# Hauck-Donner effect in ordinal generalized regression

I am running a series of ordinal regressions on a rather large data set (n=3640). With some predictors I had issues with violations of parallel lines assumptions, so I decided to run those with a generalized model (VGLM; parallel = F).

The issue I ran into then is:

Dep <- factor(data\$Walk,
levels=c(1,2,3,4,5,6), ordered = TRUE)
model4 <- vglm(factor(Dep)~Var, cumulative(parallel = F))

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept):1  0.61362    0.09021   6.802 1.03e-11 ***
(Intercept):2  1.47896    0.09137  16.187  < 2e-16 ***
(Intercept):3  2.56742    0.11034  23.269  < 2e-16 ***
(Intercept):4  3.05178    0.13048  23.388  < 2e-16 ***
(Intercept):5  3.77674    0.19040  19.836  < 2e-16 ***
Var:1         -3.70786    0.28870 -12.843  < 2e-16 ***
Var:2         -3.80696    0.26745 -14.235  < 2e-16 ***
Var:3         -4.39274    0.29064 -15.114  < 2e-16 ***
Var:4         -4.17090    0.32850 -12.697  < 2e-16 ***
Var:5         -3.27016    0.47137  -6.938 3.99e-12 ***

Warning: Hauck-Donner effect detected in the following estimate(s):
'(Intercept):4', '(Intercept):5'


As far as I understand, this would primarily affect the Wald Test, and could lead to an underestimation of the significance of the predictors. However, the predictors are significant even in the presence of the HDE.

My variable selection for a final will not be based on significance but effect size. The question is now if the HDE would still affect the validity of the model, or affect the effect size (OR) of the predictor variables on the model. Moreover, would a likelihood ratio test be recommended even if all variables are significant despite the presence of HDE?