Maximum likelihood without programming
Maximization of user-specified likelihood functions has long been a hallmark of Stata, but you have had to write a program to calculate the log-likelihood function. Now it is even easier. The only requirements are that you be able to write the log likelihood for individual observations and that the log likelihood for the entire sample be the sum of the individual values.
Stata can fit probit models, but let’s write our own.
The log-likelihood function for probit is
LL(y) = ln(normal(x'b)) if y==1 = ln(normal(-xb)) y==0
To fit a model of outcome on age and weight, we type
|Coef. Std. Err. z P>|z| [95% Conf. Interval]|
|/xb_age||.2279405 .0887648 2.57 0.010 .0539648 .4019163|
|/xb_weight||.01195 .0094324 1.27 0.205 -.0065372 .0304373|
|/b0||-9.765827 2.656796 -3.68 0.000 -14.97305 -4.558604|
Those results are exactly the same as those produced by Stata’s probit.
See the manual entry.
It’s hard to beat the simplicity of mlexp, especially for educational purposes.
mlexp is an easy-to-use interface into Stata’s more advanced maximum-likelihood programming tool that can handle far more complex problems; see the documentation for ml.
If you want to fit models via the generalized method of moments (GMM), see the documentation for Stata’s gmm.
See New in Stata 17 to learn about what was added in Stata 17.