[R-sig-Geo] Space-Time models for Time Series Cross-Sectional data

[Justice Moses K. Aheto]

Dear Geo-R List members,I have a survey data which is cross-sectional in nature collected on different sampled individuals for each survey period over 4 time periods with 5-year time interval between each survey. Information about the location of the resident were collected (geographical coordinates) and these coordinates are unique for each time period.The sampled individuals in each survey period are different from one survey time period to another, meaning different samples were used for each of the 4 surveys. My outcome variable (Y) is continuous, I have covariates such age and sex of child among others to be included in the model. The survey is conducted by same organization with same statistical methodologies over time for same age group and study settings and data collected on similar variables. Below are the codes I have put together in order to construct a fictitious data similar to my data structure:
N=10000# Number of the total observation for all the survey years
Y=rnorm(N,0,1)# my outcome variable on continuous scaleyear=c(1990,1995,2000,2005)# survey yearsyear=rep(c(1990,1995,2000,2005),times=c(2000,3100,2000,2900)) # different number of observations per survey years                                                  lon=sample(N)# longitude
lat=sample(N+1000,10000)# latitude
age=sample(0:4.9)#  age of child as covariateage=rep(age,2000)
sex=as.factor(c(rep(1,2,each=5000)))
ID=1:length(Y)# ID for individual observations
data=as.data.frame(cbind(ID,Y,year,lon,lat,age,sex))# creating data frame
head(data,10) # for the first 10 observationstail(data,10) # for the last 10 observations
Below is the first 10 observations of the data frame:
 head(data,10)    ID          Y       year   lon    lat   age sex1   1  1.3526490 1990 4202   868   1   12   2 -0.3210689 1990 8515  6549   0   13   3 -0.4126906 1990 1420  5218   4   14   4  1.7399052 1990 1100  5129   3   15   5 -1.6019068 1990 4488   294   2   16   6 -1.4383548 1990 2099  9543   1   17   7  1.2600215 1990 2518    34   0   18   8 -1.2001605 1990 6546 10809   4   19   9 -0.3020261 1990 3833  8585   3   110 10 -0.5805120 1990 5815    76   2   1 Below is the last 10 observations of the data frame:
tail(data,10)              ID           Y           year  lon     lat    age sex9991   9991 -0.44229435 2005 7884  9670   1   19992   9992 -0.74089670 2005 6824 10406   0   19993   9993  0.39667898 2005 4601  8118   4   19994   9994 -1.22391266 2005 4361  8747   3   19995   9995 -1.86094028 2005 3055  8429   2   19996   9996 -1.32859732 2005 3225 10872   1   19997   9997 -0.04749873 2005 9325  1730   0   19998   9998 -0.33076432 2005 9045  6663   4   19999   9999 -0.83026815 2005 4642  6149   3   110000 10000  0.87211988 2005 4995  8253   2   1

Now, here is my task:I wish to conduct spatio-temporal analysis on this data and possibly forecast for future observations. I have read the literature on space-time models, dynamic linear models and Kalman Filter but I am not sure if any of these could apply to my situation. 
The model I have in mind is:
St|St-1 = AtSt-1 + {sqrt(1-A^2)}Wt,   (1) where  Wt ~ MVN(0, Σ). A is a weight which guarantees stationarity, St-1                                                                                         represent the state at time t-1 before time t and St is the state at time t                                                                                   conditional on the state at time t-1. Σ is the covariance matrix                                                                                                 associated with the Gaussian noise WtYt|St = X_t^'β + DtSt + Vt,                 (2)  where Vt ~ N(0, σ_vt^2), X_t is the vector of covariates, β are the regression                                                                          coefficients, Dt is a matrix of 1’s if a child issampled from location j in time t                                                                        and zero (0) otherwise. σ_vt^2 is the variance associated with the Gaussian                                                                          noise VtFrom above, Equation (1) is my state (unobserved) equation and Equation (2) is the observed (measurement) Equation.
Please, (1) is there any available package(s) in R that could allow me to fit the above model considering the nature of my data?(2) Are there other possible space-time models that I can fit to the data above? If yes, what type of model and which R package can this be implemented in with references.
Any help is highly appreciated in advance.
Thanks 

Kind regards

*****************************************
Justice Moses K. Aheto
PhD Candidate in Medicine (Statistics, Biostatistics, Public Health and Epidemiology). 
MSc Medical Statistics. 
BSc Statistics. 
HND Statistics 

Chief Executive Officer
Statistics and Analytics Consultancy Services Ltd.

Skype: jascall12
Mobile: +447417589148.
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