| stratum | decomposition | type | df or ne |
| constant | 1 | F | 1 |
| dams | |||
| dose | F | 2 | |
| littersize | F | 1 | |
| dam | R | 27 | |
| dams.pups | |||
| sex | F | 1 | |
| dose.sex | F | 2 | |
| error | R |
Rats example dose 3 !A sex 2 !A littersize dam 27 pup 18 weight rats.asd !DOPATH 1 # Change DOPATH argument to select each PATH !PATH 1 weight ~ mu littersize dose sex dose.sex !r dam !PATH 2 weight ~ mu out(66) littersize dose sex dose.sex !r dam !PATH 3 weight ~ mu littersize dose sex !r dam !PATH 4 weight ~ mu littersize dose sexThe input file contains an example of the use of the !DOPATH qualifier. Its argument specifies which part to execute. We will discuss the models in the two parts. It also includes the !FCON qualifier to request conditional F-statistics. Abbreviated output from part 1 is presented below.
1 LogL= 74.2174 S2= 0.19670 315 df 0.1000 1.000
2 LogL= 79.1579 S2= 0.18751 315 df 0.1488 1.000
3 LogL= 83.9408 S2= 0.17755 315 df 0.2446 1.000
4 LogL= 86.8093 S2= 0.16903 315 df 0.4254 1.000
5 LogL= 87.2249 S2= 0.16594 315 df 0.5521 1.000
6 LogL= 87.2398 S2= 0.16532 315 df 0.5854 1.000
7 LogL= 87.2398 S2= 0.16530 315 df 0.5867 1.000
8 LogL= 87.2398 S2= 0.16530 315 df 0.5867 1.000
Final parameter values 0.58667 1.0000
- - - Results from analysis of weight - - -
Approximate stratum variance decomposition
Stratum Degrees-Freedom Variance Component Coefficients
dam 22.56 1.27762 11.5 1.0
Residual Variance 292.44 0.165300 0.0 1.0
Source Model terms Gamma Component Comp/SE % C
dam 27 27 0.586674 0.969770E-01 2.92 0 P
Variance 322 315 1.00000 0.165300 12.09 0 P
Wald F statistics
Source of Variation NumDF DenDF-con F-inc F-con M P-con
7 mu 1 32.0 9049.48 1099.20 b <.001
3 littersize 1 31.5 27.99 46.25 B <.001
1 dose 2 23.9 12.15 11.51 A <.001
2 sex 1 299.8 57.96 57.96 A <.001
8 dose.sex 2 302.1 0.40 0.40 B 0.673
Notice: The DenDF values are calculated ignoring fixed/boundary/singular
variance parameters using algebraic derivatives.
4 dam 27 effects fitted
SLOPES FOR LOG(ABS(RES)) on LOG(PV) for Section 1
2.27
3 possible outliers: see .res file
The iterative sequence has converged and the variance component
parameter for dam hasn't changed for the last three
iterations. The incremental Wald tests indicate that the interaction
between dose and sex is not significant.
The Fcn column helps us to assess the significance of
the other terms in the model. It confirms littersize
is significant after the other terms, that dose is
significant when adjusted for littersize and sex but ignoring
dose.sex, and that sex is
significant when adjusted for littersize and dose but ignoring
dose.sex.
These tests respect marginality to the dose.sex interaction.
We also note the comment 3 possible outliers: see .res file.
Checking the .res file, we discover
unit 66 has a standardised residual of
-8.80 (see Figure 1). The weight of this female rat, within
litter 9 is only 3.68, compared to weights of 7.26 and 6.58 for two
other female sibling pups. This weight appears erroneous, but without
knowledge of the actual experiment we retain the observation in the
following. However, part 2 shows one way of 'dropping' unit 66
by fitting an effect for it with out(66).
Source Model terms Gamma Component Comp/SE % C
dam 27 27 0.595157 0.979179E-01 2.93 0 P
Variance 322 317 1.00000 0.164524 12.13 0 P
Wald F statistics
Source of Variation NumDF DenDF-con F-inc F-con M P-con
7 mu 1 32.0 8981.48 1093.05 . <.001
3 littersize 1 31.4 27.85 46.43 A <.001
1 dose 2 24.0 12.05 11.42 A <.001
2 sex 1 301.7 58.27 58.27 A <.001
Part 4 shows what happens if we (wrongly) drop dam from this model.
Even if a random term is not 'significant', it should not be dropped
from the model if it represents a strata of the design as in this case.
Source Model terms Gamma Component Comp/SE % C
Variance 322 317 1.00000 0.253182 12.59 0 P
Wald F statistics
Source of Variation NumDF DenDF-con F-inc F-con M P-con
7 mu 1 317.0 47077.31 3309.42 . <.001
3 littersize 1 317.0 68.48 146.50 A <.001
1 dose 2 317.0 60.99 58.43 A <.001
2 sex 1 317.0 24.52 24.52 A <.001