Ecologists often use dispersion metrics and statistical hypothesis testing to infer processes of community formation such as environmental filtering, competitive exclusion, and neutral species assembly. These metrics have limited power in inferring assembly models because they rely on often-violated assumptions. Here, we adapt a model of phenotypic similarity and repulsion to simulate the process of community assembly via environmental filtering and competitive exclusion, all while parameterizing the strength of the respective ecological processes. We then use random forests and approximate Bayesian computation to distinguish between these models given the simulated data. We find that our approach is more accurate than using dispersion metrics and accounts for uncertainty in model selection. We also demonstrate that the parameter determining the strength of the assembly processes can be accurately estimated. This approach is available in the R package CAMI; Community Assembly Model Inference. We demonstrate the effectiveness of CAMI using an example of plant communities living on lava flow islands.