I've got a situation where I have a series of individuals who have two factors describing their health.  Factor A has 3 levels while factor B has 4 levels.  Biologically, level 1 of factor A appears if and only if factor B is level 1.  Therefore, I have data structured like this:

    ID   Factor A  Factor B   Score
    1      a        alpha       0.1
    2      a        alpha       0.2
    3      b        beta        0.3
    4      b        gamma       0.4
    5      b        delta       0.5
    6      c        beta        0.6
    7      c        gamma       0.7
    8      c        delta       0.8

I'm interested in studying the effects of both factors, but I'm struggling with how to properly code this.  Giving each factor their own full set of dummy codes is rank deficient and leaving out a level of either factor creates a model with impossible combinations (ie level *a* ONLY occurs with level *alpha*, and vice versa).  **How could I code these fixed effects so that I can investigate the impact of both factors on our score?**

EDIT:  For the close vote that this is off-topic, embedded in this is a request for understanding how to partition out these effects so that I know how each factor affects the score, referenced to the baseline (*a* and *alpha*).  In my experiment, I'd like to know how a change from *a* to *b*/*c* impacts score independent of a change from *alpha* to *beta*/*gamma*/*delta*.  It just so happens that if a subject is *a* and *alpha*, both of those factors must change to new levels, which makes teasing out differences difficult.