Title: exampledata. #A,B,C,D,E,F #1,3,0.117,0.044,1,1 #1,3,-0.043,0.022,1,2 #1,3,0.007,0.02,1,3 #2,3,0.142,0.044,1,1 A * # !I B * # !I C #!*10 D #!*10 E * # !I F * # !I # Check/Correct these field definitions. exampledata.csv !SKIP 1 !FCON tabulate C ~ B A F !stats tabulate C ~ B A !stats tabulate C ~ A B !stats tabulate C ~ F B !stats C ~ mu F B D F.B F.D -B.D -F.B.D, # Specify fixed model !r A # Specify random model PREDICT F B !FITMARGIN PREDICT F !PRESENT F B PREDICT B !PRESENT F B 0Notes:

A has 140 levels,

B has 6 levels,

D is a covariate

E is not used so ignored in these notes

F has 4 levels.

The combinations of B A F define the individual observations. It appears levels of A are largely nested in levels of B but not completely in that some levels of A appear in two different levels of B So there are 140 levels of A and 157 levels in A.B Use of !I says 'TREAT THE values in the data file as labels rather than directly as codes'. However it seems that they should be taken directly as level codes so I have changed !I to * so that they appear in natural order. The analysis of the example gives

- - - Results from analysis of C - - - Approximate stratum variance decomposition Stratum Degrees-Freedom Variance Component Coefficients Source Model terms Gamma Component Comp/SE % C A 140 140 0.102574E-05 0.133539E-08 0.00 0 B Variance 280 248 1.00000 0.130188E-02 11.14 0 P Warning: Code B - fixed at a boundary (!GP) F - fixed by user ? - liable to change from P to B P - positive definite C - Constrained by user (!VCC) U - unbounded S - Singular Information matrix S means there is no information in the data for this parameter. Very small components with Comp/SE ratios of zero sometimes indicate poor scaling. Consider rescaling the design matrix in such cases. Wald F statistics Source of Variation NumDF DenDFWhich shows no variance component associated with A, A big effect of F and B, and interaction. ; no effect of D So you wanted to predict these tables. Tabulation shows 18 combinations of F and B_{c}n F_{i}c F_{c}n M P_{c}n 7 mu 1 248.0 1281.91 283.34 . <.001 6 F 3 248.0 201.57 192.33 A <.001 2 B 5 248.0 11.44 11.72 A <.001 4 D 1 248.0 3.31 0.06 A 0.801 8 F.B 9 248.0 3.89 3.40 b <.001 9 F.D 3 248.0 1.06 0.98 B 0.405 10 B.D 4 248.0 1.18 1.18 B 0.323 11 F.B.D 6 248.0 1.26 1.26 C 0.277 Notice: The DenDF values are calculated ignoring fixed/boundary/singular variance parameters using algebraic derivatives. 1 A 140 effects fitted ( 2 are zero)

F1 B1 b2 B3 B4 B5 B6 F2 B1 b2 B3 - - - F3 B1 b2 B3 B4 B5 B6 F4 - - - B4 B5 B6Surprisingly, only 14 combinations are reported from predict F B The ones missing are F1B6 F3B6 F4B5 and F4B6 despite the fact that there is the correct DF (1 + 3 + 5 + 9=18)

My first guess is that this might be a scaling effect but multiplying by 10 did not solve the problem.

Second was that it was associated with the NS D regressions. Dropping the F.B.D and B.D model terms resolved the problem. Looking at the ANOVA table again, we see that these terms were deficient in DF (B.D had 4 not 5, F.B.D had 6 not 9) so these singularities were sufficient to make some cells not estimable. Now concerning the F and B tables, given the 6 missing cells, there is no standard way to calculate the margins (except F1 and F3 which are complete). There are two possibilities in ASReml but you must determine which if either is valid.ARG 25 Oct 2008