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CPS1878 Zakir H. et al.
amount of bias is substantially higher (-15% to -5%) in the misspecified model
compared to the true model.
Figure 3: Relative biases of ̂ and ̂ for M1 (true model) versus M2 (misspecified
2
2

model).

It can also be seen from the right panel of Figure 3 that the relative bias of
̂ is also negligible for the true model (M1) whereas it is substantially higher
2

(20% to 90%) for the misspecifed model (M2). Thus, both variance components
2
2
estimates ̂ and ̂ are found to be severely biased due to misspecification

of the correlation structure of the random blocks and errors.
2
2
Figure 4: SEs of ̂ and ̂ for M1 (true model) versus M2 (misspecified model).

● M1: correlated random effects ● M2: uncorrelated random effects
^
σ
σ 2 ^ 2
B
W
● 0.20 ●
●
0.8
● 0.15
●
0.6
S ● ●
E ● ● ● 0.10 ● ●
●
0.4 ● ● ● ●
● ● ● ● ● ● ●
● ● 0.05 ● ● ● ● ●
●
●
● ●
●
(2,10) (2,20) (2,40) (3,15) (3,30) (3,60) (4,20) (4,40) (4,80) (2,10) (2,20) (2,40) (3,15) (3,30) (3,60) (4,20) (4,40) (4,80)
Treatment block combinations (t, b)
Moreover, from the left panel of Figure 4 it can be seen that there is not
2
much difference in estimated SEs of ̂ between the true and misspecified

models for all nine treatment-block combinations. However, there are some
differences in the estimated SEs of ̂ between the true and misspecified
2

2
models. In all nine treatment-block combinations, SEs of ̂ are found to be

higher for the misspecified model M2 than the true model M1 due to
misspecification of the correlation structure of the random effects.

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