[R] Weight, weight - do tell me
Lenth, Russell V
russell-lenth at uiowa.edu
Mon Jul 21 17:13:32 CEST 2014
This is a question only about terminology.
Suppose I have data categorized by three factors A, B, and C, with cell means ybar_ijk and cell frequencies n_ijk, where I, j, and k index A, B, and C respectively. And suppose I want to summarize the results for factor A by computing some sort of weighted means WM_i, averaging over indices j and k with weights w_jk. Consider these four weighting schemes:
1. Use equal weights, w_jk = 1
2. Use weights of w_jk = n_+jk (where "+" shows I summed over that index)
3. Use weights w_jk = n_+j+ * n_++k (outer product of the one-factor marginal frequencies)
4. Use weights w_ijk = n_ijk (only one where we use a different set of weights for each i)
Scheme 1 yields the "unweighted" or "least-squares" means, and scheme 4 yields the ordinary means for A, ignoring B and C altogether. Scheme 3 yields weighted averages over k of weighted averages over j (or vice versa).
My question is what to call these schemes, e.g., as a character argument in an R function. Preliminarily, I am calling them "equal", "proportional", "outer", and "actual". The first one is pretty obvious. But maybe there is some existing standard terminology for some or all of the others that I am unaware of (or have forgotten). Any suggestions?
Russell V. Lenth - Professor Emeritus
Department of Statistics and Actuarial Science
The University of Iowa - Iowa City, IA 52242 USA
Voice (319)335-0712 (Dept. office) - FAX (319)335-3017
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