Stata/Binomial Outcome Models

References Regression Models for Categorical Dependent Variables Long and Freese. Example datasets and programs are available on this webpage Binomial outcome models The logit model can be estimated using logit or glm and the probit model with probit or glm. . clear . set obs 10000 obs was 0, now 10000 . gen u = invnorm(uniform()) . gen x = invnorm(uniform()) . gen ystar = x + u . gen y = (ystar > 0) . eststo clear . eststo : qui : reg ystar x (est1 stored) . eststo : qui : glm y x, family(binomial) link(logit) (est2 stored) . eststo : qui : logit y x (est3 stored) . eststo : qui : glm y x, family(binomial) link(probit) (est4 stored) . eststo : qui : probit y x (est5 stored) . esttab , se Scobit Scobit (Skewed logistic regression) was developed by Jonathan Nagler 1994 (American Journal of Political Science). The idea is to estimate a skewness parameter of the underlying distribution. . global N = 2000 . global alpha = 1 . clear . set obs $N obs was 0, now 2000 . gen u = ln(uniform()^(-1/$alpha) - 1) . gen x = uniform() . global beta = 2 . gen y = ($beta * x + u > 0) . . scobit y x Fitting logistic model: Iteration 0: log likelihood = -1190.598 Iteration 1: log likelihood = -1126.9573 Iteration 2: log likelihood = -1125.9604 Iteration 3: log likelihood = -1125.9597 Iteration 4: log likelihood = -1125.9597 Fitting full model: Iteration 0: log likelihood = -1125.9597 Iteration 1: log likelihood = -1125.9459 Iteration 2: log likelihood = -1125.8543 Iteration 3: log likelihood = -1125.8241 Iteration 4: log likelihood = -1125.8008 Iteration 5: log likelihood = -1125.7376 Iteration 6: log likelihood = -1125.731 Iteration 7: log likelihood = -1125.724 Iteration 8: log likelihood = -1125.7185 Iteration 9: log likelihood = -1125.7158 Iteration 10: log likelihood = -1125.7144 Iteration 11: log likelihood = -1125.714 Iteration 12: log likelihood = -1125.7139 Iteration 13: log likelihood = -1125.7139 Skewed logistic regression Number of obs = 2000 Zero outcomes = 565 Log likelihood = -1125.714 Nonzero outcomes = 1435 ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | 4.290739 7.563589 0.57 0.571 -10.53362 19.1151 _cons | 1.737008 4.256165 0.41 0.683 -6.604923 10.07894 -------------+---------------------------------------------------------------- /lnalpha | -1.068748 1.993377 -0.54 0.592 -4.975694 2.838198 -------------+---------------------------------------------------------------- alpha | .3434382 .6846017 .0069037 17.08495 ------------------------------------------------------------------------------ Likelihood-ratio test of alpha=1: chi2(1) = 0.49 Prob > chi2 = 0.4832 note: Likelihood-ratio tests are recommended for inference with scobit models.