calc_riskRatio_gev {climextRemes}

Compute risk ratio and uncertainty based on generalized extreme value model fit to block maxima or minima

Description

Compute risk ratio and uncertainty by fitting generalized extreme value model, designed specifically for climate data, to exceedance-only data, using the point process approach. The risk ratio is the ratio of the probability of exceedance of a pre-specified value under the model fit to the first dataset to the probability under the model fit to the second dataset. Default standard errors are based on the usual MLE asymptotics using a delta-method-based approximation, but standard errors based on the nonparametric bootstrap and on a likelihood ratio procedure can also be computed.

Usage

calc_riskRatio_gev(
  returnValue,
  y1,
  y2,
  x1 = NULL,
  x2 = NULL,
  locationFun1 = NULL,
  locationFun2 = NULL,
  scaleFun1 = NULL,
  scaleFun2 = NULL,
  shapeFun1 = NULL,
  shapeFun2 = NULL,
  nReplicates1 = 1,
  nReplicates2 = 1,
  replicateIndex1 = NULL,
  replicateIndex2 = NULL,
  weights1 = NULL,
  weights2 = NULL,
  xNew1 = NULL,
  xNew2 = NULL,
  maxes = TRUE,
  scaling1 = 1,
  scaling2 = 1,
  ciLevel = 0.9,
  ciType,
  bootSE,
  bootControl = NULL,
  lrtControl = NULL,
  optimArgs = NULL,
  optimControl = NULL,
  initial1 = NULL,
  initial2 = NULL,
  logScale1 = NULL,
  logScale2 = NULL,
  getReturnCalcs = FALSE,
  getParams = FALSE,
  getFit = FALSE
)

Arguments

returnValue

numeric value giving the value for which the risk ratio should be calculated, where the resulting period will be the average number of blocks until the value is exceeded and the probability the probability of exceeding the value in any single block.

y1

a numeric vector of observed maxima or minima values for the first dataset. See Details for how the values of y1 should be ordered if there are multiple replicates and the values of x1 are identical for all replicates. For better optimization performance, it is recommended that y1 have magnitude around one (see Details), for which one can use scaling1.

y2

a numeric vector of observed maxima or minima values for the second dataset. Analogous to y1.

x1

a data frame, or object that can be converted to a data frame with columns corresponding to covariate/predictor/feature variables and each row containing the values of the variable for the corresponding observed maximum/minimum. The number of rows should either equal the length of y1 or (if there is more than one replicate) it can optionally equal the number of observations in a single replicate, in which case the values will be assumed to be the same for all replicates.

x2

analogous to x1 but for the second dataset

locationFun1

formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the location parameter using columns from x1 for the first dataset. x1 must be supplied if this is anything other than NULL or ~1.

locationFun2

formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the location parameter using columns from x2 for the second dataset. x2 must be supplied if this is anything other than NULL or ~1.

scaleFun1

formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the (potentially transformed) scale parameter using columns from x1 for the first dataset. x1 must be supplied if this is anything other than NULL or ~1. logScale1 controls whether this determines the log of the scale or the scale directly.

scaleFun2

formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the (potentially transformed) scale parameter using columns from x2 for the second dataset. x2 must be supplied if this is anything other than NULL or ~1. logScale2 controls whether this determines the log of the scale or the scale directly.

shapeFun1

formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the shape parameter using columns from x1 for the first dataset. x1 must be supplied if this is anything other than NULL or ~1.

shapeFun2

formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the shape parameter using columns from x2 for the first dataset. x2 must be supplied if this is anything other than NULL or ~1.

nReplicates1

numeric value indicating the number of replicates for the first dataset.

nReplicates2

numeric value indicating the number of replicates for the second dataset.

replicateIndex1

numeric vector providing the index of the replicate corresponding to each element of y1. Used (and therefore required) only when using bootstrapping with the resampling by replicates based on the by element of bootControl.

replicateIndex2

numeric vector providing the index of the replicate corresponding to each element of y2. Analogous to replicateIndex1.

weights1

a vector providing the weights for each observation in the first dataset. When there is only one replicate or the weights do not vary by replicate, a vector of length equal to the number of observations. When weights vary by replicate, this should be of equal length to y. Likelihood contribution of each observation is multiplied by the corresponding weight.

weights2

a vector providing the weights for each observation in the second dataset. Analogous to weights1.

xNew1

object of the same form as x1, providing covariate/predictor/feature values for which one desires log risk ratios.

xNew2

object of the same form as x2, providing covariate/predictor/feature values for which log risk ratios are desired. Must provide the same number of covariate sets as xNew1 as the risk ratio is based on contrasting return probabilities under xNew1 and xNew2.

maxes

logical indicating whether analysis is for block maxima (TRUE) or block minima (FALSE); in the latter case, the function works with the negative of the values, changing the sign of the resulting location parameters

scaling1

positive-valued scalar used to scale the data values of the first dataset for more robust optimization performance. When multiplied by the values, it should produce values with magnitude around 1.

scaling2

positive-valued scalar used to scale the data values of the second dataset for more robust optimization performance. When multiplied by the values, it should produce values with magnitude around 1.

ciLevel

statistical confidence level for confidence intervals; in repeated experimentation, this proportion of confidence intervals should contain the true risk ratio. Note that if only one endpoint of the resulting interval is used, for example the lower bound, then the effective confidence level increases by half of one minus ciLevel. For example, a two-sided 0.90 confidence interval corresponds to a one-sided 0.95 confidence interval.

ciType

character vector indicating which type of confidence intervals to compute. See Details.

bootSE

logical indicating whether to use the bootstrap to estimate the standard error of the risk ratio

bootControl

a list of control parameters for the bootstrapping. See Details.

lrtControl

list containing a single component, bounds, which sets the range inside which the algorithm searches for the endpoints of the likelihood ratio-based confidence interval. This avoids numerical issues with endpoints converging to zero and infinity. If an endpoint is not found within the interval, it is set to NA.

optimArgs

a list with named components matching exactly any arguments that the user wishes to pass to optim. See help(optim) for details. Of particular note, 'method' can be used to choose the optimization method used for maximizing the log-likelihood to fit the model and 'control=list(maxit=VALUE)' for a user-chosen VALUE can be used to increase the number of iterations if the optimization is converging slowly.

optimControl

a list with named components matching exactly any elements that the user wishes to pass as the control list to R's optim function. See help(optim) for details. Primarily provided for the Python interface because control can also be passed as part of optimArgs.

initial1

a list with components named 'location', 'scale', and 'shape' providing initial parameter values for the first dataset, intended for use in speeding up or enabling optimization when the default initial values are resulting in failure of the optimization; note that use of scaling1, logScale1 and .normalizeX = TRUE cause numerical changes in some of the parameters. For example with logScale1 = TRUE, initial value(s) for 'scale' should be specified on the log scale.

initial2

a list with components named 'location', 'scale', and 'shape' providing initial parameter values for the second dataset, intended for use in speeding up or enabling optimization when the default initial values are resulting in failure of the optimization; note that use of scaling2, logScale2 and .normalizeX = TRUE cause numerical changes in some of the parameters. For example with logScale2 = TRUE, initial value(s) for 'scale' should be specified on the log scale.

logScale1

logical indicating whether optimization for the scale parameter should be done on the log scale for the first dataset. By default this is FALSE when the scale is not a function of covariates and TRUE when the scale is a function of covariates (to ensure the scale is positive regardless of the regression coefficients).

logScale2

logical indicating whether optimization for the scale parameter should be done on the log scale for the second dataset. By default this is FALSE when the scale is not a function of covariates and TRUE when the scale is a function of covariates (to ensure the scale is positive regardless of the regression coefficients).

getReturnCalcs

logical indicating whether to return the estimated return values/probabilities/periods from the fitted models.

getParams

logical indicating whether to return the fitted parameter values and their standard errors for the fitted models; WARNING: parameter values for models with covariates for the scale parameter must interpreted based on the value of logScale.

getFit

logical indicating whether to return the full fitted models (potentially useful for model evaluation and for understanding optimization problems); note that estimated parameters in the fit object for nonstationary models will not generally match the MLE provided when getParams is TRUE because covariates are normalized before fitting and the fit object is based on the normalized covariates. Similarly, parameters will not match if scaling is not 1.

Details

See fit_gev for more details on fitting the block maxima model for each dataset, including details on blocking and replication. Also see fit_gev for information on the bootControl argument.

Optimization failures:

It is not uncommon for maximization of the log-likelihood to fail for extreme value models. Please see the help information for fit_gev. Also note that if the probability in the denominator of the risk ratio is near one, one may achieve better numerical performance by swapping the two datasets and computing the risk ratio for the probability under dataset 2 relative to the probability under dataset 1.

ciType can include one or more of the following: 'delta', 'lrt', 'boot_norm', 'boot_perc', 'boot_basic', 'boot_stud', 'boot_bca'. 'delta' uses the delta method to compute an asymptotic interval based on the standard error of the log risk ratio. 'lrt' inverts a likelihood-ratio test. Bootstrap-based options are the normal-based interval using the bootstrap standard error ('boot_norm'), the percentile bootstrap ('boot_perc'), the basic bootstrap ('boot_basic'), the bootstrap-t ('boot_stud'), and the bootstrap BCA method ('boot_bca'). See Paciorek et al. for more details.

See fit_pot for information on the bootControl argument.

Value

The primary outputs of this function are as follows: the log of the risk ratio and standard error of that log risk ratio (logRiskRatio and se_logRiskRatio) as well the risk ratio itself (riskRatio). The standard error is based on the usual MLE asymptotics using a delta-method-based approximation. If requested via ciType, confidence intervals will be returned, as discussed in Details.

Author(s)

Christopher J. Paciorek

References

Paciorek, C.J., D.A. Stone, and M.F. Wehner. 2018. Quantifying uncertainty in the attribution of human influence on severe weather. Weather and Climate Extremes 20:69-80. arXiv preprint <https://arxiv.org/abs/1706.03388>.

Jeon S., C.J. Paciorek, and M.F. Wehner. 2016. Quantile-based bias correction and uncertainty quantification of extreme event attribution statements. Weather and Climate Extremes 12: 24-32. <DOI:10.1016/j.wace.2016.02.001>. arXiv preprint: <http://arxiv.org/abs/1602.04139>.

Examples

data(Fort, package = 'extRemes')
FortMax <- aggregate(Prec ~ year, data = Fort, max)
earlyYears <- 1900:1929
lateYears <- 1970:1999
earlyPeriod <- which(FortMax$year %in% earlyYears)
latePeriod <- which(FortMax$year %in% lateYears)
# contrast late period with early period, assuming a nonstationary fit
# within each time period and finding RR based on midpoint of each period
## Not run: 
out <- calc_riskRatio_gev(returnValue = 3,
                   y1 = FortMax$Prec[earlyPeriod], y2 = FortMax$Prec[latePeriod],
                   x1 = data.frame(years = earlyYears), x2 = data.frame(years = lateYears),
                   locationFun1 = ~years, locationFun2 = ~years,
                   xNew1 = data.frame(years = mean(earlyYears)),
                   xNew2 = data.frame(years = mean(lateYears)))

## End(Not run)