{smcl}
{* 02dec2003}{...}
{hline}
help for {hi:rcal}{right: SJ3-4: st0049, st0050, st0051)}
{hline}

{title:Regression Calibration}

{p 8 12 2}{cmd:rcal} {it:depvar} [{it:indepvars}] ({it:label:varlist}) 
[({it:label:varlist}) ... ({it:label:varlist})] [{cmd:if}
{it:exp}] [{cmd:in} {it:range}] [{cmd:,} {cmd:bstrap} {cmd:brep}{cmd:(}{it:#}{cmd:)} 
{cmd:ltolerance}{cmd:(}{it:#}{cmd:)} {cmd:iterate}{cmd:(}{it:#}{cmd:)} 
{cmd:family}{cmd:(}{it:familyname}{cmd:)} {cmd:link}{cmd:(}{it:linkname}{cmd:)} 
{cmd:message}{cmd:(}{it:#}{cmd:)} {cmd:naive} {cmd:robust} 
{cmd:suuinit}{cmd:(}...{cmd:)} {cmd:ignoresuu}
{cmd:btrim}{cmd:(}{it:#}{cmd:)} {cmd:saving}{cmd:(}{it:filename}{cmd:)} 
{cmd:replace} {cmd:seed}{cmd:(}{it:#}{cmd:)} 
{cmd:scale}{cmd:(}{cmd:x2}|{cmd:dev}|{it:#}{cmd:)}]

{p 4 4 2}where {it:familyname} is one of

{p 8 8 2}{cmdab:gau:ssian} | {cmdab:ig:aussian} |
{bind:{cmdab:b:inomial} [{it:varnameN}|{it:#N}]} | {cmdab:p:oisson} |
{bind:{cmdab:nb:inomial} [{it:#k}]} | {cmdab:gam:ma}

{p 4 4 2}and {it:linkname} is one of

{p 8 8 2}{cmdab:i:dentity} | {cmd:log} | {cmdab:l:ogit} | {cmdab:p:robit} |
{cmdab:c:loglog} | {cmdab:opo:wer} {it:#} | {cmdab:pow:er} {it:#} |
{cmdab:nb:inomial} | {cmdab:logl:og} | {cmd:logc}

{p 4 4 2} and {it:label:varlist} describes a variable measured with error.
The {it:label} is for the unknown measurement error covariate
({it:label} cannot be the same as an existing variable in the data
set). {it:varlist} is a list of variables with the replicate measurements 
for the unknown {it:label} covariate (see comments for restrictions).


{p 4 4 2}
{cmd:by} {it:...} {cmd::} may be used with {cmd:rcal}; see help {help by}.

{p 4 4 2}
{cmd:rcal} No {cmd:predict} is implemented.


{title:Description}

{p 4 4 2} 
{cmd:rcal} fits generalized linear models for measurement error data
using IRLS (maximum quasi-likelihood) and is similar in syntax to
{cmd:simex}.  This command is implemented by Stata's plug-in
mechanism. {cmd:rcal} allows one or more (see comments) covariates
measured with errors and uses regression calibration to estimate the
missing covariates. It will allow replicate data or a user specified
measurement error covariance matrix. It implements a very fast
internal bootstrap (different from the regular Stata boostrap
command).

{title:Options}

{p 4 8 2}
{cmd:bstrap} specifies that the bootstrap estimate of variance be used.

{p 4 8 2}
{cmd:brep}{cmd:(}{it:#}{cmd:)} specifies the number of bootstrap
samples to consider in forming the bootstrap estimate of variance.  The
default is {cmd:brep(199)}.

{p 4 8 2}
{cmd:ltolerance}{cmd:(}{it:#}{cmd:)} specifies the convergence
criterion for the change in deviance between iterations;
{cmd:ltolerance(1e-6)} is the default.

{p 4 8 2}
{cmd:iterate}{cmd:(}{it:#}{cmd:)} specifies the maximum number of
iterations allowed in fitting the model; {cmd:iterate(100)} is the
default.  You should seldom need to specify {cmd:iterate()}.

{p 4 8 2}
{cmd:family}{cmd:(}{it:familyname}{cmd:)} specifies the distribution of
{it:depvar}; {cmd:family(gaussian)} is the default.

{p 4 8 2}
{cmd:link}{cmd:(}{it:linkname}{cmd:)} specifies the link function; the
default is the canonical link for the {cmd:family()} specified.

{p 4 8 2}
{cmd:message}{cmd:(}{it:#}{cmd:)} The message or debug level 
from the plug-in module. The default is {cmd:message(2))}.

{p 4 8 2}
{cmd:robust} specifies that the Huber/White/sandwich estimator of
variance is to be used in place of the traditional calculation. We do
not support the {cmd:cluster) option.

{p 4 8 2}
{cmd:naive} Uses the "naive" estimator of variance. That is, the variance
is not adjusted for measurement error. This option is for pedagogical and 
diagnostic purposes and should not be otherwise used.

{p 4 8 2}
{cmd:suuinit}{cmd:(}matrixname{cmd:)} Specify the measurement error covariance
matrix. This is calculated from the replications in the measurement error
variables if it is not specified.

{p 4 8 2} 
{cmd:ignoresuu} If the measurement error covariance matrix is known,
or if one is willing to ignore the variation in its estimate use this
option. This may be relevant if the covariance comes from a large,
careful independent study, for which only summary statistics are
available.

{p 4 8 2}
{cmd:btrim}{cmd:(}{it:#}{cmd:)} Percent boostrap trimming. The default
is {cmd:btrim(.02)}.

{p 4 8 2}
{cmd:saving}{cmd:(}{it:filename}{cmd:)} Save the booststrap results to the
specified file.

{p 4 8 2}
{cmd:replace} Replace the existing 'bootstrap results' file if it exists.

{p 4 8 2}
{cmd:seed}{cmd:(}{it:#}{cmd:)} specify the seed for the random number
generator used by the boostrap. This enables for identical boostrap
runs. This option is generally not specified.

{p 4 8 2}
{cmd:scale}{cmd:(}{cmd:x2}|{cmd:dev}|{it:#}{cmd:)} overrides the
default scale parameter.  By default, {cmd:scale(1)} is assumed for
discrete distributions (binomial, Poisson, negative binomial)
and {cmd:scale(x2)} for continuous distributions
(Gaussian, gamma, inverse Gaussian).

{p 8 8 2}
{cmd:scale(x2)} specifies the scale parameter be set to the Pearson
chi-squared (or generalized chi-squared) statistic divided by the residual
degrees of freedom.

{p 8 8 2}
{cmd:scale(dev)} sets the scale parameter to the deviance divided by the
residual degrees of freedom.  This provides an alternative to {cmd:scale(x2)}
for continuous distributions and over- or under-dispersed discrete
distributions.

{p 8 8 2}
{cmd:scale}{cmd:(}{it:#}{cmd:)} sets the scale parameter to {it:#}.


{title:Special comments on multiple measurement error covariates}

{p 4 4 2}
The number of replications for a covariate measured with error can
vary across observations. When two or more measurement error covariates 
exist, they must all have the same number of replications across 
observations.

{title:Special comments on standard errors}

{p 4 4 2}
It can take a very long time to calculate the default and sandwich
variance estimates for large data sets. An estimated time to
completion is printed if the variance calculation will require more
than 30 seconds. It takes considerably less time to calculate the
bootstrap variance estimator for large data sets.

{title:Remarks}

{p 4 4 2}
The allowed link functions are

{center:Link function            {cmd:glm} option     }
{center:{hline 40}}
{center:identity                 {cmd:link(identity)} }
{center:log                      {cmd:link(log)}      }
{center:logit                    {cmd:link(logit)}    }
{center:probit                   {cmd:link(probit)}   }
{center:complementary log-log    {cmd:link(cloglog)}  }
{center:odds power               {cmd:link(opower} {it:#}{cmd:)} }
{center:power                    {cmd:link(power} {it:#}{cmd:)}  }
{center:negative binomial        {cmd:link(nbinomial)}}
{center:log-log                  {cmd:link(loglog)}   }
{center:log-compliment           {cmd:link(logc)}     }

{p 4 4 2}
The allowed distribution families are

{center:Family                 {cmd:glm} option       }
{center:{hline 40}}
{center:Gaussian(normal)       {cmd:family(gaussian)} }
{center:Inverse Gaussian       {cmd:family(igaussian)}}
{center:Bernoulli/binomial     {cmd:family(binomial)} }
{center:Poisson                {cmd:family(poisson)}  }
{center:Negative binomial      {cmd:family(nbinomial)}}
{center:Gamma                  {cmd:family(gamma)}    }

{p 4 4 2}
Reasonable combinations of {cmd:family()} and {cmd:link()} are

	  {c |} id  log  logit  probit  clog  pow  opower  nbinomial  loglog  logc
{hline 10}{c +}{hline 67}
Gaussian  {c |}  x   x                         x
inv. Gau. {c |}  x   x                         x
binomial  {c |}  x   x     x      x       x    x     x                  x      x
Poisson   {c |}  x   x                         x
neg. bin. {c |}  x   x                         x              x
gamma     {c |}  x   x                         x

{p 4 11 2}
Note:  Nonstandard combinations other than those marked out above
are allowed, but the user is responsible for seeing that the data fit
the combination and for the interpretation of the results.

{p 4 4 2}
If you specify {cmd:family()} but not {cmd:link()}, you obtain the canonical
link for the family:

{center:{cmd:family()}                default {cmd:link()}}
{center:{hline 38}}
{center:{cmd:family(gaussian)}        {cmd:link(identity)}}
{center:{cmd:family(igaussian)}       {cmd:link(power -2)}}
{center:{cmd:family(binomial)}        {cmd:link(logit)}   }
{center:{cmd:family(poisson)}         {cmd:link(log)}     }
{center:{cmd:family(nbinomial)}       {cmd:link(log)}     }
{center:{cmd:family(gamma)}           {cmd:link(power -1)}}


{p 4 4 2}

{title:Examples}

{p 4 8 2}{cmd:. * generate some data}{p_end}
{p 4 8 2}{cmd:. set obs 1000}{p_end}
{p 4 8 2}{cmd:. gen x1 = uniform()}{p_end}
{p 4 8 2}{cmd:. gen x2 = uniform()}{p_end}
{p 4 8 2}{cmd:. gen x3 = uniform()}{p_end}
{p 4 8 2}{cmd:. gen err = invnorm(uniform())}{p_end}
{p 4 8 2}{cmd:. gen y = 1+2*x1+3*x2+4*x3+err}{p_end}

{p 4 8 2}{cmd:. * estimate with x3 known}{p_end}
{p 4 8 2}{cmd:. qvf y x1 x2 x3, bstrap}{p_end}

{p 4 8 2}{cmd:. * simulate measurement error covariate}{p_end}
{p 4 8 2}{cmd:. gen a1 = x3 + .3*invnorm(uniform())}{p_end}
{p 4 8 2}{cmd:. gen a2 = x3 + .3*invnorm(uniform())}{p_end}

{p 4 8 2}{cmd:. * estimate x1, x2 & w3 using regression calibration}{p_end}
{p 4 8 2}{cmd:. rcal (y=x1 x2) (w3: a1 a2), bstrap}{p_end}
{p 4 8 2}{cmd:. rcal (y=x1 x2) (w3: a1 a2), bstrap saving("rcalboot.txt") replace}{p_end}
{p 4 8 2}{cmd:. eret list}{p_end}

{p 4 8 2}{cmd:. * display and use a covariance error matrix}{p_end}
{p 4 8 2}{cmd:. mat list e(suu)}{p_end}
{p 4 8 2}{cmd:. mat suu = ( .1)}{p_end}
{p 4 8 2}{cmd:. rcal (y=x1 x2) (w3: a1 a2), bstrap suuinit(suu)}{p_end}

{title:Also see}

{p 4 13 2}
Online:  help for {help qvf}, {help simex}
