[R-sig-Geo] Spatial and multilevel model with kriging/interpolation in R

Justice Moses K. Aheto justiceaheto at yahoo.com
Thu Sep 25 04:25:25 CEST 2014

Dear All,
Please, I wish to analyse a spatial data in R through multilevel approach with my main primary objective been to interpolate for unsampled locations in my study region. Children in my data set are nested within households in the study locations and my multilevel model (without spatial) showed significant household random effects hence my choice to employ spatial analysis with multilevel approach. 
The need to include household random effects in my spatial model makes it a bit difficult for me to implement in R unlike the standard geostatical analysis. 
I have 'SpatialPointsDataFrame' containing my geographical coordinates (longitude and latitude) as well as my response and covariates.  
The spatial mixed effects model I wish to fit and interpolate is: Yij(t) = Xij(t)β +hj+S(t)+Ɛij           (1)
i=individual child, j=household, X(t)= spatial referenced non-random covariates, S(t)= spatially correlated stationary Gaussian process. 
Ɛij =nugget effect/measurement error, Yij(t) = response of
child i in household j at location t and is a continuous variable, hj =household level random effects and β=regression coefficients (spatial trend parameter). 
Specifically, S(t)~N(0,σ2H11(ɸ) ), where σ2  is the variance (partial sill),  H11(ɸ) is the correlation
matrix based on valid correlation function h(u; ɸ), where u is the distance
between locations and ɸ is the correlation parameter (range).
hj~N(0, σ2h), where σ2h is the household level variance
Ɛij~N(0,τ2), where τ2 is
the nugget effect/measurement error. 

I am trying to achieve the above task through geostatistical analysis but other methods which can be implemented in R are also welcomed.

Please, could somebody help me with some papers in the literature, existing packages in R which are related to my problem as well as providing me with R codes to implement this assuming someone has already done this kind of multilevel spatial regression and interpolation in R or other packages. 

Many thanks for your help in advance. 

Kind regards

Justice Moses K. Aheto
PhD Candidate in Medicine (United Kingdom)
MSc Medical Statistics (United Kingdom)
BSc Statistics (Ghana)
HND Statistics (Ghana)

Chief Executive Officer
Statistics and Analytics Consultancy Services Ltd.

Skype: jascall12
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