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CPS1878 Zakir H. et al.
3.1 Results of misspecification of the correlation structure
We simulate Poisson data from M1 with correlated and normally
distributed random effects. We then t the misspecified model M2 with
uncorrelated random effects and the true model M1 with correlated random
effects to the same set of simulated data. It can be seen from Figure 1 that the
percent relative biases of ̂ , ̂ and ̂ are very close for the true model (M1)
3
2
1
and the misspecified model (M2). Figure 2 also shows that SEs of ̂ , ̂ , ̂ are
1
2
3
almost the same in all nine treatment-block combinations for M1 and M2. It
follows that the misspecification of the correlation structure of the random
effects has hardly any effect on the estimated fixed treatment effect
parameters.
Figure 1: Relative biases of ̂ , ̂ and ̂ for M1 (true model) versus M2
1
3
2
(misspecified model).
● M1: correlated random effects ● M2: uncorrelated random effects
^ α 2 ^
^
α 3
α 1
●
R ●
el 5
at ●
iv ●
e ● ● ●
bi ● ● ● ● ● ● ●
as 0 ● ● ● ● ● ● ●
( ● ● ● ● ● ●
% ●
) ● ● ● ●
−5
●
●
(2,10) (2,20) (2,40) (3,15) (3,30) (3,60) (4,20) (4,40) (4,80) (3,15) (3,30) (3,60) (4,20) (4,40) (4,80) (4,20) (4,40) (4,80)
Treatment block combinations (t, b)

Figure 2: SEs of ̂ , ̂ and ̂ for M1 (true model) versus M2
2
1
3
(misspecified model).

2
It can be seen from the left panel that the percent relative bias of ̂ for

the true model is negligible (ranges from -5 % to 5 %) in all nine treatment-
block combinations. However, ̂ seems to be consistently underestimated in
2

all nine treatment-block combinations for the misspecified model M2 due to
misspecification of the correlation structure for the random effects. The

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