Haicheng's Epi624 Home Page
Kriging ILL County Breast Cancer Mortality Rates
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Introduction
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Original ILL breast cancer mortality rates
(-9: missing)
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ILL breast cancer mortality rates contour
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ILL breast cancer mortality rates circle plot
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To find out whether there is trend and decide whether to use ordinary
or universal kriging accordingly, we check the
perspective plot
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To test for normality, check QQ plot
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variogram cloud
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sample variogram
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To apply kriging method, we'd like to check whether the underlying
process is isotropic , i.e., the variogram
cloud at different directions are similar, 'cause then theoretical
variogram model can be handled easily. We achieve that by viewing
variogram plot at 4 ranges of angles.
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Theoretical (spherical)
variogram fitted according to sample variograms with Splus,
where the parameters are found to be: range=8, sill=0.35, nugget= 2.8
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Globally Krigged ILL breast cancer mortality rates
, by which I mean the rate is considered distributed all over ILL
(instead of at counties (centers) only); standard
error surface ; and 95% confidence surfaces.
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Krigged mortality rates where there are no observed values, essentially,
an imputation with kriging
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Finally, graphical display of krigged ILL breast cancer mortality rates
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Discussions:
- Another type of kriging: noiseless, not available in Splus
- Some doubt on Normality: Transformation might give better results,
but adjustment is needed to ensure unbiasedness.
- Or even better, Data essentially (irregular) lattice discrete data
(counts). Therefore,
- Conditional Auto Poission model (ref: (6.5.6) (6.6.7) of Cressie
1993).
- Hierarchical Poisson model: Underlying mortality rate \lambda(s) is
a continuous process, given which as parameters, the counts independently follow
Poisson distribution.
The data and scripts used to produce these Splus
analyses are available.
The postscript report.
Website maintained by haicheng.
Comments
appreciated.
haicheng@umich.edu