{smcl} {* *! version 1.0.0 29oct2017}{…} {cmd:help brglm} {hline} {title:Title} {p2colset 5 19 21 2}{...} {p2col :{bf: brglm} {hline 2}}Bias reduced estimators for binary response models {p_end} {p2colreset}{...} {marker syntax}{...} {title:Syntax} {p 8 12 2} {cmd:brglm} {depvar} [{indepvars}] {ifin} [{cmd:,} {it:options}] {synoptset 26 tabbed}{...} {synopthdr} {synoptline} {syntab :Model} {synopt :{opth m:odel(brglm##modelname:modelname)}}model for the distribution of {depvar}; default is {opt probit} {p_end} {synopt :{opt nocon:stant}}suppress constant term{p_end} {syntab :Options} {synopt :{opth iter:ations(##)}}maximum number of iterations; default is 5000{p_end} {synopt :{opth tol:erances(##)}}tolerance level; default is 1.000e-6{p_end} {marker modelname}{...} {synoptset 23}{...} {synopthdr:modelname} {synoptline} {synopt :{opt logit}}Logit{p_end} {synopt :{opt probit}}Probit{p_end} {synopt :{opt cloglog}}Cloglog{p_end} {synoptline} {p2colreset}{...} {p 4 6 2} {it:indepvars} may contain time-series operators or factor variables, see {help fvvarlist}.{p_end} {marker description}{...} {title:Description} {pstd} {opt brglm} estimates bias-reduced probit, logit and cloglog models by iterative weighted least squares (IWLS). {p_end} {pstd} - Cross-sectional properties are derived by Kosmidis and Firth (2009). {p_end} {pstd} - 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).{p_end} {marker examples}{...} {title:Example: Cross-Section} {pstd}Setup{p_end} {phang2}{cmd:. webuse union}{p_end} {pstd}Biased-reduced probit model{p_end} {phang2}{cmd:. brglm union age grade i.not_smsa south if year==88 , model(probit) } {p_end} {title:Example: Panel} {pstd}Setup{p_end} {phang2}{cmd:. webuse ships}{p_end} {pstd}Prepare dataset{p_end} {phang2}{cmd:. g y=accident>0}{p_end} {phang2}{cmd:. bys ship: g time=_n}{p_end} {phang2}{cmd:. xi i.ship}{p_end} {pstd}Biased-reduced fixed effects probit model{p_end} {phang2}{cmd:. brglm y _Iship* time, model(probit)} {p_end} {marker results}{...} {title:Stored results} {pstd} {cmd:brglm,} stores the following in {cmd:e()}: {synoptset 20 tabbed}{...} {p2col 5 20 24 2: Scalars}{p_end} {synopt:{cmd:e(N)}}number of observations{p_end} {synopt:{cmd:e(ll)}}log likelihood{p_end} {synopt:{cmd:e(converged)}}{cmd:1} if converged, {cmd:0} otherwise{p_end} {synoptset 20 tabbed}{...} {p2col 5 20 24 2: Matrices}{p_end} {synopt:{cmd:e(b)}}coefficient vector{p_end} {synopt:{cmd:e(V)}}variance-covariance matrix of the estimators{p_end} {synoptset 20 tabbed}{...} {p2col 5 20 24 2: Macros}{p_end} {synopt:{cmd:e(cmd)}}brglm{p_end} {synopt:{cmd:e(model)}}{bf:modelname} {p_end} {synopt:{cmd:e(depvar)}}name of dependent variable {p_end} {synoptset 20 tabbed}{...} {p2col 5 20 24 2: Functions}{p_end} {synopt:{cmd:e(sample)}}marks estimation sample{p_end} {p2colreset}{...} {title:References} {synoptset 20 tabbed}{...} Kosmidis, Ioannis & David Firth. 2009. ‘Bias reduction in exponential family nonlinear models.’ {it: 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.’ {it: SSRN Working Paper No.} 3074193.