The last two decades have seen growing awareness of and emphasis on the replication of empirical findings. While this is a large literature, very little of it has focused on or considered the interaction of replication and psychometrics. This is unfortunate given that sound measurement is crucial when considering the complex constructs studied in psychological research. If the psychometric properties of a scale fail to replicate, then inferences made using scores from that scale are questionable at best. In this dissertation, I begin to address replication issues in factor analysis – a widely used psychometric method in psychology. After noticing inconsistencies across results for studies that factor analyzed the same scale, I sought to gain a better understanding of what replication means in factor analysis as well as address issues that affect the replicability of factor analytic models. With this work, I take steps toward integrating factor analysis into the broader replication discussion. Ultimately, the goal of this dissertation was to highlight the importance of psychometric replication and bring attention to its role in fostering a more replicable scientific literature.