Molecular phylogenetics is a powerful tool for inferring both the process and pattern of evolution from genomic sequence data. Statistical approaches, such as maximum likelihood and Bayesian inference, are now established as the preferred methods of inference. The choice of models that a researcher uses for inference is of critical importance, and there are established methods for model selection conditioned on a particular type of data, such as nucleotides, amino acids, or codons. A major limitation of existing model selection approaches is that they can only compare models acting upon a single type of data. Here we extend model selection to allow comparisons between models describing different types of data by introducing the idea of adapter functions, which project aggregated models onto the originally observed sequence data. These projections are implemented in the program ModelOMatic and used to perform model selection on 3,722 families from the PANDIT database, 68 genes from an arthropod phylogenomic data set, and 248 genes from a vertebrate phylogenomic data set. For the PANDIT and arthropod data, we find that amino acid models are selected for the overwhelming majority of alignments; with progressively smaller numbers of alignments selecting codon and nucleotide models, and no families selecting RY-based models. In contrast, nearly all alignments from the vertebrate data set select codon-based models. The sequence divergence, the number of sequences, and the degree of selection acting upon the protein sequences may contribute to explaining this variation in model selection. Our ModelOMatic program is fast, with most families from PANDIT taking fewer than 150 seconds to complete, and should therefore be easily incorporated into existing phylogenetic pipelines.