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Scobit: An Alternative Estimator to Logit and Probit

Jonathan Nagler:

American Journal of Political Science, Vol. 38, No. 1. (Feb., 1994), pp. 230-255.Abstract:

Logit and probit, the two most common techniques for estimation of models with a dichotomous dependent variable, impose the assumption that individuals with a probability of .5 of choosing either of two alternatives are most sensitive to changes in independent variables. This assumption is imposed by the estimation technique because both the logistic and normal density functions are symmetric about zero. Rather than let methodology dictate substantive assumptions, I propose an alternative distribution for the disturbances to the normal or logistic distribution. The resulting estimator developed here, scobit (or skewed-logit), is shown to be appropriate where individuals with any initial probability of choosing either of two alternatives are most sensitive to changes in independent variables. I then demonstrate that voters with initial probability of voting of less than .5 are most sensitive to changes in independent variables. And I examine whether individuals with low levels of education or high levels of education are most sensitive to changes in voting laws with respect to their probability of voting.

## 7 comments:

I think I tried scobit once (having stumbled on it in Stata). It didn't make much difference but its nice to have alternatives to the usual suspects. In general I prefer probit because it leads more easily to generalizations.

I've used the scobit (or skewed logit) to test for the presence of skewness in a logit model (using a likelihood ratio approach).

I'm not aware of how to test for non-normality in a probit or logit model (or if it is in fact possible). However, (ignoring kurtosis) using the scobit to test for skewness may be the best that we can do.

I use heteroskedastic probit in a similar fashion, to test for the presence of heteroskedasticity in a probit model.

Invented by Scoby?

...for scobes everywhere.

There are a bunch of specification tests for probit. Anthony Murphy published a few papers on this years ago, in

Economics LettersI think.Thanks for flagging these papers Kevin. From what I can see, he looks at:

(i) LM tests of mis-specification for ordered logit models

(ii) score tests of normality in bivariate probit models

http://ideas.repec.org/e/pmu76.html

In relation to the Trinity of Testing Procedures (LR/LM/Wald), it seems that score tests are analagous to the LR approach, if I follow the Murphy paper correctly...

There's also:

Convenient Specification Tests for Logit and Probit Models, Davidson and MacKinnon

http://ideas.repec.org/p/qed/wpaper/514.html

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