The linear regression-based reliable change index (RCI) is widely used to identify memory impairments through longitudinal assessment. However, the minimum sample size required for estimates to be reliable has never been specified. Using data from 920 participants from the Alzheimer's Disease Neuroimaging Initiative data as true parameters, we run 12,000 simulations for samples of size 10-1,000 and analyzed the percentage of times the estimates are significant, their coverage rate, and the accuracy of the models including both the true-positive rate and the true-negative rate. We compared the linear RCI with a logistic RCI for discrete, bounded scores. We found that the logistic RCI is more accurate than the linear RCI overall, with the linear RCI approximating the logistic RCI for samples of size 200 or greater. We provide an R package to compute the logistic RCI, which can be downloaded from the Comprehensive R Archive Network (CRAN) at https://cran.r-project.org/web/packages/LogisticRCI/, and the code to reproduce all results in this article at https://github.com/rafamoral/LogisticRCIpaper/. (PsycInfo Database Record (c) 2022 APA, all rights reserved).