Linguists have long debated the proper role of psychology in grammatical theorizing. Rather than taking the traditional formalist or functionalist positions in this debate, this paper instead advocates testing grammatical claims using the methods, but not necessarily the concepts, of psychology. This means developing explicit models of the links between hypothesized mental entities and observed data, often with the use of quantitative analysis. This more skeptical approach is applied in analyses of two phonological issues: epenthesis and vowel harmony in the Formosan language Pazih, and a comparison between the handshape inventories of Taiwan Sign Language and American Sign Language. In both case studies, the linking model approach undermines certain conclusions that might otherwise have been accepted uncritically, but at the same time it strengthens our confidence in others.