
A Change in Attitudes Toward Muslims? A Bayesian Investigation of Pre and Post 9/11 Public Opinion

 Unformatted Document Text:
persion (Crouchley 1995; Agresti 1999). The formal expression of the model is:
y
it
∼ Categorical (π
it
) , i = 1, 2, . . . , 8842, t = 1, 2, 3, 4
π
it
= logit
−1
(z
it,κ−1
) − logit
−1
(z
it,κ
) , κ = 1, 2, 3
z
it,κ
= X
it
β − c
t,κ
β ∼ N (0, 1000)
c
t,1
∼ N (0, 1000)I(, c
t,2
)
c
t,2
∼ N (0, 1000)I(c
t,1
, c
t,3
)
c
t,3
∼ N (0, 1000)I(c
t,2
, )
where we assign uninformative priors β ∼ N (0, 1000) for the coeﬃcients of the pre
dictors and constrained uninformative priors for the cutpoints c’s.
4
For each imputed
dataset, we run 10000 iterations, discard ﬁrst 5000 as the burnin, and thin the re
maining iterates by 5. Strong evidence of convergence of these Markov chains are
provided by standard diagnostics (graphic methods and Gelman and Rubin (1992)).
We combine the estimates by pooling the estimates across three imputed datasets,
thus:
ˆ
β =
1
m
3
m=1
ˆ
β
m
, m = 1, 2, 3
V
β
= V
within
+ (1 +
1
m
)V
between
where V
within
=
1
m
3m=1
s
2
and V
between
=
1
m
3m=1
( ˆ
β − ˆ
β
m
)
2
(Gelman and Hill 2007).
Figure 7 displays posterior means ˆ
β and 95% intervals (±2
V
β
) for each of the
coeﬃcients, including the cutpoints. The estimates of predictors are similar to those
of the pooled model or the model with no pooling. Likewise, the major quantities
4
We implement the analysis using WinBUGS (Spiegelhalter, Thomas, Best, Gilks, and Lunn 1996,2003) and do the postestimation using R package R2WinBUGS (Sibylle, Uwe, and Gelman 2005).
17

 Authors: Kalkan, Kerem. and Su, YuSung. 




y
it
∼ Categorical (π
it
) , i = 1, 2, . . . , 8842, t = 1, 2, 3, 4
π
it
= logit
−1
(z
it,κ−1
) − logit
−1
(z
it,κ
) , κ = 1, 2, 3
z
it,κ
= X
it
β − c
t,κ
β ∼ N (0, 1000)
c
t,1
∼ N (0, 1000)I(, c
t,2
)
c
t,2
∼ N (0, 1000)I(c
t,1
, c
t,3
)
c
t,3
∼ N (0, 1000)I(c
t,2
, )
where we assign uninformative priors β ∼ N (0, 1000) for the coeﬃcients of the pre
dictors and constrained uninformative priors for the cutpoints c’s.
4
For each imputed
dataset, we run 10000 iterations, discard ﬁrst 5000 as the burnin, and thin the re
maining iterates by 5. Strong evidence of convergence of these Markov chains are
We combine the estimates by pooling the estimates across three imputed datasets,
thus:
ˆ
β =
1
m
3
m=1
ˆ
β
m
, m = 1, 2, 3
V
β
= V
within
+ (1 +
1
m
)V
between
where V
within
=
1
m
3 m=1
s
2
and V
between
=
1
m
3 m=1
( ˆ
β − ˆ
β
m
)
2
Figure 7 displays posterior means ˆ
β and 95% intervals (±2
V
β
) for each of the
coeﬃcients, including the cutpoints. The estimates of predictors are similar to those
of the pooled model or the model with no pooling. Likewise, the major quantities
4
17


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