Dis./Avantadges of estimating of binary response model with OLS

[endlessend25]

In the Maximum Likelihood Estimator context, I can't find answers for those two questions:
- What are the advantages and disadvantages of estimating of a binary response model with OLS ?
- Same questions but compared to MLE ?

I thank you in advance

 

[hlsmith]

What do you think the issues may be? Or how may sample size come into play?

 

[hlsmith]

What type of estimates do you get when running linear and logistic models?

 

[endlessend25]

Well if we have a binary model, OLS will just get 0 and 1 and it will not be as precise as if it was more precise value, right ? If we have a big sample, OLS wouldn't be able to show the variety of the different values.

I'm supposed to get a consistent and if possible efficient estimates when I run a model as far as I know.

 

[hlsmith]

Well one kicks out average values and the other kick out log(odds). Two completely different types of numbers and not inter-changeable. I think my sample size comment is moot, I was thinking of Poisson regression.

 

[endlessend25]

Alright, I see your point. What I have up to now are the following:

+ of ML
- Consistency, efficiency, asymptotic normality
- Unifiied, general theory of estimation and testing

- of ML
- Need to specify the distribution
- Danger of Misspecification
- All results are asymptotic (why is that a problem ? )

+ of Linear Probability Model:
- Simple OLS estimation (with robust s.e.)
- Straightforward interpretation of parameters
- Other linear methods can be easily applied

- of LPM
- Heteroskedastic s.e.
Predictions sometimes outside the unit interval

Do you agree with that ?

 

[hlsmith]

So for clarification, your question is what are the disadvantages of using a linear regression model when your dependent variable is binary, correct?

 

[endlessend25]

Yes, and the advantages. Same for the ML.

 

[Dragan]

- of LPM
- Heteroskedastic s.e.
Predictions sometimes outside the unit interval

Do you agree with that ?

OLS will also most likely violate the assumption of normality.