# Model fitting and validation for spatio-temporal data from moving sensors in time. ```r Bmoving_sptime( formula, data, coordtype, coords, prior.sigma2 = c(2, 1), prior.tau2 = c(2, 1), prior.phi = NULL, prior.phi.param = NULL, scale.transform = "NONE", ad.delta = 0.8, t.depth = 12, s.size = 0.01, N = 2500, burn.in = 1000, no.chains = 1, validrows = 10, predspace = FALSE, newdata = NULL, mchoice = TRUE, plotit = FALSE, rseed = 44, verbose = TRUE, knots.coords = NULL, g_size = 5 ) ``` ## Arguments - `formula`: An object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. - `data`: The data frame for which the model formula is to be fitted. The data frame should be in long format having one row for each location and time combination. The data frame must be ordered by time within each site, and should optionally have a column, named s.index, providing the site indices. Thus the data, with n sites and T times within each site, should be organized in the order: (s1, t1), (s1, t2), ... (s1, T), ... (sn, t1), ... (sn, T). The data frame should also contain two columns giving the coordinates of the locations for spatio temporal model fitting. - `coordtype`: Type of coordinates: utm, lonlat or plain with utm (supplied in meters) as the default. Distance will be calculated in units of kilometer if this argument is either utm or lonlat. Euclidean distance will be calculated if this is given as the third type plain. If distance in meter is to be calculated then coordtype should be passed on as plain although the coords are supplied in UTM. - `coords`: A vector of size 2 giving the column numbers of the data frame which contain the coordinates of the data locations. Here the supplied data frame must contain a column named `time` which should indicate the time index of the data row. The values in the column `time` should be positive integers starting from 1. - `prior.sigma2`: Shape and scale parameter value for the gamma prior on 1/sigma^2, the precision. - `prior.tau2`: Shape and scale parameter value for the gamma prior on tau^2, the nugget effect. - `prior.phi`: Specifies the prior distribution for $\phi$ only when package is one of Stan, spTimer or spTDyn. Distribution options uniform specified by "Unif" and gamma specified by "Gamm" have been implemented in both Stan and spTimer. Additionally a half-Cauchy prior distribution specified as "Cauchy" has been implemented in Stan. In the case of spTimer the uniform distribution is discrete while in the case of Stan the uniform distribution is continuous. In the case of spTimer the option "FIXED" can be used to keep the value fixed. In that case the fixed value can be given by by a scalar value as the argument `prior.phi.param` below or it can be left unspecified in which case the fixed value of $\phi$ is chosen as 3/maximum distance between the data locations. The "FIXED" option is not available for the Stan package. - `prior.phi.param`: Lower and upper limits of the uniform prior distribution for phi the spatial decay parameter. For the default uniform distribution the values correspond to an effective range that is between 1% and 100% of the maximum distance between the data locations. For the Gamma distribution the default values are 2 and 1 and for the Cauchy distribution the default values are 0, 1 which specifies a half-Cauchy distribution in $(0, \infty)$. - `scale.transform`: Transformation of the response variable. It can take three values: SQRT, LOG or NONE. Default value is "NONE". - `ad.delta`: Adaptive delta controlling the behavior of Stan during fitting. - `t.depth`: Maximum allowed tree depth in the fitting process of Stan. - `s.size`: step size in the fitting process of Stan. - `N`: MCMC sample size. - `burn.in`: How many initial iterations to discard. Only relevant for MCMC based model fitting, i.e., when package is spBayes or Stan. - `no.chains`: Number of parallel chains to run in Stan. - `validrows`: Either a number of randomly selected data rows to validate or a vector giving the row numbers of the data set for validation. - `predspace`: A 0-1 flag indicating whether spatial predictions are to be made. - `newdata`: A new data frame with the same column structure as the model fitting data set. - `mchoice`: Logical scalar value: whether model choice statistics should be calculated. - `plotit`: Logical scalar value: whether to plot the predictions against the observed values. - `rseed`: Random number seed that controls the starting point for the random number stream. A set value is required to help reproduce the results. - `verbose`: Logical scalar value: whether to print various estimates and statistics. - `knots.coords`: Only relevant for GPP models fitted by either spTimer or spTDyn. Optional two column matrix of UTM-X and UTM-Y coordinates of the knots in kilometers. It is preferable to specify the g_size parameter instead. - `g_size`: Only relevant for GPP models fitted by either spTimer or spTDyn. The grid size c(m, n) for the knots for the GPP model. A square grid is assumed if this is passed on as a scalar. This does not need to be given if knots.coords is given instead. ## Returns A list containing: * params - A table of parameter estimates * fit - The fitted model object. * datatostan - A list containing all the information sent to the rstan package. * prior.phi.param - This contains the values of the hyperparameters of the prior distribution for the spatial decay parameter $phi$. * prior.phi - This contains the name of of the prior distribution for the spatial decay parameter $phi$. * validationplots - Present only if validation has been performed. Contains three validation plots with or without segment and an ordinary plot. See `obs_v_pred_plot` for more. * fitteds - A vector of fitted values. * residuals - A vector of residual values. * package - The name of the package used for model fitting. This is always stan for this function. * model - The name of the fitted model. * call - The command used to call the model fitting function. * formula - The input formula for the regression part of the model. * scale.transform - The transformation adopted by the input argument with the same name. * sn - The number of data locations used in fitting. * tn - The number of time points used in fitting for each location. * computation.time - Computation time required to run the model fitting. ## Examples ```r deep <- argo_floats_atlantic_2003[argo_floats_atlantic_2003$depth==3, ] deep$x2inter <- deep$xinter*deep$xinter deep$month <- factor(deep$month) deep$lat2 <- (deep$lat)^2 deep$sin1 <- round(sin(deep$time*2*pi/365), 4) deep$cos1 <- round(cos(deep$time*2*pi/365), 4) deep$sin2 <- round(sin(deep$time*4*pi/365), 4) deep$cos2 <- round(cos(deep$time*4*pi/365), 4) deep[, c( "xlat2", "xsin1", "xcos1", "xsin2", "xcos2")] <- scale(deep[,c("lat2", "sin1", "cos1", "sin2", "cos2")]) f2 <- temp ~ xlon + xlat + xlat2+ xinter + x2inter M2 <- Bmoving_sptime(formula=f2, data = deep, coordtype="lonlat", coords = 1:2, N=11, burn.in=6, validrows =NULL, mchoice = FALSE) summary(M2) plot(M2) names(M2) # Testing for smaller data sets with different data pattern d2 <- deep[1:25, ] d2$time <- 1:25 # Now there is no missing times M1 <- Bmoving_sptime(formula=f2, data = d2, coordtype="lonlat", coords = 1:2, N=11, burn.in=6, mchoice = FALSE) summary(M1) d2[26, ] <- d2[25, ] # With multiple observation at the same location and time M1 <- Bmoving_sptime(formula=f2, data = d2, coordtype="lonlat", coords = 1:2, N=11, burn.in=6, mchoice = FALSE) summary(M1) d2[27, ] <- d2[24, ] d2[27, 3] <- 25 # With previous location re-sampled M1 <- Bmoving_sptime(formula=f2, data = d2, coordtype="lonlat", coords = 1:2, N=11, burn.in=6, mchoice = FALSE) summary(M1) ``` ## See Also `Bsptime` for spatio-temporal model fitting.

Bmoving_sptime function