Page 24 - Contributed Paper Session (CPS) - Volume 1

CPS653 Chang-Yun L.

is retained for inference (this process is known as thinning) to decrease the
autocorrelation between the iterations. Total 2000 samples for each parameter
are saved and the distribution of the latent variables is calculated. In Table 2,
we list the top five models which have highest joint posterior probabilities of
the latent variables. It shows that the model with highest posterior probability
has the same model terms with the true model and the other four models are
all submodels of the true model. Figure 1 is a plot for the marginal posterior
probability of each effect being active. It shows that the probabilities for
effects , , , , and being active are significantly higher than the
13
1
3
11
33
others. In Table 2, we also list the models selected by the two regression
methods, MSR and FSR, with significance level α = .05. Results show that the
MSR method correctly selects the active effects but the FSR method fails to
identify the interaction of and . The FSR method also falsely selects
3
1
and into the model. With the FSR method, we obtain ̂ = 0, which
2 7

5
implies that the FSR method cannot detect the split-plot structure for this
example. In addition, the model selected by the FSR method disobeys the
effect heredity principle.

5. Concluding remarks
In this paper, we propose the SSVS method to analyze data for SPDS
and BDS designs. This method overcomes the problem of σˆγ = 0 with the
REML method and the problem of being unable to estimate effects with
the GLS method when the degrees of freedom are not

Table 2: Models selected by the SSVS, MSR, and FSR methods for the SPDS design.
Method Model Probability
SSVS , , , , .097
2
2
3
3
1
1 3
1
2
2
, , , .086
3
3
1
1
, .041
2
3
3
2
, , .039
1
3
1
2
, , , .038
3
1
1 3
3
MSR , , , , -
2
2
3
1
1 3
3
1
2
2
FSR , , , , , -
3
1
3
5
1
2 7
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