Hauck-Donner Effect: Severity Measures

Computes the severity of the Hauck-Donner effect for each regression coefficient of a fitted VGLM.

hdeffsev(object, hdiff = 0.005, eta0 = 0,
    subset = NULL, maxderiv = 6,
    severity.table = c("None", "Faint", "Weak",
             "Moderate", "Strong", "ExtremeI",
             "ExtremeII", "ExtremeIII",
             "ExtremeIV+", "Undetermined"),
    lookup = c(0, 0.5, 0.7, 1, 1.3, 2:5),
    tx.some = TRUE, wsdmvec = NULL, ...)

Arguments

object

A fitted vglm object, although not all VGAM family functions will work, e.g., GAITD regression. Alternatively, use wsdm.

eta0, subset, hdiff

Fed into wsdm.

maxderiv, ...

Fed into wsdm.

severity.table

Character vector of descriptors, plus the last value for initialization. Usually users should not assign anything to this argument. Used in conjunction with lookup.

lookup

Numeric, thresholds used for assigning severity.table values based on WSDM statistics. This look-up table should be sorted and the first element equal to 0. Usually users should not assign anything to this argument, else be careful when using it.

tx.some

Logical, transform WSDM before comparisons? Applies to certain links only (and if object was inputted), currently loglink and cauchitlink. This is because it is possible to slightly improve the calibration between WSDM statistics and the look-up table. In particular, a square root transformation shrinks certain values towards unity.

wsdmvec

The WSDM statistics can be inputted directly into the function here.

Details

This function is intended to replace all previous code for measuring HDE severity. In particular, hdeffsev0 and hdeffsev2 are old and are not recommended. Details behind this function spring from wsdm.

Value

By default this function (hdeffsev) returns a labelled vector with names names(coef(object)) and elements selected from severity.table.

References

Yee, T. W. (2022). On the Hauck-Donner effect in Wald tests: Detection, tipping points and parameter space characterization, Journal of the American Statistical Association, 117, 1763–1774. doi:10.1080/01621459.2021.1886936 .

Author

Thomas W. Yee.

Warning

For VGAM version 1.1-13, hdeffsev() was renamed to hdeffsev0(), hdeffsev2() to hdeffsev2() [no change], and hdeffsev() is new and based on wsdm(vglmfit).

Note

This function has not been tested extensively and the thresholds may change slightly in the future. Improvements are intended. The function was written specifically for binomialff, but they should work for almost all other family functions.

See also

seglines, hdeff, hdeffsev0, wsdm which is superior.

Examples

example(genpoisson0)
#> 
#> gnpss0> gdata <- data.frame(x2 = runif(nn <- 500))
#> 
#> gnpss0> gdata <- transform(gdata, y1 = rgenpois0(nn, theta = exp(2 + x2),
#> gnpss0+                                          logitlink(1, inverse = TRUE)))
#> 
#> gnpss0> gfit0 <- vglm(y1 ~ x2, genpoisson0, data = gdata, trace = TRUE)
#> Iteration 1: loglikelihood = -2294.282
#> Iteration 2: loglikelihood = -2258.2725
#> Iteration 3: loglikelihood = -2255.347
#> Iteration 4: loglikelihood = -2255.3314
#> Iteration 5: loglikelihood = -2255.3314
#> 
#> gnpss0> coef(gfit0, matrix = TRUE)
#>             loglink(theta) logitlink(lambda)
#> (Intercept)       1.988143          1.021921
#> x2                1.041146          0.000000
#> 
#> gnpss0> summary(gfit0)
#> 
#> Call:
#> vglm(formula = y1 ~ x2, family = genpoisson0, data = gdata, trace = TRUE)
#> 
#> Coefficients: 
#>               Estimate Std. Error z value Pr(>|z|)    
#> (Intercept):1  1.98814    0.05230   38.02   <2e-16 ***
#> (Intercept):2  1.02192    0.05200   19.65   <2e-16 ***
#> x2             1.04115    0.07552   13.79   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Names of linear predictors: loglink(theta), logitlink(lambda)
#> 
#> Log-likelihood: -2255.331 on 997 degrees of freedom
#> 
#> Number of Fisher scoring iterations: 5 
#> 
#> No Hauck-Donner effect found in any of the estimates
#> 
summary(gfit0, wsdm = TRUE)
#> 
#> Call:
#> vglm(formula = y1 ~ x2, family = genpoisson0, data = gdata, trace = TRUE)
#> 
#> Coefficients: 
#>               Estimate Std. Error z value Pr(>|z|) WSDM    
#> (Intercept):1  1.98814    0.05230   38.02   <2e-16 0.57 ***
#> (Intercept):2  1.02192    0.05200   19.65   <2e-16 0.48 ***
#> x2             1.04115    0.07552   13.79   <2e-16 0.46 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Names of linear predictors: loglink(theta), logitlink(lambda)
#> 
#> Log-likelihood: -2255.331 on 997 degrees of freedom
#> 
#> Number of Fisher scoring iterations: 5 
#> 
#> No Hauck-Donner effect found in any of the estimates
#> 
#> Max-WSDM (excluding intercepts): 0.463
#> 
hdeffsev(gfit0)
#> (Intercept):1 (Intercept):2            x2 
#>        "Weak"        "None"       "Faint"