Agriculture Reference
In-Depth Information
Table 7.2 Relative efficiency of the sample mean (MSE/MSE
SRS
) for each design, estimated
using 10,000 replicated samples of the clustered population, for different sample sizes, trends, and
homogeneity
No trend
Linear trend
Quadratic trend
Homogeneity
Homogeneity
Homogeneity
Design
n
Low
Med
High
Low
Med
High
Low
Med
High
GRTS
10
0.99
0.97
0.81
0.64
0.65
0.55
0.75
0.75
0.65
CUBE 1
10
0.99
0.98
0.94
0.54
0.54
0.45
0.97
0.97
0.92
CUBE 2
10
0.99
0.99
0.92
0.54
0.54
0.45
0.60
0.59
0.51
DUST 1
10
1.28
1.28
1.09
0.48
0.45
0.35
0.68
0.62
0.58
DUST 2
10
1.24
1.22
0.98
0.46
0.42
0.33
0.58
0.57
0.55
SCPS
10
1.00
1.00
0.78
0.57
0.59
0.48
0.77
0.76
0.67
LPM 1
10
0.99
0.99
0.76
0.58
0.58
0.47
0.75
0.74
0.64
LPM 2
10
1.00
0.98
0.76
0.57
0.59
0.47
0.76
0.74
0.64
GRTS
50
0.99
0.99
0.64
0.52
0.52
0.35
0.65
0.62
0.49
CUBE 1
50
1.01
0.99
0.92
0.50
0.49
0.38
0.96
0.97
0.91
CUBE 2
50
1.00
1.00
0.93
0.50
0.49
0.39
0.53
0.53
0.44
DUST 1
50
2.93
2.76
1.90
0.91
0.83
0.57
1.12
1.04
0.78
DUST 2
50
2.54
2.28
1.48
0.78
0.70
0.44
0.87
0.82
0.57
SCPS
50
1.00
0.97
0.59
0.50
0.50
0.32
0.62
0.60
0.46
LPM 1
50
1.00
0.97
0.58
0.51
0.50
0.32
0.62
0.59
0.45
LPM 2
50
0.99
0.97
0.57
0.51
0.51
0.32
0.61
0.59
0.45
GRTS
100
1.00
0.93
0.56
0.50
0.49
0.30
0.60
0.58
0.42
CUBE 1
100
1.00
0.98
0.92
0.49
0.48
0.37
0.96
0.96
0.89
CUBE 2
100
1.00
1.00
0.91
0.49
0.48
0.37
0.51
0.52
0.42
DUST 1
100
4.00
3.79
2.32
1.27
1.09
0.71
1.45
1.35
0.84
DUST 2
100
3.33
3.01
1.64
1.03
0.87
0.52
1.05
0.98
0.57
SCPS
100
1.00
0.93
0.50
0.50
0.47
0.28
0.57
0.53
0.37
LPM 1
100
1.00
0.95
0.50
0.50
0.49
0.28
0.57
0.53
0.37
LPM 2
100
0.99
0.94
0.51
0.49
0.48
0.28
0.58
0.55
0.37
more difficult for the algorithm to select units within an acceptable distance of the
rest of the sample.
However, any strategy that respects a set of fixed
ˀ
k
s and simultaneously draws
samples using an increased
π
kl
for units that are far apart appears to be appealing.
Generally, SCPS, LPM 1, and LPM 2 had encouraging results. They appear to
effectively identify any existing spatial data structure, and use it to locate units in
the study region. The clustering of the population, the presence of a trend, and the
homogeneity have clear effects on the reduction of the variance of the HT estima-
tors in the spatially balanced sampling designs, even if their joint impact is, of
course, extremely moderated.
Table
7.4
reports the CPU times in seconds for each of the algorithms on a
3.06 GHz Intel Core 2 Duo using
R
and
C
versions of the codes. They were used to
select ten samples for varying population and sample sizes. The extent to which the
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