For a novice, understanding how formulas are used to model linear mixed models (e.g., using packages such as lme4) can be difficult. Below are some nice examples and explanations from link exchange to get you started:

- http://stats.stackexchange.com/questions/18428/formula-symbols-for-mixed-model-using-lme4
- http://stats.stackexchange.com/questions/13166/rs-lmer-cheat-sheet/13173#13173

And a detailed description of how using contrasts can lead to rank-deficient design matrices:

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