Binary Dep for kids Flashcards
What three models do we have?
Logit, Probit, LPM
How do we interpret Binary dependent variable regression
interpreted as a conditional probability function
What is conditional probability
Conditional probability is the probability of one thing being true given that another thing is true
Difference between Probit & Logit and LPM
- Probit, Logit allows for non-linear relationship between dependent and regressors
- Probit, Logit will be between 0 to 1
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R2 Interpretation
No meaningful interpretation
- regression line never able to fit the data perfectly because y is binary and regressors are continious
R2 relies on ___ which make it unusable
linear relationshipt between X and Y
What measures the fit of the model
PseudoR2 measureas the fit using the likelihood function
What is a good PseudoR2 value
Rule of thumb is between 0,2 and 0,4
PsuedoR2 is also called
McFadden
Standard errors in LPM are always
Heteroscedastic, so we use robust standard errors
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When Y is the binary variable -> explain the regression
The population regression function shows the probability that Y = 1 given the value of the regressors
Why is it called LPM
Because the probability that Y = 1 is a linear function of the regressors
What is Probit and Logit regressions
They are regression models that are nonlinear when Y is used as a binary variable
Difference between LPM and Probit & Logit
Probit & Logit regressions ensure that the predicted probability will be between 0 and 1
Probit Regression uses …..
Cumulative Distribution function
What is cumulative distribution function
It is the probability that the variable takes a value less than or equal to X
What does Probit and Logit regression allow for that LPM doesnt
Probit and Logit models allows for non-linear relationship between regressors and dependent variable.
Logit Model uses _________
Logistic cumulative distribution function
Logit and Probit Models are appropriate when attempting to model ___
a dichotomus dependent variable, e.g. yes/no, agree/disagree, like/dislike.
How does the Probit and Logit model look like? Shape
S-Shape, y is between 0 and 1
Y axis shows
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
where infinity come from
when p = 1, we get log(1) - log(0). This equals positive infinity, we now got both positive and negative infinity
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What is the z value
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)
Why cant we use Least Squares method
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
Maximum Likelihood Intuitive of the mean
- Imagine that you have a line of observed values.
- Then imagine that you test every point on that line for where you get the highest likelihood of observing the data
- when all areas are checked you pick the one that maximizes the likelihood
likelihood in statistics means
trying to find the optimal value for the mean or std for a distribution
How do wee find the best regression line
maximum likelihood
if p-value is < 0,05
there is a statistically significant association between the response variable and dependent
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Consistency means:
Increased sample will make the Beta converge to the real beta
Unbiasedness means
The expected value of the beta will on average be correct.
Not an overestimate or underestimate
What are the assumptions on the parameters
- Consitency: increase sample = converge to true population value
- Unbiased: Expected B will equal true B
What do we use instead of R2
PseudoR2 (Mcfdden)
is there a reason to use LPM over Probit, Lobit?
- more easy to interpret
- it can be discussed if there are not extreme prop values
how to interpret probit coeff
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
What are the tests for parameters
z - test: one parameter
likelihood ratio test: several parameters
What are the interpretation for the marginal effects in the three models
LPM assumes a that the distribution
Marginal effects of Probit and Logit
Use Probability Distribution Function to find it
When can LPM be used
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.
rule of thumb for when to use LPM versus logit
- 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.
LPM is bad with
very large or very small probabilities
