When developing regression models in which the response variable is a proportion between 0 and 1, linear regression models are not appropriate. If proportions are obtained from discrete counts, they can be analyzed with beta regression or logistic regression. While the use of logistic regression is preferred by some researchers for proportions consisting of two categories due to its simplicity (Douma & Weedon, 2019), beta regression and zero/one inflated beta regression (ZOIB) are more appropriate by better reflecting the continuous nature of proportion responses. We showcase the use of beta regression models in an analysis of 3,141 U.S. counties to identify social, mental health, health, and criminal factors that predict jail population rates. We compare inference based on beta regression and ZOIB to logistic regression, and examine the impact of non-concavity of the log-likelihood on the numerical stability of established algorithms for fitting beta regression models in the presence of many categorical predictors. Recommendations are provided for practitioners on when logistic models can be used with minimum model bias if fitting beta regression models causes convergence issues.