*! version 1.0.0 29oct2017
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help brglm

Title

brglm -- Bias reduced estimators for binary response models

Syntax

brglm
depvar
[indepvars]
[if] [in]
[, options]

Model
model(brglm##modelname:modelname) model for the distribution of depvar; default is probit

noconstant suppress constant term

Options
iterations(##) maximum number of iterations; default is 5000

tolerances(##) tolerance level; default is 1.000e-6

modelname

logit Logit

probit Probit

cloglog Cloglog

indepvars may contain time-series operators or factor variables, see fvvarlist.

Description

brglm estimates bias-reduced probit, logit and cloglog models by iterative weighted least squares (IWLS).

- Cross-sectional properties are derived by Kosmidis and Firth (2009).

- Panel models with fixed effects can be estimated by including an indicator variable for each panel unit as shown by Kunz, Staub and Winkelmann (2017).

Example: Cross-Section

Setup

. webuse union

Biased-reduced probit model

. brglm union age grade i.not_smsa south if year==88 , model(probit)

Example: Panel

Setup

. webuse ships

Prepare dataset

. g y=accident>0

. bys ship: g time=_n

. xi i.ship

Biased-reduced fixed effects probit model

. brglm y _Iship* time, model(probit)

Stored results

brglm, stores the following in e():

Scalars

e(N) number of observations

e(ll) log likelihood

e(converged) 1 if converged, 0 otherwise

Matrices

e(b) coefficient vector

e(V) variance-covariance matrix of the estimators

Macros

e(cmd) brglm

e(model) modelname

e(depvar) name of dependent variable

Functions

e(sample) marks estimation sample

References

Kosmidis, Ioannis & David Firth. 2009.
‘Bias reduction in exponential family nonlinear models.’ Biometrika, 96(4):793–804.

Kunz, Johannes S., Kevin E. Staub & Rainer Winkelmann. 2017.
‘Estimating fixed effects: Perfect prediction and bias in binary response panel models,
with an application to the Hospital Readmissions Reduction Program.’ SSRN Working Paper No. 3074193.