How does a child's vocabulary production change over time? Past research has focused on characterizing population statistics of acquisition. We develop models that attempt to predict when a specific word will be learned by a particular child. The models are based on two qualitatively different sources of information: a representation describing the child (age, sex, and vocabulary skill) and a representation describing the specific words a child knows. Using longitudinal data from children aged 15-36 months, we construct logistic regression models to predict whether a word is learned in the coming month. Models based on child- or word representations outperform a baseline model. An ensemble that averages the predictions of the child- and word-feature models has significantly higher accuracy, indicating that the two sources of information are complementary. With this approach we gain an understanding of the factors that influence language learning, which should inform cognitive theories of development.