Extensive economic and environmental damage has been caused by invasive exotic plant species in many ecosystems worldwide. Many comparative studies have therefore attempted to predict, from biological traits, which species among the pool of naturalized non-natives become invasive. However, few studies have investigated which species establish and/or become pests from the larger pool of introduced species and controlled for time since introduction. Here we present results from a study aimed at quantifying predicting three classes of invasive species cultivated in Hawaii. Of 7,866 ornamental species cultivated in Hawaii between 1840 and 1999, 420 (5.3%) species naturalized, 141 (1.8%) have been classified as weeds, and 39 (0.5%) were listed by the state of Hawaii as noxious. Of the 815 species introduced >80 years ago, 253 (31%) have naturalized, 90 (11%) are classed as weeds, and 22 (3%) as noxious by the state of Hawaii. Using boosted regression trees we classified each group with nearly 90% accuracy, despite incompleteness of data and the low proportion of naturalized or pest species. Key biological predictors were seed mass and highest chromosome number standardized by genus which, when data on residence time was removed, were able to predict all three groups with 76-82% accuracy. We conclude that, when focused on a single region, screening for potential weeds or noxious plants based on a small set of biological traits can be achieved with sufficient accuracy for policy and management purposes.