{smcl}
{* 22feb2002}{...}
{hline}
help for {hi:triprobit}{right:Antoine Terracol, terracol@univ-paris1.fr}
{hline}

{title:Trivariate probit model using the GHK simulator}

{p 4 12}{cmd:triprobit} {cmd:(} {it:depvar1} = {it:varlist1} 
[, {cmdab:nocons:tant}]{cmd:)} {cmd:(}{it:depvar2} = {it:varlist2} [, {cmdab:nocons:tant}] {cmd:)} {cmd:(} 
{it:depvar3} = {it:varlist3} [, {cmdab:nocons:tant}] {cmd:)} 
    [{it:weight}] [{cmd:if} {it:exp}] [{cmd:in} {it:range}] [{cmd:,}
    {cmdab:r:obust} {cmdab:cl:uster(}{it:varname}{cmd:)}
    {cmdab:dr:aws(}{it:#}{cmd:)} {cmdab:seed:(}{it:#}{cmd:)} {cmdab:noinit:} {it: maximize_options}]

{p}{cmd:pweight}s, {cmd:fweight}s, {cmd:aweight}s, and {cmd:iweight}s are allowed; see help
{help weights}.

{title:Description}

{p}{cmd:triprobit} estimates simulated maximum-likelihood three-equation probit models using the GHK smooth recursive simulator.

{p} The simulated maximum likelihood technique consists in 
simulating the multivariate normal integrals which are involved 
in the likelihhod equation. The simulated probabilities are fed 
into the likelihood function which is then maximized using 
traditional techniques. See Greene (2000, pp 184-185) for a 
description of the simulation algorithm used here.

{p} {cmd:triprobit} performs a likelihood-ratio test of no 
correlation between the equations.

{p} {hi:Warning}: due to the estimation technique, convergence can be {hi:very} slow in large samples (and/or with a large number of draws)

{title:Options}

{p 0 4}{cmd:robust} specifies that the Huber/White/sandwich estimator of
variance is to be used in place of the traditional calculation; see
{hi:[U] 23.11 Obtaining robust variance estimates}.  {cmd:robust} combined
with {cmd:cluster()} allows observations which are not independent within
cluster (although they must be independent between clusters).  If you specify
{help pweight}s, {cmd:robust} is implied.

{p 0 4}{cmd:cluster(}{it:varname}{cmd:)} specifies that the observations are
independent across groups (clusters) but not necessarily within groups.
{it:varname} specifies to which group each observation belongs; e.g.,
{cmd:cluster(personid)} in data with repeated observations on individuals.  See
{hi:[U] 23.11 Obtaining robust variance estimates}.  {cmd:cluster()} can be
used with {help pweight}s to produce estimates for unstratified
cluster-sampled data.  Specifying {cmd:cluster()} implies {cmd:robust}.

{p 0 4}{cmd:draws} specifies the number of draws to be used in 
the simulation process. Default is 25, which is usually 
considered as a reasonable number of draws to make.

{p 0 4}{cmd:seed} specifies the seed to be set in the simulation 
process, default is 123456789

{p 0 4}{cmd:noinit} prevents that parameters values from three 
independant probits are specified as starting values for the 
estimation process. 

{p 0 4}{it: maximize_options} control the maximization process; see help {help maximize}.

{title:Saved results}

{p 0 4}In addition to the results saved by {cmd:maximize} (see {hi:[R] maximize}), 
{cmd:triprobit} also saves the following results.  

 {p 0 4}{hi:e(ll_c)} stores the likelihood value of the comparison 
model

{p 0 4}{hi:e(chi2_c)} stores the chi2 statistic of the LR test against 
the comparison model

{p 0 4}{hi:e(rho12)} stores the estimated correlation coefficient 
between equation 1 and equation 2

{p 0 4}{hi:e(rho12_se)} stores the estimated standard-error of the 
correlation coefficient between equation 1 and equation 2

{p 0 4}{hi:e(rho13)} stores the estimated correlation coefficient 
between equation 1 and equation 3

{p 0 4}{hi:e(rho13_se)} stores the estimated standard-error of the 
correlation coefficient between equation 1 and equation 3

{p 0 4}{hi:e(rho23)} stores the estimated correlation coefficient 
between equation 2 and equation 3

{p 0 4}{hi:e(rho23_se)} stores the estimated standard-error of the 
correlation coefficient between equation 2 and equation 3

{p 0 4}{hi:e(draws)} stores the number of draws used in the simulation

{p 0 4}{hi:e(seed)} stores the seed which is set for the simulation

{p 0 4}{hi:e(depvar)} stores the names of the dependat variables 

{p 0 4}{hi:e(cmd)} stores the command name (i.e: {it:triprobit})


{title:Note}

{p 0 4} rho12 represents the correlation coefficient between equation 1 and equation 2

{p 0 4} rho13 represents the correlation coefficient between equation 1 and equation 3

{p 0 4} rho23 represents the correlation coefficient between equation 2 and equation 3



{title:Examples}

{p 8 12}{inp:. triprobit (y1 = x1 x2 x3) (y2 = z1 z2 z3) (y3 = v1 v2 v3), draws(30) }


{title:Also see}

{p 0 19}On-line:  help for {help biprobit} {help probit}{p_end}

{title:References}

{p 0 19}Greene, W.H. (2000) {it:Econometric Analysis}, 
Prentice-Hall, fourth edition.
