CCM: Convergent cross mapping using simplex projection

In rEDM: Empirical Dynamic Modeling ('EDM')

Convergent cross mapping using simplex projection

Description

The state-space of a multivariate dynamical system (not a purely stochastic one) encodes coherent phase-space variable trajectories. If enough information is available, one can infer the presence or absence of cross-variable interactions associated with causal links between variables. CCM measures the extent to which states of variable Y can reliably estimate states of variable X. This can happen if X is causally influencing Y.

If cross-variable state predictability converges as more state-space information is provided, this indicates a causal link. CCM performs this cross-variable mapping using Simplex, with convergence assessed across a range of observational library sizes as described in Sugihara et al. 2012.

Usage

CCM(pathIn = "./", dataFile = "", dataFrame = NULL,
  E = 0, Tp = 0, knn = 0, tau = -1,
  exclusionRadius = 0, columns = "", target = "", libSizes = "",
  sample = 0, random = TRUE, seed = 0, 
  embedded = FALSE, includeData = FALSE, parameterList = FALSE,
  verbose = FALSE, showPlot = FALSE, noTime = FALSE)

Arguments

pathIn	path to dataFile.
dataFile	.csv format data file name. The first column must be a time index or time values unless noTime is TRUE. The first row must be column names.
dataFrame	input data.frame. The first column must be a time index or time values unless noTime is TRUE. The columns must be named.
E	embedding dimension.
Tp	prediction horizon (number of time column rows).
knn	number of nearest neighbors. If knn=0, knn is set to E+1.
tau	lag of time delay embedding specified as number of time column rows.
exclusionRadius	excludes vectors from the search space of nearest neighbors if their relative time index is within exclusionRadius.
columns	string of whitespace separated column name(s) in the input data used to create the library.
target	column name in the input data used for prediction.
libSizes	string of 3 whitespace separated integer values specifying the intial library size, the final library size, and the library size increment. Can also be a list of strictly increasing library sizes.
sample	integer specifying the number of random samples to draw at each library size evaluation.
random	logical to specify random (TRUE) or sequential library sampling. Note random = FALSE is not convergent cross mapping.
seed	integer specifying the random sampler seed. If seed=0 then a random seed is generated.
embedded	logical specifying if the input data are embedded.
includeData	logical to include statistics and predictions for every prediction in the ensemble.
parameterList	logical to add list of invoked parameters.
verbose	logical to produce additional console reporting.
showPlot	logical to plot results.
noTime	logical to allow input data with no time column.

Details

CCM computes the X:Y and Y:X cross-mappings in parallel using threads.

Value

A data.frame with 3 columns. The first column is LibSize specifying the subsampled library size. Columns 2 and 3 report Pearson correlation coefficients for the prediction of X from Y, and Y from X.

if includeData = TRUE a named list with the following data.frames data.frame Combo_rho columns:

LibMeans	CCM mean correlations for each library size
CCM1_PredictStat	Forward cross map prediction statistics
CCM1_Predictions	Forward cross map prediction values
CCM2_PredictStat	Reverse cross map prediction statistics
CCM2_Predictions	Reverse cross map prediction values

If includeData = TRUE and parameterList = TRUE a named list "parameters" is added.

References

Sugihara G., May R., Ye H., Hsieh C., Deyle E., Fogarty M., Munch S., 2012. Detecting Causality in Complex Ecosystems. Science 338:496-500.

Examples

data(sardine_anchovy_sst)
df = CCM( dataFrame = sardine_anchovy_sst, E = 3, Tp = 0, columns = "anchovy",
target = "np_sst", libSizes = "10 70 10", sample = 100 )

rEDM documentation built on Nov. 10, 2023, 5:08 p.m.