Lateral gene transfer is an important mechanism for evolution among bacteria. Here, genome-wide gene insertion and deletion rates are modeled in a maximum-likelihood framework with the additional flexibility of modeling potential missing data. The performance of the models is illustrated using simulations and a data set on gene family phyletic patterns from Gardnerella vaginalis that includes an ancient taxon. A novel application involving pseudogenization/genome reduction magnitudes is also illustrated, using gene family data from Mycobacterium spp. Finally, an R package called indelmiss is available from the Comprehensive R Archive Network at https://cran.r-project.org/package=indelmiss, with support documentation and examples.