Political science studies commonly uses panel data. In particular, many of these studies involve the analysis of a truncated dependent variable, such as aggregate-level voter turnout or a party's vote share. Unfortunately, panel regression, which is the standard method of analyzing panel data, contains three methodological problems: boundary violations, parameter estimation, and model specification. These issues raise concerns about the panel regression method's validity. In this article, I explain the nature of these problems and propose three models to solve boundary violations by applying constrained optimization in the least squares and maximum likelihood paradigm. Major findings indicate that the current method is sensitive to different centering methods and tends to generate false significance results. Throughout a comparative study in the admissibility of parameter estimates, I demonstrate how the three revised models can conditionally or fully eliminate boundary violations. Methodological advice is also provided regarding when and how the new methods should be employed.