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help for ^williams^
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Logistic Regression Using Williams Procedure
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^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