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help for ^gammalog^                                               [STB-53: sg126]
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Gamma distribution-log link MLE model
-------------------------------------

    ^gammalog^ depvar [indepvars] [weight] [^if^ exp] [^in^ range] [^,^ ^ir^r ^ef^orm
                    ^e^xposure^(^varname^)^ ^o^ffset^(^varname^)^ ^r^obust ^cl^uster^(^varname^)^
		    ^sc^ore^(^newvarnames^)^ ^nocon^stant ^l^evel^(^#^)^ maximize_options ]


^fweight^s, ^iweight^s, and ^pweight^s are allowed; see help @weights@.

^gammalog^ shares the features of all estimation commands; see help @est@.


The syntax of @predict@ following ^gammalog^ is

	^predict^ [type] newvarname [^if^ exp] [^in^ range] [^,^ statistic ^nooff^set]

where statistic is

	^n^               predicted values of depvar; the default
	^ir^              incidence rate (equiv. to ^predict^ ..., ^n nooffset^)
	^xb^              linear prediction
	^stdp^            standard error of the linear prediction

These statistics are available both in and out of sample; type "^predict^ ...
^if e(sample)^ ..." if wanted only for the estimation sample.


Description
-----------

^gammalog^ estimates a full-information maximum-likelihood version of the gamma
family-log link generalized linear model.  That is, the coefficient estimates
produced by ^gammalog^ are approximately equal to the coefficient estimates
produced by ^glm^ ...^, family(gamma) link(log)^; see help @glm@.  The standard
errors, however, will be slightly different since the log link is not the
canonical link for the gamma family.

^gammalog^ estimates over- or underdispersion models; as such, it can be
considered an alternative to the negative binomial model; see help @nbreg@.
The mean of the ^gammalog^ model is given by exp(x*b) and the dispersion is
phi*exp(x*b). Hence, the dispersion is directly proportional to the mean.

Note, however, that ^gammalog^ differs from ^nbreg^ and other count models in
that the outcome variable is assumed to be continuous and strictly greater
than zero.  (^gammalog^ does not allow depvar to take on the value zero
or any negative value.)


Options
-------

^irr^ and ^eform^ both do the same thing.  They report estimated coefficients
    transformed to incidence-rate ratios.

^exposure(^varname^)^ and ^offset(^varname^)^ are different ways of specifying the same
    thing.  ^exposure()^ specifies a variable that reflects the amount of expo-
    sure over which depvar events were observed for each observation.  ^offset()^
    specifies a variable that is to be entered directly into the log-link func-
    tion with coefficient 1; thus exposure is assumed to be exp(varname).

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

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

^score(^newvars^)^ creates newvar containing each observation's contribution to the
    score; see ^[U] 23.12 Obtaining scores^.  If two new varnames are specified,
    then the score from the ancillary parameter equation is also saved.

^noconstant^ suppresses the constant term (intercept) in the regression.

^level(^#^)^ specifies the confidence level, in percent, for confidence intervals;
    see help @level@.

maximize_options control the maximization process; see help @maximize@.  You
    should never have to specify them.


Options for ^predict^
-------------------

^n^, the default, calculates the predicted value of depvar, which is exp(x_j*b)
    if neither ^offset()^ nor ^exposure()^ was specified when the model was
    estimated, or exp(x_j*b + offset) if ^offset()^ was specified, or
    exp(x_j*b)*exposure if ^exposure()^ was specified.

^ir^ calculates the incidence rate exp(x_j*b), the predicted value of depvar
    when exposure is 1.  This is equivalent to ^n^ when neither ^offset()^ nor
    ^exposure()^ was specified when the model was estimated.

^xb^ calculates the linear prediction.

^stdp^ calculates the standard error of the linear prediction.

^nooffset^ is relevant only if you specified ^offset()^ or ^exposure()^ when you
    estimated the model.  The above calculations are then made ignoring the
    exposure or offset variable and thus, for instance, ^n^ == ^ir^).


Examples
--------

	. ^gammalog deaths coh2 coh3^
	. ^gammalog deaths coh2 coh3, exposure(obstime)^
	. ^predict dhat if e(sample)^
	. ^predict rate, ir^


Authors
-------

^gammalog^ was written by Bill Sribney of StataCorp with invaluable assistance
provided by Joe Hilbe.

For questions about this program or to report a problem, please contact
Bill Sribney at sribney@@fcc.net.


Also see
--------

 Manual:  ^[U] 23 Estimation and post-estimation commands^,
	  ^[U] 29 Overview of model estimation in Stata^,
On-line:  help for @est@, @postest@; @glm@, @nbreg@, @poisson@, @zinb@