  We consider the problem of variable selection when the response is ordinal,
that is an ordered categorical variable. In particular, we are interested in
selecting quantitative explanatory variables linked with the ordinal response
variable and we want to determine which predictors are relevant. In this
framework, we choose to use the polytomous ordinal logistic regression model
using cumulative logits which generalizes the logistic regression. We then
introduce the Lasso estimation of the regression coefficients using the
Frank-Wolfe algorithm. To deal with the choice of the penalty parameter, we use
the stability selection method and we develop a new method based on the
knockoffs idea. This knockoffs method is general and suitable to any regression
and besides, gives an order of importance of the covariates. Finally, we
provide some experimental results to corroborate our method. We then present an
application of this regression method for network inference of zero-inflated
variables and use it in practice on real abundance data in an agronomic
context.
