Fits ordinal regression models with elastic net penalty. Supported model families include cumulative probability, stopping ratio, continuation ratio, and adjacent category. These families are a subset of vector glm's which belong to a model class we call the elementwise link multinomial-ordinal (ELMO) class. Each family in this class links a vector of covariates to a vector of class probabilities. Each of these families has a parallel form, which is appropriate for ordinal response data, as well as a nonparallel form that is appropriate for an unordered categorical response, or as a more flexible model for ordinal data. The parallel model has a single set of coefficients, whereas the nonparallel model has a set of coefficients for each response category except the baseline category. It is also possible to fit a model with both parallel and nonparallel terms, which we call the semi-parallel model. The semi-parallel model has the flexibility of the nonparallel model, but the elastic net penalty shrinks it toward the parallel model. For details, refer to Wurm, Hanlon, and Rathouz (2021) <doi:10.18637/jss.v099.i06>.