Chapter 14 Resources for the User

14.1 Introduction

Section 14.2 lists the R packages that we have used in the different chapters. Section 14.3 shows a few examples of custom functions we have developed to facilitate some repetitive calculations; details are available in the GitHub link associated with the book. A user must source these files before running the code in each chapter. Section 14.4 presents often used R-INLA items, pulled into one place for the user.

14.2 Packages used in the book

package	version	source
astsa	1.13	CRAN (R 4.1.0)
dlm	1.1-5	CRAN (R 4.1.0)
gridExtra	2.3	CRAN (R 4.1.0)
gtools	3.8.2	CRAN (R 4.1.0)
INLA	21.02.23	local
kableExtra	1.3.4	CRAN (R 4.1.0)
lubridate	1.7.10	CRAN (R 4.1.0)
mapview	2.9.0	CRAN (R 4.1.0)
marima	2.2	CRAN (R 4.1.0)
Matrix	1.5-1	CRAN (R 4.1.2)
matrixcalc	1.0-5	CRAN (R 4.1.0)
mvtnorm	1.1-1	CRAN (R 4.1.0)
quantmod	0.4.20	CRAN (R 4.1.2)
raster	3.4-10	CRAN (R 4.1.0)
readxl	1.3.1	CRAN (R 4.1.0)
sf	0.9-8	CRAN (R 4.1.0)
spdep	1.1-8	CRAN (R 4.1.0)
tables	0.9.6	CRAN (R 4.1.0)
tidyverse	1.3.1	CRAN (R 4.1.0)
tmap	3.3-1	CRAN (R 4.1.0)
vars	1.5-6	CRAN (R 4.1.0)

14.3 Custom functions used in the book

We show different custom functions that we have developed for the user. They are grouped by functionality. The user must source the file containing these functions before running the code, as we show in the beginning of each chapter in the book. All codes and datasets used in the book can be accessed from https://github.com/ramanbala/dynamic-time-series-models-R-INLA.

Basic plotting functions

multiline.plot <-
  function(plot.data,
           title = "",
           xlab = "",
           ylab = "",
           line.type = "solid",
           line.size = 1,
           line.color = "auto") {
    cpalette <-
      c("#000000",
        "#56B4E9",
        "#009E73",
        "#0072B2",
        "#D55E00",
        "#CC79A7") 
    cname <- c("black", "blue", "green", "blue", "red", "purple")
    mp <- plot.data %>%
      pivot_longer(-time, names_to = "key", values_to = "dat")
    u <- unique(mp$key)
    mp$key <- factor(mp$key, levels = u)
    levels(mp$key) <- u
    mp.auto.color <- mp %>%
      ggplot(aes(x = time, y = dat, color = key)) +
      geom_line(size = line.size, linetype = line.type) +
      labs(x = xlab, y = ylab, colour = "") +
      ggtitle(title)
    mp.custom.color <- mp %>%
      ggplot(aes(x = time, y = dat, color = key)) +
      geom_line(size = line.size, linetype = line.type) +
      scale_color_manual(values = cpalette[match(line.color, cname)]) +
      labs(x = xlab, y = ylab, colour = "") +
      ggtitle(title)
  ifelse(line.color == "auto", return(mp.auto.color),
         return(mp.custom.color))
  }

Functions for forecast evaluation

mae <- function(yhold,
                yfore,
                text = NA,
                round.digit = 3) {
  efore <- yhold - yfore 
  mae <-  mean(abs(efore))
  if (is.na(text)) {
    return(paste("MAE is", round(mae, round.digit), sep = " "))
  } else {
    return(paste(text, round(mae, round.digit), sep = " "))
  }
}

mape <- function(yhold,
                 yfore,
                 text = NA,
                 round.digit = 3) {
  efore <- yhold - yfore 
  mape <-  mean(abs(efore / yhold))
  if (is.na(text)) {
    return(paste("MAPE is", round(mape * 100, round.digit), sep = " "))
  } else {
    return(paste(text, round(mape * 100, round.digit), sep = " "))
  }
}

Function for model comparison

# Model Selection Criteria - DIC, WAIC, PSBF and PIT
model.selection.criteria <- function(inla.result, plot.PIT = FALSE,
                                     n.train) {
  dic <- inla.result$dic$dic
  waic <- inla.result$waic$waic
  cpo <- inla.result$cpo$cpo
  psbf <- sum(log(cpo[1:n.train]))
  PIT <- inla.result$cpo$pit
  msc <- cbind(DIC=dic, WAIC = waic, PsBF = psbf)
  if(isTRUE(plot.PIT)){
    pit.hist <- hist(PIT, plot = F)
    return(list(msc = msc, hist=plot(pit.hist, main ="")))
  } else{
    return(msc = msc)
  }
  
}

Function for the filtering algorithm in DLM

filt.inla <-
  function(data.series,
           model = "rw1",
           ar.order = 0,
           trend = "no",
           alpha = "no") {
    pt <- proc.time()
    ### model formula
    eg <- expand.grid(
      model = c("rw1", "ar"),
      trend = c("yes", "no"),
      alpha = c("yes", "no")
    )
    eg <- apply(eg, 2, as.character)
    choice <- paste0(c(model, trend, alpha), collapse = ".")
    
    
    dat <- filt <- vector("list", length(data.series))
    for (k in 1:length(data.series)) {
      dat[[k]] <- data.series[1:k]
    }
    
    get.filter <- function(df, ar.order) {
      id <- trnd <- 1:length(df)
      inla.dat <- cbind.data.frame(data.series = df, trnd, id)
      ar.order <- as.numeric(ar.order)
      formula <- switch(
        choice,
        "rw1.no.no" = as.formula(
          paste0("data.series~-1+", "f(id, model='rw1', constr=FALSE)")
        ),
        "rw1.yes.no" = as.formula(
          paste0(
            "data.series~-1+trnd+",
            "f(id, model='rw1', constr=FALSE)"
          )
        ),
        "rw1.no.yes" = as.formula(
          paste0("data.series~ 1+", "f(id, model='rw1', constr=FALSE)")
        ),
        "rw1.yes.yes" = as.formula(
          paste0("data.series~ 1+trnd+", "f(id, model='rw1', constr=FALSE)")
        ),
        "ar.no.no" = as.formula(
          paste0("data.series~ -1+", "f(id, model='ar', order = ar.order)")
        ),
        "ar.yes.no" = as.formula(
          paste0(
            "data.series~ -1+trnd+",
            "f(id, model='ar', order = ar.order)"
          )
        ),
        "ar.no.yes" = as.formula(
          paste0("data.series~ 1+", "f(id, model='ar', order = ar.order)")
        ),
        "ar.yes.yes" = as.formula(
          paste0(
            "data.series~ 1+trnd+",
            "f(id, model='ar', order = ar.order)"
          )
        ),
      )
      model.inla <- inla(
        formula,
        family = "gaussian",
        data = inla.dat,
        control.predictor = list(compute = TRUE),
        control.compute = list(
          dic = T,
          config = TRUE,
          cpo = TRUE
        ),
        verbose = T
      )
      filt <- tail(model.inla$summary.random$id, 1)
      return(filt = filt)
    }
    #### model execution
    require(doParallel)
    require(foreach)
    cores <-  detectCores()
    if (cores > 2) {
      registerDoParallel(cores = detectCores() - 1)
    }
    
    if (ar.order > 1) {
      filt.all <-
        foreach (
          d = (2 + ar.order):length(data.series),
          .packages = c('tidyverse', 'INLA'),
          .verbose = T
        ) %dopar% {
          get.filter(dat[[d]], ar.order = ar.order)
        }
    } else{
      filt.all <-
        foreach (
          d = 2:length(data.series),
          .packages = c('tidyverse', 'INLA'),
          .verbose = T
        ) %dopar% {
          get.filter(dat[[d]], ar.order = ar.order)
        }
    }
    filt.all.bind <- bind_rows(filt.all)
    # filt.est <- c(NA, filt.all$mean)
    inla.time <- proc.time() - pt
    return(list(filt.all.bind = filt.all.bind, time.taken = inla.time))
  }

14.3.1 `rgeneric()` function for DLM-VAR model

inla.rgeneric.VAR_1 <-
  function(cmd = c("graph",
                   "Q",
                   "mu",
                   "initial",
                   "log.norm.const",
                   "log.prior",
                   "quit"),
           theta = NULL)
  {
    interpret.theta <- function() {
      n.phi <- k * k * p
      n.prec <- k
      n.tot <- n.phi + n.prec
      phi.VAR <-
        sapply(theta[as.integer(1:n.phi)], function(x) {
          x
        })
      # W matrix  precisions
      wprec <-
        sapply(theta[as.integer((n.phi + 1):(n.phi + n.prec))],
               function(x) {
                 exp(x)
               })
      param <- c(phi.VAR, wprec)
      W <- diag(1, n.prec)
      st.dev <- 1 / sqrt(wprec)
      st.dev.mat <-
        matrix(st.dev, ncol = 1) %*% matrix(st.dev, nrow = 1)
      W <- W * st.dev.mat
      PREC <- solve(W)
      return(list(
        param = param,
        VACOV = W,
        PREC = PREC,
        phi.vec = c(phi.VAR)
        ,
        n.phi = n.phi,
        n.prec = n.prec
      ))
    }
    #Precision matrix
    Q <- function() {
      param <- interpret.theta()
      phi.mat <- matrix(param$phi.vec, nrow = k)
      sigma.w.inv <- param$PREC
      A <- t(phi.mat) %*% sigma.w.inv %*% phi.mat
      B <- -t(phi.mat) %*% sigma.w.inv
      C <- sigma.w.inv
      # Construct mid-block:
      zero.mat <- matrix(0, nrow = 2, ncol = 2 * n)
      # Define the matrix block:
      mat <- cbind(t(B), A + C, B)
      # Initializing column id and matrix list:
      col.id <- list()
      mat.list <- list()
      col.id[[1]] <- 1:(3 * k)
      mat.list[[1]] <- zero.mat
      mat.list[[1]][, col.id[[1]]] <- mat
      for (id in 2:(n - 2)) {
        start.id <- col.id[[id - 1]][1] + k
        end.d <-  start.id + (3 * k - 1)
        col.id[[id]] <- start.id:end.d
        mat.list[[id]] <- zero.mat
        mat.list[[id]][, col.id[[id]]] <- mat
      }
      mid.block <- do.call(rbind, mat.list)
      tau.val <- 0.1
      diffuse.prec <- tau.val * diag(1, k)
      # Construct first and last row blocks and then join with mid block:
      first.row.block <-
        cbind(A + diffuse.prec, B, matrix(0, nrow = k, ncol = (k * n - k ^ 2)))
      last.row.block <-
        cbind(matrix(0, nrow = k, ncol = k * n - k ^ 2), t(B), C)
      toep.block.mat <-
        rbind(first.row.block, mid.block, last.row.block)
      # Changing to a sparse Matrix:
      prec.mat <- Matrix(toep.block.mat, sparse = TRUE)
      return(prec.mat)
    }
    # Graph function: Essentially Q matrix
    graph = function() {
      return (inla.as.sparse(Q()))
    }
    #Mean of model
    mu <- function() {
      return(numeric(0))
    }
    # Log normal constant:
    log.norm.const <- function() {
      Q <- Q()
      log.det.val <-
        Matrix::determinant(Q, logarithm = TRUE)$modulus
      val <- (-k * n / 2) * log(2 * pi) + 0.5 * log.det.val
      return (val)
    }
    log.prior <- function() {
      param <- interpret.theta()
      pars <- param$param
      k <- k
      total.par <- param$n.phi + param$n.prec
      # Normal prior for phi's:
      theta.phi <- theta[1:param$n.phi]
      phi.prior <-
        sum(sapply(theta.phi, function(x)
          dnorm(
            x,
            mean = 0,
            sd = 1,
            log = TRUE
          )))
      theta.prec <-
        theta[(param$n.phi + 1):(param$n.phi + param$n.prec)]
      prec.prior <-
        sum(sapply(theta.prec, function(x)
          dgamma(
            x,
            shape = 1,
            scale = 1,
            log = TRUE
          )))
      prec.jacob <- sum(theta.prec) # This is for precision terms
      prior.val <- phi.prior + prec.prior + prec.jacob
      return (prior.val)
    }
    initial = function() {
      phi.init <- c(0.1, 0.1, 0.1, 0.1)
      prec.init <- rep(1, k)
      init <- c(phi.init, prec.init)
      return (init)
    }
    if (as.integer(R.version$major) > 3) {
      if (!length(theta))
        theta <- initial()
    } else {
      if (is.null(theta)) {
        theta <- initial()
      }
    }
    val <- do.call(match.arg(cmd), args = list())
    return (val)
  }

14.4 Often used `R-INLA` items

Control options

Control options in the inla() function allow us to specify choices about the estimation process and output reporting. In Table 14.1, we list (in alphabetical order) a set of control options that are most relevant for dynamic time series modeling, along with their descriptions. Each control option has a manual page that can be accessed in the usual way, e.g., ?control.compute, with detailed information about the option. In addition, the list of options for each control argument and their default values can be obtained with functions inla.set.control.default(), where CONTROL refers to the control argument. For example, for the argument control.compute, the list of options and default values can be obtained with inla.set.control.compute.default(). More details on these, as well as other inla() control options, can be seen on the R-INLA website.

TABLE 14.1: Common control options – a quick lookup.
Options	Descriptions	Used in Chapter
control.compute	Specify what to actually compute during model fitting	Ch. 5-7
control.family	Specify model likelihood	Ch. 3-12
control.fixed	Options on fixed effects in a model	Ch. 3-4
control.group	Defines the order of the model, as in AR(p)	Ch. 3, 8
control.inla	Options on how the method is used in model fitting	Ch. 3, 12
control.lincomb	Options on how to compute linear combinations	Ch. 12
control.link		Ch. 12
control.predictor	Options on computing the linear predictor	Ch. 3-12

Options for computing marginals

Often used options for computing various marginal distributions are shown in Table 14.2. We have used some of these options in various sections in the book.

TABLE 14.2: Functions on marginals
Function	Description
inla.dmarginal	Compute the density function
inla.pmarginal	Compute the cumulative probability function
inla.qmarginal	Compute a quantile
inla.rmarginal	Draw a random sample
inla.hpdmarginal	Compute the highest posterior density (HPD) credible interval
inla.smarginal	Spline smoothing of the posterior marginal
inla.emarginal	Compute the expected value of a function
inla.mmarginal	Compute the posterior mode
inla.tmarginal	Transform a marginal using a function
inla.zmarginal	Compute summary statistics

Random effect specifications

R-INLA allows several specifications for handling random effects under different situations. Table 14.3 shows a collection of available effects from which a user may choose a suitable specification.

TABLE 14.3: Random Effects in R-INLA.
Name	Description
iid	Independent and identically distributed Gaussian random effect
z	Classical specification of random effects
generic0	Generic specification (type 0)
generic1	Generic specification (type 1)
generic2	Generic specification (type 2)
generic3	Generic specification (type 3)
rw1	Random walk of order 1
rw2	Random walk of order 2
crw2	Continuous random walk of order 2
seasonal	Seasonal variation with a given periodicity
ar1	Autoregressive model of order 1
ar	Autoregressive model of arbitrary order
iid1d	Correlated random effects of dimension 1
iid2d	Correlated random effects of dimension
iid3d	Correlated random effects of dimension 3
iid4d	Correlated random effects of dimension 4
iid5d	Correlated random effects of dimension 5

Prior specifications

Table 14.4 shows a list of priors available in R-INLA. This table is similar to Table 5.2 in Gómez-Rubio (2020). These specifications enable a user to set priors for latent effects or hyperparameters. More details are available on the R-INLA website.

TABLE 14.4: Summary of priors implemented in R-INLA.
Prior	Description	Parameters
normal	Gaussian prior	mean, precision
gaussian	Gaussian prior	mean, precision
loggamma	log-Gamma prior	shape, rate
logtnormal	Truncated (positive) Gaussian prior	mean, precision
logtgaussian	Truncated (positive) Gaussian prior	mean, precision
flat	Flat (improper) prior on \(\theta\)
logflat	Flat (improper prior) on \(\exp(\theta)\)
logiflat	Flat (improper prior) on \(\exp(-\theta)\)
mvnorm	Multivarite Normal prior
dirichlet	Dirichlet prior	\(\alpha\)
betacorrelation	Beta prior for correlation	\(a,~b\)
logitbeta	Beta prior, logit-scale	\(a,~ b\)
jeffreystdf	Jeffreys prior
table	User defined prior
expression	User defined prior

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https://mc-stan.org/docs/2_29/reference-manual-2_29.pdf ↩︎
private communication with Hvard Rue (https://www.r-inla.org/contact-us)↩︎
https://GitHub.com/beltoforion/muparser ↩︎
https://groups.google.com/g/r-inla-discussion-group/c/0dlvlVyiIRQ ↩︎
https://archive.ics.uci.edu/ml/datasets/Metro+Interstate+Traffic+Volume ↩︎
https://rdrr.io/GitHub/inbo/INLA/f/vignettes/multinomial.Rmd ↩︎
https://www.ctcrash.uconn.edu/↩︎
https://www.kaggle.com/juliajemals/bike-sharing-washington-dc.↩︎
private communication with Hvard Rue (https://www.r-inla.org/contact-us)↩︎

References