Biomedical Engineering Reference
In-Depth Information
To study the impacts of choice of working correlation structure, we com-
pare every procedures under three working correlation structures: working
independence, AR(1) and compound symmetry; these are abbreviated as
Ind, AR, CS in Table 1.
Table 1.
Comparison of GEE Model Selection (Continuous Response)
Criterion
10
Mean ME
Prop. True Models
Working Corr. Matrix:
Ind
AR
CS
Ind
AR
CS
Full
2.87
1.25
1.69
0.00
0.00
0.00
Na
ive AIC
1.87
0.77
1.13
0.63
0.65
0.63
Na
ive C
p
1.87
0.77
1.13
0.63
0.66
0.63
AIC (Pan)
1.87
0.85
1.11
0.58
0.35
0.41
C
p
(Cantoni)
1.87
0.80
1.08
0.63
0.44
0.42
LASSO (Fu)
2.18
1.14
2.03
0.08
0.40
0.25
SCAD
1
1.68
0.64
1.04
0.50
0.41
0.33
SCAD
2
1.73
0.64
1.12
0.70
0.62
0.50
Correct Deletions
Erroneous Deletions
Working Corr. Matrix:
Ind
AR
CS
Ind
AR
CS
Full
0.00
0.00
0.00
0.00
0.00
0.00
Na
ive AIC
4.59
4.60
4.59
0.06
0.03
0.06
Na
ive C
p
4.59
4.61
4.59
0.06
0.03
0.06
AIC (Pan)
4.53
4.08
4.21
0.04
0.01
0.02
C
p
(Cantoni)
4.59
4.26
4.24
0.06
0.01
0.02
LASSO (Fu)
2.66
4.14
3.70
0.00
0.00
0.01
SCAD
1
4.26
4.17
4.04
0.03
0.00
0.01
SCAD
2
4.63
4.51
4.39
0.03
0.00
0.01
From Table 1, taking correlation into account led to much better es-
timation performance than using working independence. Not surprisingly
using the correct correlation structure, AR(1), was better than using an
incorrect (compound symmetric) correlation structure. In general, parsi-
monious methods outperformed less parsimonious ones, partly because the
true model in this example is rather simple. SCAD tended to give smaller
models than LASSO, and generally better estimation performance. Over-
all, SCAD outperforms the other procedures in terms of model errors and
model complexity.
Example 2. In this example, we compare the variable selection procedures
for data with correlated binary responses. The simulations were conducted
using R code since we used the correlated random binary data generator
by Leisch and Weingessel
26
. We conducted 200 simulations, and in each
simulation, n = 100 subjects with J = 10 observations (i.e., all n
i
equals
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