Stata/Binomial Outcome Models

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 developped by Jonathan Nagler 1994 (American Journal of Political Science). The idea is two 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.