widals.snow: Fit WIDALS
In widals: Weighting by Inverse Distance with Adaptive Least Squares

Description Usage Arguments Details Value See Also Examples

Locate the WIDALS hyperparameters

1 2	widals.snow(j, rm.ndx, Z, Hs, Ht, Hst.ls, locs, lags, b.lag, cv = 0, geodesic = FALSE, wrap.around = NULL, GP.mx, stnd.d = FALSE, ltco = -16)

`j`	Index used by `snowfall`. A scalar integer. Which row of `GP.mx` to use for the ALS hyperparameters, `GP`.
`rm.ndx`	A list of vectors of indices to remove for k-fold cross-validation.
`Z`	Data. A τ x n numeric matrix.
`Hs`	Spacial covariates. An n x p_s numeric matrix.
`Ht`	Temporal covariates. A τ x p_t numeric matrix.
`Hst.ls`	Space-time covariates. A list of length τ, each element containing a n x p_st numeric matrix.
`locs`	Locations of supporting sites. An n x 2 numeric matrix, first column is spacial x, second column is spacial y. If the `geodesic` is `TRUE`, make sure latitude is in the first column.
`lags`	Temporal lags for stochastic smoothing. An integer vector or scalar. E.g., if the data's time increment is daily, then `lags = c(-1,0,1)` would tell the enclosed function `crispify` smooth today's predictions using yesterdays, today's, and tomorrow's observed residuals.
`b.lag`	ALS lag. A scalar integer, typically -1 (a-prior), or 0 (a-posteriori).
`cv`	Cross-validation switch. Currently takes on a value of `-2` or `2`. See Details below.
`geodesic`	Use geodesic distance? Boolean. If true, distance (used internally) is in units kilometers.
`wrap.around`	**Unused.
`GP.mx`	Hyperparameters. A k.glob x 2 non-negative matrix. See `MSS.snow`.
`stnd.d`	Spacial compression. Boolean.
`ltco`	Weight threshold. A scalar number. A value of, e.g., -10, will instruct `crispify` to ignore weights less than 10^(-10) when smoothing.

When the cv is set to 2, then this function uses spacial k-fold validation, according to the site indices present in rm.ndx. When cv is set to -2, self-referencing sites are given zero-weight, i.e., a site's value is not allowed to contribute to its predicted value.

A τ x n matrix. The WIDALS predictions at locs.

crispify, H.als.b, widals.predict.

	
set.seed(99999)

library(SSsimple)

tau <- 100
n.all <- 35

Hs.all <- matrix(rnorm(n.all), nrow=n.all)
Ht <- matrix(rnorm(tau*2), nrow=tau)
Hst.ls.all <- list()
for(i in 1:tau) { Hst.ls.all[[i]] <- matrix(rnorm(n.all*2), nrow=n.all) }

Hst.combined <- list()
for(i in 1:tau) { 
    Hst.combined[[i]] <- cbind( Hs.all, matrix(Ht[i, ], nrow=n.all, ncol=ncol(Ht), 
    byrow=TRUE), Hst.ls.all[[i]] ) 
}

locs.all <- cbind(runif(n.all, -1, 1), runif(n.all, -1, 1))
D.mx.all <- distance(locs.all, locs.all, FALSE)
R.all <- exp(-2*D.mx.all) + diag(0.01, n.all)

######## use SSsimple to simulate
sssim.obj <- SS.sim.tv( 0.999, Hst.combined, 0.01, R.all, tau )


n <- n.all
locs <- locs.all

Z.all <- sssim.obj$Z
Z <- Z.all


Hst.ls <- Hst.ls.all
Hs <- Hs.all

test.rng <- 20:tau

################  WIDALS, true cross-validation

rm.ndx <- create.rm.ndx.ls(n, 10)

cv <- 2
lags <- c(0)
b.lag <- 0

GP <- c(1/8, 1/12, 5, 0, 1)
GP.mx <- matrix(GP, ncol=length(GP))
Zwid <- widals.snow(j=1, rm.ndx, Z, Hs, Ht, Hst.ls, locs, lags, b.lag, cv = cv, 
geodesic = FALSE, wrap.around = NULL, GP.mx, stnd.d = FALSE, ltco = -16) 

errs.sq <- (Z - Zwid)^2
sqrt( mean(errs.sq[test.rng, ]) )


################  WIDALS, pseudo cross-validation

rm.ndx <- I(1:n)

cv <- -2
lags <- c(0)
b.lag <- -1

GP <- c(1/8, 1/12, 5, 0, 1)
GP.mx <- matrix(GP, ncol=length(GP))
Zwid <- widals.snow(j=1, rm.ndx, Z, Hs, Ht, Hst.ls, locs, lags, b.lag, cv = cv, 
geodesic = FALSE, wrap.around = NULL, GP.mx, stnd.d = FALSE, ltco = -16) 

errs.sq <- (Z - Zwid)^2
sqrt( mean(errs.sq[test.rng, ]) )