statsmodels.genmod.families.family.Binomial.resid_anscombe

Binomial.resid_anscombe(endog, mu)

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.