Generalized Linear Models                                        [STB-11: sg16]
-------------------------

^glm^ depvar [cases] varlist, ^f(^[^gau^|^bin^|^poi^|^gam^|^invg^]^) l(^[^l^|^p^|^c^|^log^|^id^]^)^ 
                            [^g^] [^s^] [^r^] [^le(.)^] [^it(.)^] [^ex(.)^] [^o(.)^] ^eform^

where ^f^ indicates the error or family distribution, and ^l^ is the link.
The user has a choice of the following distributions and links: 
    ^gau^  = gaussian; also default if no f(.) specified.
    ^bin^  = binomial, either ^bernoulli^ [0,1] or ^grouped^. The ^g^ option must
           be specified to use the grouped version. 
             ^l(l)^   = logit link (canonical)
             ^l(p)^   = probit link
             ^l(c)^   = complementary log-log link (cloglog) 
    ^poi^  = poisson; log link default (canonical)       
             ^l(id)^  = identity link
    ^gam^  = gamma; inverse link default (canonical)
             ^l(log)^ = log link
             ^l(id)^  = identity link
    ^invg^ = inverse gaussian; squared inverse link default (canonical) 
             ^l(log)^ = log link
             ^l(id)^  = identity link
             

The ^s^ option calculates the linear predictor, _eta, and the predicted  
probability _mu.  The ^r^ option calculates diagnostic variables appropriate 
for each distribution. At present, the following diagnostics have been 
implemented:
   
binomial: ^_Presid^  = Pearson residual       ^_Dresid^  = Deviance residual
          ^_Lresid^  = Likelihood residual    ^_Aresid^  = Anscombe residual
          ^_Dpr^     = Delta Pearson          ^_Dbeta^   = Delta beta 
          ^_Ddev^    = Delta deviance         ^_hat^     = hat

poisson, gamma, inverse gaussian:  ^_Presid^, ^_Dresid^, and ^_Aresid^ 

[^cases^] is a variable used for grouped binomial model denominators with the  
^g^ option. For such models, the response variable (numerator) must be the 
first variable called after ^glm^, and [cases] the second. 

^if^ expression of ^in^ range options may be used.

^ex(.)^ allows specification of an exposure variable.

^o(.)^ allows specification of an offset variable.

^eform^ allows exponentiated coefficients to be displayed following binomial
and poisson regression. Other statistical results are appropriately 
adjusted. For logistic regression, exponentiation results in odds ratios; 
for poisson regression the result is incidence rate ratios.

^le(.)^ allows specification of the percent confidence interval.

^it(.)^ allows specification of the number of iteration. This is useful 
when there is a problem with convergence.

^lt(.)^ allows specification of a convergence threshold for the iterative 
change in deviance. Default is .0001.

The output includes a statistic for dispersion which is defined as Chi2/nu 
where nu is the model degrees of freedom. This statistic is used to adjust 
standard errors for gamma and inverse gaussian distributions. It may be 
used as a general specification indicator for other distributions, but is  
not used to adjust standard error calculations.

Additional details on ^glm^ modeling with examples can be found in sg16.


Prime References: (see STB-11: sg16 for additional references)
--------------------------------------------------------------
Collett, D. 1991.  ^Modelling Binary Data^.  Chapman & Hall.

McCullagh, P. and J. A. Nelder. 1989.  ^Generalized Linear Models^. 2d ed.
    Chapman & Hall.

Author and support:
-------------------

  Joseph Hilbe, 10952 N. 128th Pl., Scottsdale, AZ 85259-4464
  Phone: 602-860-4331; Fax  : 602-860-1446
  E-mail: Bitnet - atjmh@@asuacad    Internet - atjmh@@asuvm.inre.asu.edu

  or: Department of Sociology, Arizona State University, Tempe, AZ. 85287
also: College of Law, Arizona State University, Tempe, AZ. 85287