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Independent component analysis (ICA) has found wide application in a variety of areas, and analysis of functional magnetic resonance imaging (fMRI) data has been a particularly fruitful one. Maximum likelihood provides a natural formulation for ICA and allows one to take into account multiple statistical properties of the data—forms of diversity. While use of multiple types of diversity allows for additional flexibility, it comes at a cost, leading to high variability in the solution space. In this paper, using simulated as well as fMRI-like data, we provide insight into the trade-offs between estimation accuracy and algorithmic consistency with or without deviations from the assumed model and assumptions such as the statistical independence. Additionally, we propose a new metric, cross inter-symbol interference, to quantify the consistency of an algorithm across different runs, and demonstrate its desirable performance for selecting consistent run compared to other metrics used for the task.