*! version 1.0.0 19feb2025

Title

goprobit2 -- Generalized ordered probit regression

Syntax

goprobit2
depvar
[indepvars]
[if] [in]
[weight]
[, options]

Model
distribution(goprobit2##distname:distname) specify distribution for link function; default is distribution(normal)

SE/Robust
vce(vcetype) vcetype may be oim, opg,
robust, cluster clustvar, bootstrap, or
jackknife

Maximization
maximize_options control the maximization process; seldom used

fweights, iweights, and pweights are allowed;
see weight.

distname

SGT family
normal normal distribution; the default

snormal skewed normal distribution

laplace Laplace distribution

slaplace skewed Laplace distribution

ged generalized error distribution

sged skewed generalized error distribution

t t distribution

st skewed t distribution

gt generalized t distribution

sgt skewed generalized t distribution

Description

goprobit2 is a community-contributed module which fits ordered response
regression models of ordinal variable depvar on the independent variables
indepvars. It extends oprobit by offering a variety of link functions based
on the SGT family of statistical distributions.

Options

Model

distribution(goprobit2##distname:distname) specifies the distribution of
the link function. This means the CDF of distname is the link function;
with dist(normal), the default, the Normal CDF is used, producing the same
results as oprobit.

SE/Robust

Maximization

maximize_options:
difficult,
technique(maximize##algorithm_spec:algorithm_spec),
iterate(#), [no]log, trace,
gradient, showstep,
hessian,
showtolerance,
tolerance(#),
ltolerance(#),
nrtolerance(#), and
nonrtolerance; see [R] Maximize.
These options are seldom used.

Examples

Setup

. webuse fullauto

Ordered response regression with Skewed Generalized t CDF link function

. oprobit rep77 foreign length mpg, dist(sgt)

Stored results

goprobit2 stores the following in e():

Scalars

e(N) number of observations

e(k_cat) number of categories

e(k) number of parameters

e(k_aux) number of auxiliary parameters

e(k_eq) number of equations in e(b)

e(k_eq_model) number of equations in overall model test

e(k_dv) number of dependent variables

e(df_m) model degrees of freedom

e(ll) log likelihood

e(N_clust) number of clusters

e(chi2) chi-squared

e(p) p-value for model test

e(rank) rank of e(V)

e(ic) number of iterations

e(rc) return code

e(converged) 1 if converged, 0 otherwise

Macros

e(cmd) goprobit2

e(cmdline) command as typed

e(distribution) distribution entered in distribution(distname)

e(depvar) name of dependent variable

e(wtype) weight type

e(wexp) weight expression

e(title) title in estimation output

e(chi2type) Wald or LR; type of model chi-squared test

e(vce) vcetype specified in vce()

e(vcetype) title used to label Std. err.

e(opt) type of optimization

e(which) max or min; whether optimizer is to perform
maximization or minimization

e(ml_method) type of ml method

e(user) name of likelihood-evaluator program

e(technique) maximization technique

e(properties) b V

e(predict) program used to implement predict

Matrices

e(b) coefficient vector

e(Cns) constraints matrix

e(ilog) iteration log (up to 20 iterations)

e(gradient) gradient vector

e(cat) category values

e(V) variance-covariance matrix of the estimators

e(V_modelbased) model-based variance

Functions

e(sample) marks estimation sample

Future Features

This vesion of goprobit2 is fully functional, although not yet optimized in
terms of computational performance. A future version will prioritize such
optimization to make this program tractable with big data. If you would like to
help, please contact the author.

Authors

Jacob Triplett authored this program with help from authors of a paper describing this estimator (see Johnston, McDonald & Quist (2019), referenced below). Please
contact Jacob with questions or comments.

Jacob Triplett

The University of North Carolina

Kenan-Flagler Business School

jacob_triplett@kenan-flagler.unc.edu

References

Johnston, C., McDonald, J., & Quist, K. (2019). A generalized ordered Probit model. Communications in Statistics - Theory and Methods, 49(7), 1712–1729. https://doi.org/10.1080/03610926.2019.1565780

Related software packages include:

oprobit (Stata)

ologit (Stata)

goprobit (Community-contributed)

gologit (Community-contributed)

gologit2 (Community-contributed)