From: <arthur.gilmour_at_DPI.NSW.GOV.AU>

Date: Fri, 24 Oct 2008 10:37:04 +1100

Date: Fri, 24 Oct 2008 10:37:04 +1100

Dear ASReml users

I enclose my response to an ASReml user whi had trouble predicting a

twoway table and its margins.

Since the example is instructive, I have taken the liberty of sharing it

for your interest.

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

0

Notes:

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 nateral 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 DenDF_con F_inc F_con M

P_con

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)

Which 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

F1 B1 b2 B3 B4 B5 B6

F2 B1 b2 B3 - - -

F3 B1 b2 B3 B4 B5 B6

F4 - - - B4 B5 B6

Surprisingly, 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 possabilities in ASReml but you must determine which if

either is valid.

I have added !FITMARGIN to PREDICT F B

and this generates marginal means from the F B table assuming that

interaction effects associated

with missing cells are zero.

I have added !PRESENT F B to the other two predict statements

so that marginal means are calculated just from those cells in the

row/column of F x B table which are present.

Neither of these approaches is necessarily appropriate or reasonable.

Given the large F effects, B means using the PRESENT strategy will be

confounded with the F effects

(at least comparisons between the B1 B2 B3 set and the B4 B5 B6 set.

I trust this helps.

May Jesus Christ continue to be gracious to you,

Arthur Gilmour, His servant .

Mixed model regression mapping for QTL detection in experimental crosses.

Computational Statistics and Data Analysis 51:3749-3764 at

http://dx.doi.org/10.1016/j.csda.2006.12.031

Profile:http://www.dpi.nsw.gov.au/research/staff/arthur-gilmour

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Skype: arthur.gilmour

mailto:Arthur.Gilmour_at_dpi.nsw.gov.au, arthur_at_cargovale.com.au

Principal Research Scientist (Biometrics)

NSW Department of Primary Industries

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Received on Sun Oct 24 2008 - 10:37:04 EST

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