Lecture 6: Linear Probability Models

Probit and Logit difference

Probit models the conditional probability as the CDF of standard normal distribution

Logit models it as the CDF of the standard logistic distribution

(both guaranteed to take values between 0 and 1)

what is the logistic function

differences between Logit and Probit (function used, error dsitribution, computational simplicity, variance)

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what is MLE used for

to find the β that maximises the likelihood function L(β)

what is maximum likelihood estimation (MLE)

a statistical method used to estimate the parameters (β) of a probability distribution by maximising the likelihood function

ie find the β that make the observed data most probable

how to do MLE

write out likelihood function (start with PMF for single observation then do joint likelihood which is product of all)

then do natural log of L(β) to turn product into sums

find best β using numerical optimisation

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obtaining MLE of Logit model

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marginal effects of probit and logit

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marginal effects vary with xi, smaller effects are closest to extremes 0 or 1

3 ways to calculate marginal effects

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