Analysis of Stratified Surveys - distancesampling.org...It is a Model Selection Problem Criterion...
Transcript of Analysis of Stratified Surveys - distancesampling.org...It is a Model Selection Problem Criterion...
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Analysis of Stratified Surveys
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Stratification• Why stratify?
• Stratification by:
• Geographic area• Survey• Species / cluster size
• Limitations of Distance
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Stratification is used to:• reduce variance and improve precision• and for producing estimates in regions of interest
Stratify by:• AREA or GEOGRAPHIC REGION
- the study region is partitioned into smaller regions
• SURVEY- used when different surveys cover the same geographic area
• POPULATION/SPECIES/CLUSTER SIZE- same geographic region with different ‘sub-stocks’ in it
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Area/Geographic stratification
Estimate density in each sub-region
321 AAAA
A1
A2
A3
321 DDD ˆ,ˆ,ˆ
333
222
111
DAN
DAN
DAN
ˆˆ
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Total size of study region
Abundance in each sub-region is given by
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ii
i DA
A
DA
AD
A
AD
A
A
AAA
DADADA
A
ND
ˆ
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1
33
22
11
321
332211
332211
321
DADADA
NNNN
ˆˆˆ
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Total abundance is Overall (Global in Distance) density is
Note form of equation
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Example: SCANS II (2005)
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SCANS IIsurvey effort
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Example of stratified data
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Example: Full geographic stratification
D
f1(0) f2(0) f3(0)
E1(s) E2(s) E3(s)
(n/L)1 (n/L)2 (n/L)3
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Example: f(0) pooled
D
f123(0)
E1(s) E2(s) E3(s)
(n/L)1 (n/L)2 (n/L)3
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Pooled vs Stratified f(0)
Pooled n=88
Stratified
Ideal Habitat n=39
Marginal Habitat n=49
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It is a Model Selection Problem
Criterion for stratification of f(0):Fit separate f(0) for each strata if
stratastratumpooled
AICAIC
Pooled Stratum 1 Stratum 2 StratumSum
Log likelihood loge(L) -180.490 -72.699 -104.676 -177.375
No. parameters (q) 2 2 2 4
AIC 364.980 149.398 213.352 362.75
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Non-geographic stratification -- Stratification by survey
Survey 1
Survey 2
ii
i DL
L
DLL
LD
LL
LD
ˆ
ˆˆˆ
2
1
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21
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1
Let Li be effort for survey i
Global density is given by
This is the same form as before, but weightingfactor now depends on effort
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Stratification by survey
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Stratification by species
21 spsp DDD ˆˆˆ
Species 1
Species 2
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Limitations in Distance
• Distance cannot currently do multilevel stratificationin one run
• Two runs are necessary– Estimate f(0), E[s] and n/L by stratum
– Combine strata 1 and 2 to estimate f12(0)
• Care must be taken when calculating CVs because thedensity estimates for stratum 1 and 2 have anestimated f(0) in common
D
f12(0) f3(0)
E1[s] E2[s] E3[s]
(n/L)1 (n/L)2 (n/L)3
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Alternatives to stratification in Distance
• Small sample sizes can lead to low precision in stratum-specific estimates
• An alternative approach to reducing bias due to heterogeneity is Multiple Covariates Distance Sampling (MCDS)
• Covariates, other than distance, are incorporated into the scale parameter of the detection function
• MCDS can be used to fit the detection function at multiple levels e.g. stratum-specific density estimatescan be obtained even if you don't have enough data to fit separate detection functions for each stratum
• MCDS methods are covered in an upcoming lecture.