Parallel evolution, defined as identical changes arising in independent populations, is often attributed to similar selective pressures favoring the fixation of identical genetic changes. However, some level of parallel evolution is also expected if mutation rates are heterogeneous across regions of the genome. Theory suggests that mutation and selection can have equal impacts on patterns of parallel evolution; however empirical studies have yet to jointly quantify the importance of these two processes. Here, we introduce several statistical models to examine the contributions of mutation and selection heterogeneity to shaping parallel evolutionary changes at the gene-level. Using this framework, we analyze published data from forty experimentally evolved Saccharomyces cerevisiae populations. We can partition the effects of a number of genomic variables into those affecting patterns of parallel evolution via effects on the rate of arising mutations, and those affecting the retention versus loss of the arising mutations (i.e. selection). Our results suggest that gene-to-gene heterogeneity in both mutation and selection, associated with gene length, recombination rate, and number of protein domains drive parallel evolution at both synonymous and nonsynonymous sites. While there are still a number of parallel changes that are not well described, we show that allowing for heterogeneous rates of mutation and selection can provide improved predictions of the prevalence and degree of parallel evolution.