Data represent dependent and independent variables used in logistic modeling for a study entitled "Evaluating Establishment Success of Non-native Fishes Introduced to Inland Aquatic Habitats of Tropical Pacific Islands." The phases of invasion of nonnative species are transport, introduction, establishment, and spread. To understand likelihood of establishment of species moved to new regions, investigators often use analytical methods that include life-history attributes, ecophysiological parameters, distributional factors, propagule pressure, introduction pathways, and other salient features that contribute to successful establishment. Introductions that fail to result in establishment are often unknown. In this study we apply an information-theoretic approach to evaluate the establishment success of 80 freshwater fish species introduced to insular habitats of Hawaii and Guam, including records of species that successfully became established as well as those that failed. Eleven independent variables were analysed to examine establishment success by creating 21 a priori logistic regression models that were ranked using Akaike’s Information Criterion adjusted for small sample size. An additional 8 post-hoc models were included that comprised the best a priori model and various combinations of individual variables. The best overall model of establishment probability included taxonomic affinity (family), an effect of prior establishment success on other tropical islands, and an effect of hypoxia tolerance. Establishment success in Hawaii and Guam was highest for those species established on many other islands, and according to our best model air-breathing fishes were more likely to become established. Notable families with a moderate number of species and overall high probability of establishment success include the Centrarchidae, Cichlidae, Clariidae, Loricariidae, and Poeciliidae. Many established species are of substantial human value and were intentionally introduced to Hawaii, Guam, and other Pacific islands, including those used as food and important in aquaculture or stocked to enhance wild fisheries, sport fishes, species in the ornamental trade, and taxa introduced for biocontrol. Our results are consistent with many other studies of freshwater fish introductions globally that identify historical occurrences and propagule pressure as major determinants of establishment success.