# The cumulative probability model with ordinalNet, using an elastic net penalty: more coefficients than expected equal to zero

I am trying to fit a cumulative probability model (ordinal logistic regression with 17 categories and 827 observations) with elastic net penalty using the ordinalNet function from the ordinalNet package in R.

I have 33 covariates and observe the following:

1. When I include all 33 covariates, all coefficients are set to zero.
2. When I include only 31 of the 33 covariates, many coefficients are different from zero.

The datasets in 1 and 2 are the same.

I did not expect that removing covariates would lead to less coefficients equal to zero. Rather the opposite. What could be the cause of this?

The code I use looks as follows:

ordinalNet(x = as.matrix(dataSet[, ..tested.factors]),
y = dataSet[, category_number],
family = "cumulative",
standardize = FALSE)


dataSet is a data.table.

The first step, if you are not using unsupervised learning (data reduction), is to show evidence that there is a predictive signal. Fit the full model without penalty and get the likelihood ratio $$\chi^2$$ test with say 33 degrees of freedom. This corrects for having 33 chances to find something. If this $$\chi^2$$ is not large you do not have a basis for finding predictors.