant we use Least Squares method

Answer 27

Intuitively we want to draw the best line with least squares as in OLS simple regressions, but our residuals go to infinity, so cant use Least Squares

Question 28

Maximum Likelihood Intuitive of the mean

Answer 28

1. Imagine that you have a line of observed values.
2. Then imagine that you test every point on that line for where you get the highest likelihood of observing the data
3. when all areas are checked you pick the one that maximizes the likelihood

Question 29

likelihood in statistics means

Answer 29

trying to find the optimal value for the mean or std for a distribution

Question 30

How do wee find the best regression line

Answer 30

maximum likelihood

Question 31

if p-value is < 0,05

Answer 31

there is a statistically significant association between the response variable and dependent

Question 32

.

Answer 32

.

Question 33

Consistency means:

Answer 33

Increased sample will make the Beta converge to the real beta

Question 34

Unbiasedness means

Answer 34

The expected value of the beta will on average be correct.

Not an overestimate or underestimate

Question 35

What are the assumptions on the parameters

Answer 35

• Consitency: increase sample = converge to true population value
• Unbiased: Expected B will equal true B

Question 36

What do we use instead of R2

Answer 36

PseudoR2 (Mcfdden)

Question 37

is there a reason to use LPM over Probit, Lobit?

Answer 37

• more easy to interpret

- it can be discussed if there are not extreme prop values

Question 38

how to interpret probit coeff

Answer 38

A positive coefficient means that an increase in the predictor leads to an increase in the predicted probability.

A negative coefficient means that an increase in the predictor leads to a decrease in the predicted probability

Question 39

What are the tests for parameters

Answer 39

z - test: one parameter

likelihood ratio test: several parameters

Question 40

What are the interpretation for the marginal effects in the three models

Answer 40

LPM assumes a that the distribution

Question 41

Marginal effects of Probit and Logit

Answer 41

Use Probability Distribution Function to find it

Question 42

When can LPM be used

Answer 42

The basic insight is that the linear probability model can be used whenever the relationship between probability and log odds is approximately linear over the range of modeled probabilities.

Question 43

rule of thumb for when to use LPM versus logit

Answer 43

• if the probabilities are extreme, like yes/no, close to 0 or 1, logit is better
• if they are more moderate, like between 0,20 and 0,8, LPM can be used —then the linear and logistic models fit about equally well, and the linear model should be favored for its ease of interpretation.

Question 44

LPM is bad with

Answer 44

very large or very small probabilities