Logistic Regression Using Williams Procedure ---------------------------------------------
^williams^ numerator denominator [varlist] [^if^ exp] [^in^ range] [^, ef^orm ^le^vel(#) ^lt^olera ^nolo^g ^res^id
eform : provides estimates in terms of odds ratios
level : allows specification of confidence interval other than the default of 95
ltolera : allows change in default dispersion convergence of .0001 nolog : suppresses display of iteration
resid : the following residuals are created: _mu : mu, fitted value _lp : eta, linear predictor _Pear : Pearson residuals _Dev : Deviance residuals _Hat : hat matrix diagonal _Anscom : Anscombe residuals _StandP : Standardized Pearson residuals _StandD : Standardized deviance residuals
Be certain that you have sufficient variable space to add 8 additional variables to the data in memory. If not, then use ^set maxvar=x^ command to make adjustment. The final weighted logistic regression displays p-values based on t-statistics per recommendation of D. Collett (1991), Modeling Binary Data, Chapman & Hall, p 196.
The Williams procedure iteratively reduces the Chi2-based dispersion to approximately 1.0. An extra parameter, called ^phi^, is used to scale the variance function. It changes with each iteration. The value of phi which results in a chi2-based dispersion of 1.0 is then used to weight a standard grouped logistic regression. The weighting formula is: 1/(1+(m-1)*phi) where m is the binomial denominator.
CHI2 = -2(LL0 - LLf): p-value evaluates the null hypothesis that all coefficients in the model, except the intercept, equal 0. Degree of freedom is the number of predictors. CHI2 is to be distinguished from the traditional GLM Chi2 which is defined as SUM{(y-mu)^^2/V} where V=variance.
Pseudo R2 = 1-LLf/LL0: This is standard Stata output; however there are several alternative R2 formulations in common use.
For additional information contact: Joseph Hilbe, email: hilbe@@asu.edu