statsmodels.genmod.families.family.Binomial.resid_anscombe
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Binomial.resid_anscombe(endog, mu)
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The Anscombe residuals
Parameters: endog : array-like
Endogenous response variable
mu : array-like
Fitted mean response variable
Returns: resid_anscombe : array
The Anscombe residuals as defined below.
Notes
sqrt(n)*(cox_snell(endog)-cox_snell(mu))/(mu**(1/6.)*(1-mu)**(1/6.))
where cox_snell is defined as cox_snell(x) = betainc(2/3., 2/3., x)*betainc(2/3.,2/3.) where betainc is the incomplete beta function
The name ?cox_snell? is idiosyncratic and is simply used for convenience following the approach suggested in Cox and Snell (1968). Further note that cox_snell(x) = x**(2/3.)/(2/3.)*hyp2f1(2/3.,1/3.,5/3.,x) where hyp2f1 is the hypergeometric 2f1 function. The Anscombe residuals are sometimes defined in the literature using the hyp2f1 formulation. Both betainc and hyp2f1 can be found in scipy.
References
- Anscombe, FJ. (1953) ?Contribution to the discussion of H. Hotelling?s
- paper.? Journal of the Royal Statistical Society B. 15, 229-30.
- Cox, DR and Snell, EJ. (1968) ?A General Definition of Residuals.?
- Journal of the Royal Statistical Society B. 30, 248-75.
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