On Sat, Jul 09, 2011 at 08:12:27AM +0000, John Darrington wrote: > On Fri, Jul 08, 2011 at 03:09:24PM -0400, Jason Stover wrote: > > category (5 categories --> 4 degrees of freedom): > a --> 0 0 0 0 > b --> 0 0 0 1 > c --> 0 0 1 0 > d --> 0 1 0 0 > e --> 1 0 0 0 > > drug (3 categories --> 2 degrees of freedom): > 1 --> 0 0 > 2 --> 1 0 > 3 --> 0 1 > > drug * category ((5 - 1) * (3 - 1) = 8 degrees of freedom): > a1 --> 0 0 0 0 0 0 0 0 > a2 --> 0 0 0 0 0 0 0 0 > a3 --> 0 0 0 0 0 0 0 0 > b1 --> 0 0 0 0 0 0 0 0 > b2 --> 0 0 0 1 0 0 0 0 > b3 --> 0 0 0 0 0 0 0 1 > c1 --> 0 0 0 0 0 0 0 0 > c2 --> 0 0 1 0 0 0 0 0 > c3 --> 0 0 0 0 0 0 1 0 > d1 --> 0 0 0 0 0 0 0 0 > d2 --> 0 1 0 0 0 0 0 0 > d3 --> 0 0 0 0 0 1 0 0 > e1 --> 0 0 0 0 0 0 0 0 > e2 --> 1 0 0 0 0 0 0 0 > e3 --> 0 0 0 0 1 0 0 0 > > This is not the only valid encoding, but it's the one that occurred to > me first. Many different encodings could be considered as being > correct. The only constraint is that we need to estimate the mean of > each factor/level combination by summing the coefficients available. > And we do not want any more coefficients than necessary, lest we lose > degrees of freedom for error (and hence our ability to estimate the > variability). > > So there needs to be no particular relationship between the encoding of the > interaction > and the encoding of its composite variables? The only rules are: > 1. Exactly N non-zero rows must be present, where N is the degrees of freedom. > 2. In any row there may be no more than one non-zero elements. > Hence, would the following also be a valid encoding? > > drug * category ((5 - 1) * (3 - 1) = 8 degrees of freedom): > a1 --> 0 0 0 0 0 0 0 1 > a2 --> 0 0 0 0 0 0 1 0 > a3 --> 0 0 0 0 0 1 0 0 > b1 --> 0 0 0 0 1 0 0 0 > b2 --> 0 0 0 1 0 0 0 0 > b3 --> 0 0 1 0 0 0 0 0 > c1 --> 0 1 0 0 0 0 0 0 > c2 --> 1 0 0 0 0 0 0 0 > c3 --> 0 0 0 0 0 0 0 0 > d1 --> 0 0 0 0 0 0 0 0 > d2 --> 0 0 0 0 0 0 0 0 > d3 --> 0 0 0 0 0 0 0 0 > e1 --> 0 0 0 0 0 0 0 0 > e2 --> 0 0 0 0 0 0 0 0 > e3 --> 0 0 0 0 0 0 0 0
Yes, that one is fine. _______________________________________________ pspp-dev mailing list [email protected] https://lists.gnu.org/mailman/listinfo/pspp-dev
