= Parameterization =

'''Parameterization''' is the process of transforming a variable with levels so as to estimate their differences.

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== Reference Parameterization ==

An arbitrary level, conventionally the first, is singled out as a reference. The effect of this reference level is implicitly the intercept. All other levels receive a distinct parameter, indicating a difference from the reference.

For a variable with ''k'' levels, there are ''k-1'' fitted parameters coded as follows:

||'''Case Number'''||'''Parameterized Variable'''||'''Dummy 1'''||'''Dummy 2'''||'''Dummy 3'''||
||1||A||0||0||0||
||2||B||1||0||0||
||3||C||0||1||0||
||4||D||0||0||1||

The consequence of this coding is that the significance tests of parameters cannot be interpreted directly. A level may not be significantly different from the reference, but still be significantly different from other levels. Joint tests must be additionally computed.

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== Effects Parameterization ==

The first level is coded as the absence of all others as:

||'''Case Number'''||'''Parameterized Variable'''||'''Dummy 1'''||'''Dummy 2'''||'''Dummy 3'''||
||1||A||-1||-1||-1||
||2||B||1||0||0||
||3||C||0||1||0||
||4||D||0||0||1||

The average effect is the intercept, and each level has a distinct calculable effect. A positive effect is therefore a greater than average effect.



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CategoryRicottone