VGAM (version 1.0-4)

hdeff: Hauck-Donner effects: detection test for Wald tests


A detection test for Hauck-Donner effects of each regression coefficient in a VGLM regression model.


hdeff(object, ...)
hdeff.vglm(object, derivative = NULL, se.arg = FALSE, ...)



A vglm object. Currently only a limited number of family functions have the HDE detection test: binomialff, cumulative, erlang, poissonff, topple, uninormal, zipoissonff, and zipoisson. More will be implemented in the short future!


Numeric. Either 1 or 2. Currently only a few models having one linear predictor are handled when derivative = 2, e.g., binomialff, poissonff.


Logical. If TRUE then the derivatives of the standard errors are returned as well, otherwise the derivatives are of the Wald statistics.

further arguments passed into the other methods functions.


By default, a vector of logicals. Setting deriv = 1 returns a vector of first derivatives of the Wald statistics. Setting deriv = 2 returns a 2-column matrix of first and second derivatives of the Wald statistics. Setting se.arg = TRUE returns an additional 1 or 2 columns.

For those VGAM family functions whose HDE test has not yet been implmented a NULL is returned.


Some 2nd derivatives are NA, meaning that they have not been programmed in yet.


Hauck and Donner (1977) first observed an aberration of the Wald test statistic not monotonically increasing as a function of increasing distance between the parameter estimate and the null value (called the Hauck-Donner effect, or HDE, here). This "disturbing" and "undesirable" underappreciated effect has since been observed in other regression models by various authors. This function computes the first, and possibly second, derivative of the Wald statistic for each regression coefficient. A negative value of the first derivative is indicative of the HDE being present.

By default this function returns a labelled logical vector; a TRUE means the HDE is affirmative for that coefficient. Hence ideally all values are FALSE. Any TRUE values suggests that the MLE is near the boundary of the parameter space, and that the p-value for that regression coefficient is biased upwards.


Hauck, J. W. W. and A. Donner (1977) Wald's test as applied to hypotheses in logit analysis. Journal of the American Statistical Association, 72, 851--853. Corrigenda: JASA, 75, 482.

Yee, T. W. (2017) Detecting the Hauck-Donner effect in Wald tests (in preparation).

See Also

summaryvglm, vglm, lrp.vglm.


Run this code
pneumo <- transform(pneumo, let = log(exposure.time))
fit <- vglm(cbind(normal, mild, severe) ~ let, data = pneumo,
            cumulative(reverse = TRUE,  parallel = TRUE))
hdeff(fit, deriv = 1)
hdeff(fit, deriv = 2)
# }

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