sensRange: Sensitivity Ranges of a Timeseries or 1-D Variables

Description

Given a model consisting of differential equations, estimates the global effect of certain (sensitivity) parameters on a time series or on 1-D spatial series of selected sensitivity variables.

This is done by drawing parameter values according to some predefined distribution, running the model with each of these parameter combinations, and calculating the values of the selected output variables at each output interval.

This function thus produces 'envelopes' around the sensitivity variables.

Usage

sensRange(func, parms = NULL, sensvar = NULL, dist = "unif",
          parInput = NULL, parRange = NULL, parMean = NULL, 
          parCovar = NULL, map = 1, num = 100,  ...)
  
# S3 method for sensRange
summary(object, ...)
# S3 method for summary.sensRange
plot(x, xyswap = FALSE,
              which = NULL, legpos = "topleft",
              col = c(grey(0.8), grey(0.7)),
              quant = FALSE, ask = NULL, obs = NULL, 
              obspar = list(), ...)
# S3 method for sensRange
plot(x, xyswap = FALSE,
              which = NULL, ask = NULL, ...)

Value

a data.frame of type sensRange containing the parameter set and the corresponding values of the sensitivity output variables.

The list returned by sensRange has a method for the generic functions summary,plot and

plot.summary -- see note.

Arguments

func: an R-function that has as first argument parms and that returns a matrix or data.frame with the values of the output variables (columns) at certain output intervals (rows), and -- optionally -- a mapping variable (by default the first column).
parms: parameters passed to func; should be either a vector, or a list with named elements. If NULL, then the first element of parInput is taken.
sensvar: the output variables for which the sensitivity needs to be estimated. Either NULL, the default, which selects all variables, or a vector with variable names (which should be present in the matrix returned by func), or a vector with indices to variables as present in the output matrix (note that the column of this matrix with the mapping variable should not be selected).
dist: the distribution according to which the parameters should be generated, one of "unif" (uniformly random samples), "norm", (normally distributed random samples), "latin" (latin hypercube distribution), "grid" (parameters arranged on a grid). The input parameters for the distribution are specified by parRange (min,max), except for the normally distributed parameters, in which case the distribution is specified by the parameter means parMean and the variance-covariance matrix, parCovar. Note that, if the distribution is "norm" and parRange is given, then a truncated distribution will be generated. (This is useful to prevent for instance that certain parameters become negative). Ignored if parInput is specified.
parRange: the range (min, max) of the sensitivity parameters, a matrix or (preferred) a data.frame with one row for each parameter, and two columns with the minimum (1st) and maximum (2nd) value. The rownames of parRange should be parameter names that are known in argument parms. Ignored if parInput is specified.
parInput: a matrix with dimension (*, npar) with the values of the sensitivity parameters.
parMean: only when dist is "norm": the mean value of each parameter. Ignored if parInput is specified.
parCovar: only when dist is "norm": the parameter's variance-covariance matrix.
num: the number of times the model has to be run. Set large enough. If parInput is specified, then num parameters are selected randomly (from the rows of parInput.
map: the column number with the (independent) mapping variable in the output matrix returned by func. For dynamic models solved by integration, this will be the (first) column with time. For 1-D spatial output, this column will be some distance variable. Set to NULL if there is no mapping variable. Mapping variables should not be selected for estimating sensitivity ranges; they are used for plotting.
object: an object of class sensRange.
x: an object of class sensRange.
legpos: position of the legend; set to NULL to avoid plotting a legend.
xyswap: if TRUE, then x-and y-values are swapped and the y-axis is from top to bottom. Useful for drawing vertical profiles.
which: the name or the index to the variables that should be plotted. Default = all variables.
col: the two colors of the polygons that should be plotted.
quant: if TRUE, then the median surrounded by the quantiles q25-q75 and q95-q95 are plotted, else the min-max and mean +- sd are plotted.
ask: logical; if TRUE, the user is asked before each plot, if NULL the user is only asked if more than one page of plots is necessary and the current graphics device is set interactive, see par(ask=...) and dev.interactive.
obs: a data.frame or matrix with "observed data" that will be added as points to the plots. obs can also be a list with multiple data.frames and/or matrices containing observed data. The first column of obs should contain the time or space-variable. If obs is not NULL and which is NULL, then the variables, common to both obs and x will be plotted.
obspar: additional graphics arguments passed to points, for plotting the observed data. If obs is a list containing multiple observed data sets, then the graphics arguments can be a vector or a list (e.g. for xlim, ylim), specifying each data set separately.
...: additional arguments passed to func or to the methods.

Author

Karline Soetaert <karline.soetaert@nioz.nl>

Details

Models solved by integration (i.e. by using one of 'ode', 'ode.1D', 'ode.band', 'ode.2D'), have the output already in a form usable by sensRange.

References

Soetaert, K. and Petzoldt, T. 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME. Journal of Statistical Software 33(3) 1--28. tools:::Rd_expr_doi("10.18637/jss.v033.i03")

Examples

Run this code


## =======================================================================
## Bacterial growth model from Soetaert and Herman, 2009
## =======================================================================

pars <- list(gmax = 0.5,eff = 0.5,
              ks = 0.5, rB = 0.01, dB = 0.01)

solveBact <- function(pars) {
  derivs <- function(t,state,pars) {    # returns rate of change
    with (as.list(c(state,pars)), {
      dBact <- gmax*eff * Sub/(Sub + ks)*Bact - dB*Bact - rB*Bact
      dSub  <- -gmax    * Sub/(Sub + ks)*Bact + dB*Bact
      return(list(c(dBact,dSub)))
    })
  }

  state <- c(Bact = 0.1,Sub = 100)
  tout  <- seq(0, 50, by = 0.5)
  ## ode solves the model by integration ...
  return(as.data.frame(ode(y = state, times = tout, func = derivs,
    parms = pars)))
}

out <- solveBact(pars)

mf  <-par(mfrow = c(2,2))

plot(out$time, out$Bact, main = "Bacteria",
     xlab = "time, hour", ylab = "molC/m3", type = "l", lwd = 2)

## the sensitivity parameters
parRanges <- data.frame(min = c(0.4, 0.4, 0.0), max = c(0.6, 0.6, 0.02))
rownames(parRanges)<- c("gmax", "eff", "rB")
parRanges

tout <- 0:50
## sensitivity to rB; equally-spaced parameters ("grid")
SensR <- sensRange(func = solveBact, parms = pars, dist = "grid",
                   sensvar = "Bact", parRange = parRanges[3,], num = 50)

Sens  <-summary(SensR)
plot(Sens, legpos = "topleft", xlab = "time, hour", ylab = "molC/m3",
     main = "Sensitivity to rB", mfrow = NULL)

## sensitivity to all; latin hypercube
Sens2 <- summary(sensRange(func = solveBact, parms = pars, dist = "latin",
           sensvar = c("Bact", "Sub"), parRange = parRanges, num = 50))

## Plot all variables; plot mean +- sd, min max
plot(Sens2, xlab = "time, hour", ylab = "molC/m3",
     main = "Sensitivity to gmax,eff,rB", mfrow = NULL)

par(mfrow = mf)

## Select one variable for plotting; plot the quantiles
plot(Sens2, xlab = "time, hour", ylab = "molC/m3", which = "Bact", quant = TRUE)

## Add data
data <- cbind(time = c(0,10,20,30), Bact = c(0,1,10,45))
plot(Sens2, xlab = "time, hour", ylab = "molC/m3", quant = TRUE, 
  obs = data, obspar = list(col = "darkblue", pch = 16, cex = 2))

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