Late talkers (LTs)---children who show a marked delay in vocabulary learning---are at risk for Specific Language Impairment (SLI), and much research has focused on identifying factors contributing to this phenomenon. We use a computational model of word learning to further shed light on these factors. In particular, we show that variations in the attentional abilities of the computational learner can be used to model various identified differences in LTs compared to normally-developing children: delayed and slower vocabulary growth, greater difficulty in novel word learning, and decreased semantic connectedness among learned words.