The good news is, that I found and fixed a bug which was causing the Effects Coding to produce garbage results. The surprising news (surprising to me anyway) is that having fixed it, Effects Coding produces identical results to Dummy Coding.
The dissapointing news is that we still don't get the same results as SPSS for unbalanced designs. However, I've been looking at various examples on the net, and perhaps I've stumbled onto something: 1. There's a worked example at https://netfiles.uiuc.edu/dgs/www/stat324/notes/041604.pdf (for R) It doesn't say which "Type" of SSQ it's using, but it does say that the results are dependent upon the order in which the effects are presented in the design matrix, which I understood to be true for Type I. The example results are for the SUPP variable as the first variable: Df Sum Sq Mean Sq F value Pr(>F) supp 1 174.46 174.46 17.3664 0.0011049 doselev 2 375.75 187.87 18.7012 0.0001495 supp:doselev 2 17.70 8.85 0.8808 0.4377931 Residuals 13 130.60 10.05 and for the DOSLEV variable as the first variable: Df Sum Sq Mean Sq F value Pr(>F) doselev 2 396.08 198.04 19.7131 0.0001158 supp 1 154.13 154.13 15.3428 0.0017685 doselev:supp 2 17.70 8.85 0.8808 0.4377931 Residuals 13 130.60 10.05 Note that the two main effects are quite different. Now when I run the same data with PSPP, I get: #Corrected Model# 567,91| 5| 113,58| 11,31| ,00# #Intercept # 5956,05| 1| 5956,05|592,87| ,00# #supp # 154,13| 1| 154,13| 15,34| ,00# #doselev # 375,75| 2| 187,87| 18,70| ,00# #supp * doselev # 17,70| 2| 8,85| ,88| ,44# #Error # 130,60|13| 10,05| | # #Total # 6654,56|19| | | # #Corrected Total# 698,51|18| | | # Note that PSPPs DOSLEV ssq is identical to Rs DOSLEV ssq in the first example above, and the SUPP ssq is identical to that in the second example. The interaction is the same for both. 2. Another example, this time for SAS, at http://www.sfu.ca/sasdoc/sashtml/stat/chap30/sect52.htm I copied the data given there, and ran it through PSPP and got: #===============#=======================#==#============#==========#=======# # Source #Type III Sum of Squares|df| Mean Square| F | Sig. # #===============#=======================#==#============#==========#=======# #Corrected Model# 4259,338506|11| 387,212591| 3,505692|,001298# #Intercept # 20672,844828| 1|20672,844828|187,164963|,000000# #drug # 3063,432863| 3| 1021,144288| 9,245096|,000067# #disease # 418,833741| 2| 209,416870| 1,895990|,161720# #drug * disease # 707,266259| 6| 117,877710| 1,067225|,395846# #Error # 5080,816667|46| 110,452536| | # #Total # 30013,000000|58| | | # #Corrected Total# 9340,155172|57| | | # Now these numbers are exactly what the SAS example gives for the type II sums of squares, (although PSPP is labelling them as Type III) 3. A concise but quite useful description of the various ssq "types" can be found at http://afni.nimh.nih.gov/sscc/gangc/SS.html It says this about Type III : "SS gives the sum of squares that would be obtained for each variable if it were entered last into the model. That is, the effect of each variable is evaluated after all other factors have been accounted for. Therefore the result for each term is equivalent to what is obtained with Type I analysis when the term enters the model as the last one in the ordering." This would seem to be consistent with our results in 1. 4. However, none of the SPSS examples I have found which feature unbalanced designs actually correspond to what PSPP currently produces for type III ssq. The interactions are the same, but the main effects quite different. The forgoing leads me to infer that SPSS has the meaning of Type II and Type III transposed, in comparison to the rest of the world. This sounds somewhat incredible, but seems to be consistent with the evidence so far. I can only suggest that we try to implement the Type II next, and see what happens. J' -- PGP Public key ID: 1024D/2DE827B3 fingerprint = 8797 A26D 0854 2EAB 0285 A290 8A67 719C 2DE8 27B3 See http://pgp.mit.edu or any PGP keyserver for public key.
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