addTemporalCovariates: addTemporalCovariates function
Description
A function to 'bolt on' temporal data onto a spatial covariate design matrix. The function takes a spatial design matrix, Z(s) and
converts it to a spatiotemporal design matrix Z(s,t) when the effects can be separably decomposed i.e.,
Z(s,t)beta = Z_1(s)beta_1 + Z_2(t)beta_2
An example of this function in action is given in the vignette "Bayesian_lgcp", in the section on spatiotemporal data.
a formula of the form t ~ tvar1 + tvar2 etc. Where the left hand side is a "t". Note there should
not be an intercept term in both of the the spatial and temporal components.
T
the time point of interest
laglength
the number of previous time points to include in the analysis
tdata
a data frame with variable t minimally including times (T-laglength):T and var1, var2 etc.
Zmat
the spatial covariates Z(s), obtained by using the getZmat function.
Value
A list of design matrices, one for each time, Z(s,t) for t in (T-laglength):T
Details
The main idea of this function is: having created a spatial Z(s) using getZmat, to create a dummy dataset tdata and temporal
formula corresponding to the temporal component of the separable effects. The entries in the model matrix Z(s,t) corresponsing to
the time covariates are constant over the observation window in space, but in general vary from time-point to time-point.
Note that if there is an intercept in the spatial part of the model e.g., X ~ var1 + var2, then in the temporal model,
the intercept should be removed i.e., t ~ tvar1 + tvar2 - 1