wcc

Description

Functions for Windowed Cross Correlation.

Details

Calculates Windowed Cross Correlation for estimating association between pairs of nonstationary time series. Provides support for surrogate analysis for nonparametric test of significance. Calculates aggregate statistics over a range of parameter values. Plots the results as wcc plots and heat maps.

Author(s)

Steven Boker, Minquan Xu, Sareena Chadha, Christopher Welker, Jingyun Wu, Pascal Deboeck

Maintainer: Steven Boker <smb3u@virginia.edu>

References

Boker, S. M., Rotondo, J. L., Xu, M., & King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological methods, 7(3), 338.

Moulder, R., Boker, S., Ramseyer, F., & Tschacher, W. (2018). Determining synchrony between behavioral time series: An application of surrogate data generation for establishing falsifiable null-hypotheses. Psychological Methods. 23:4 pp 757–773

See Also

See wccCalc for the core function that calculates a windowed cross correlation matrix.
See wccPeakPick for the core function that estimates time lag of maximum association from a windowed cross correlation matrix.
See wccAggregate to call wcc and wccPeakPick and then calculate aggregate statistics from a windowed cross correlation matrix.
See wccPlot to plot a section of a windowed cross correlation matrix and peak picking line from a file created by wccAggregate.
See wccSurrogateDyads to generate a distribution of the aggregate statistics conforming to the null hypothesis that the pairing of the dyad does not matter.
See wccFindDyadParam to explore a range of parameter values for wcc that are compared between surrogate and real dyads.
See wccHeatmap to visualize results of selected aggregated statistics for combinations of parameters calculated by wccFindDyadParam.

Examples

#Create a windowed cross correlation plot
tSeries1 <- sin(c(1:1000)/10) + rnorm(1000, mean=0, sd=.5)
tSeries2 <- sin(1+c(1:1000)/10) + rnorm(1000, mean=0, sd=.5)
wccPlot(inSeries1=tSeries1, inSeries2=tSeries2, startwindow=1, endwindow=500, 
    wMax=100, tMax=100, wInc=1, tInc=1, Lsize=8, pspan=.25, type="Max", 
    samplespersecond=10)

# Create two arrays of timeseries with dyadic dependence
array1 <- matrix(NA, nrow=10, ncol=500)
array2 <- matrix(NA, nrow=10, ncol=500)
for(i in 1:10) {
    array1[i,] <- sin(c(1:500)/runif(1, min=5, max=20)) + rnorm(500, mean=0, sd=.5)
    array2[i,] <- array1[i,] + rnorm(500, mean=0, sd=.5)
}
# Select parameters to explore
wMaxVec <- c(50,100)
tMaxVec <- c(25,50)
wccFDPout <- wccFindDyadParam(inArray1=array1, inArray2=array2, wMaxvector=wMaxVec,
    tMaxvector=tMaxVec, nSurrogates=30, samplespersecond=1, windcross=FALSE)
# Plot a heatmap
wccHeatmap(xparam=wccFDPout$wMax, yparam=wccFDPout$tMax, aggstat=wccFDPout$maxMean,
    xlabel="Window Max", ylabel="Max Lag")

wccAggregate

Description

This function runs wccCalc and peakpicking on a pair of time series and returns aggregate statistics.

Usage

wccAggregate(inSeries1=NA, inSeries2=NA, wMax=50, tMax=50, wInc=1, tInc=1, Lsize=8,
     pspan=.25, type="Max", samplespersecond=1, windcross=TRUE, embedD=9) 

Arguments

Details

wccAggregate is a wrapper for the wccCalc and wccPeakpick functions. The returns from these two function calls are then aggregated into 10 different statistics representing characteristics of wccCalc and wccPeakpick for the pair of input time series. wccAggregate also must be called with a filename in the ‘savefile’ argument prior to calling wccPlot so that the raw results can be plotted. The wccAggregate function returns a single row dataframe so that it can be called repeatedly by the wccSurrogateDyad function to create a distribution of surrogate Windowed Cross Correlation results. The arguments are also saved in this dataframe so that the wccFindDyadParam function can explore the space of arguments to find appropriate values from a hold-out set of timeseries to then be used to calculate surrogate distributions for the full data set.

Value

wccAggregate returns a data frame with one row and the following columns:

References

Boker, S. M., Rotondo, J. L., Xu, M., & King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological methods, 7(3), 338.

See Also

wccCalc, wccPeakPick.

Examples

#Calculate aggregated statistics for windowed cross correlation between two time series
tSeries1 <- sin(c(1:1000)/10) + rnorm(1000, mean=0, sd=.5)
tSeries2 <- sin(c(1:1000)/15) + rnorm(1000, mean=0, sd=.5)
wccAggregate(inSeries1=tSeries1, inSeries2=tSeries2, wMax=50, tMax=50, wInc=1, tInc=1,
     Lsize=8, pspan=.25, type="Max", samplespersecond=10, windcross=TRUE)

Windowed Cross Correlation function

Description

This function calculates a windowed cross correlation matrix from two time series

Usage

wccCalc(inSeries1, inSeries2, wMax=50, tMax=50, wInc=1, tInc=1, windcross=TRUE) 

Arguments

Details

wccCalc calculates cross correlations between windows, i.e., sampled sections of two time series. These windows are sampled at time lagged intervals from one another so that the association between the time series can be estimated even though the time lag of maximum association between the two time series may be itself time varying. For instance, when two individuals converse, their body motions may be associated such that the leader and follower take turns as speaker and listener. This same kind of nonstationary association has been observed between many physiological time series. At any particular elapsed time, the maximum correlation closest to a lag of zero (whether a positive or negative lag) is taken to be the lagged offset between the two time series. For series that have oscillatory structure (such as head nodding in conversation) the maximum correlation closest to a lag of zero can be interpreted as the phase lag between the series.

Value

Returns an N x P matrix of numeric values of cross correlations, where N is the number of windows calculated and P is 2*floor(tMax/tInc) + 1, the total lagged values of each window. Each row of the returned matrix represents one elapsed time at sample t. The number of columns is always odd and the center column, C = floor(tMax/tInc) + 1 is the cross correlation for zero lag for the windows from inSeries1 and inSeries2 whose last element occurs at elapsed sample t. Columns l less than the center column contain the cross correlation values for the windows where the window from inSeries1 occurs l*tInc samples earlier than the window from inSeries2 whose last value is at sample t. Similarly columns l greater than the center column contain cross corrlations for windows where the window from inSeries2 occurs l*tInc samples earlier than the window from inSeries1 whose last value is at sample t.

References

Boker, S. M., Rotondo, J. L., Xu, M., & King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological methods, 7(3), 338.

Examples

#Calculate windowed cross correlation between two time series
tSeries1 <- sin(c(1:1000)/10) + rnorm(1000, mean=0, sd=.5)
tSeries2 <- sin(c(1:1000)/15) + rnorm(1000, mean=0, sd=.5)
wccCalcOut <- wccCalc(inSeries1=tSeries1, inSeries2=tSeries2, wMax=50, tMax=50, wInc=1,
     tInc=1, windcross=FALSE)

wccFindDyadParam

Description

This function calculates the difference between surrogate and actual dyads for a range of possible arguments to wccCalc and wccPeakPick.

Usage

wccFindDyadParam(inArray1=NA, inArray2=NA, wMaxvector=c(50), tMaxvector=c(50),
    wIncvector=c(1), tIncvector=c(1), Lsizevector=c(8), pspanvector=c(.25), type="Max",
    nSurrogates=NA, samplespersecond=1, windcross=TRUE, embedD=9)

Arguments

Details

This function iterates over vectors of possible argument values given to wccCalc and wccPeakPick and for each combination of arguments returns the difference between the surrogate dyadic null hypothesis distribution and the true distribution of each of the statistics returned by wccAggregate. The intended use of this function is to explore the space of possible argument values using a small hold-out set of dyadic timeseries in order to inform the selection of parameters to use for the full dataset. It is recommended that between 10 and 20 dyadic timeseries be used as the hold-out set to input to this function. The two arguments ‘wMax’ and ‘tMax’ are the most commonly explored parameters since they tend to have the most impact on results.

Results from combinations of parameters can be visualized using the wccHeatmap function. For any particular hypothesis, one or more aggregate statistics may be most useful in assessing the association between a dyad's time series. Thus, one may wish to focus in on that statistic when choosing parameters. wccHeatmapwMaxtMax allows the visualization of the effect of selecting the ‘wMax’ and ‘tMax’ parameters on the statistic of interest.

Note that surrogate and real dyads will be calculated for all combinations of parameters in the argument vectors. Thus, if one wishes to explore the effects of 8 choices of ‘wMax’ and 8 choices of ‘tMax’, a total of 64 surrogate analyses will be run. If one uses a holdout set of 20 and asks for 100 surrogates, this will result in 7,680 calls to wccAggregate. Such an exploration of the parameter space can take hours to run. Add to that 2 choices of ‘wInc’ and 2 choices of ‘tInc’ and you may be talking about days of processing. Be careful when choosing how many combinations to explore at one time.

Value

Returns a dataframe with the columns from the wccAggregate function and the following extra columns. For each aggregated statistic a column giving the proportion of real dyads' statistics are greater than .95 or less than .05 of the values in the surrogate statistics distribution. For each aggregated statistic a column giving the two sided Kolmogorov-Smirnov Test probabilities comparing the surrogate and real dyad distributions. For each aggregated statistic a column giving the quantile difference scores for the difference between the surrogate distribution and the real distribution of dyadic timeseries. Each row in the dataframe presents the results from one combination of chosen parameters.

References

Boker, S. M., Rotondo, J. L., Xu, M., & King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological methods, 7(3), 338.

William J. Conover (1971). Practical Nonparametric Statistics. New York: John Wiley & Sons. Pages 295-301 (one-sample Kolmogorov test), 309-314 (two-sample Smirnov test).

See Also

wccHeatmap visualizes results selected aggregated statistics for combinations of parameters. See wccAggregate for definitions of the statistics that are compared between surrogate and real dyads. See ks.test for definition of the two tailed Kolmogorov-Smirnov Test.

Examples

# Create two arrays of timeseries with dyadic dependence
array1 <- matrix(NA, nrow=10, ncol=500)
array2 <- matrix(NA, nrow=10, ncol=500)
for(i in 1:10) {
    array1[i,] <- sin(c(1:500)/runif(1, min=5, max=20)) + rnorm(500, mean=0, sd=.5)
    array2[i,] <- array1[i,] + rnorm(500, mean=0, sd=.5)
}
# Select parameters to explore
wMaxVec <- c(50,100)
tMaxVec <- c(25,50)
wccFindDyadParam(inArray1=array1, inArray2=array2, wMaxvector=wMaxVec, tMaxvector=tMaxVec,
    nSurrogates=30, samplespersecond=1, windcross=TRUE)

wccGLLAEmbed

Description

This function creates a time delay embedded matrix from a time series.

Usage

wccGLLAEmbed(x, embed=4, tau=1, groupby=NA, label="x", idColumn=TRUE)

Arguments

Details

wccGLLAEmbed creates a time delay embedded matrix from a time series. A time delay embedded matrix has rows corresponding to the samples of elapsed time in the time series and columns that are lagged by tau samples from each other. For example, for a time series x of length N composed of a single group and with embed = 3 and tau=1, the time delay embedding matrix would have N-2 rows and 3 columns. Column 1 would contain x[1:(N-2)], column 2 would contain x[2:(N-1)], and column 3 would contain x[3:N]. Thus each row contains a time lagged vector representing not only the state of the system at a moment in time, but also a snapshot of the dynamics of the system at that moment. The number of columns in a N x D time delay embedding matrix is often referred to as the embedding dimension of the matrix, since each row can be thought of as a point in a D dimensional space.

When multiple groups' or individuals' time series are time delay embedded, one must prevent the data from group 1 to overlap on the same row with data from group 2 and so forth. Thus, if a group has N elements, the resulting submatrix for that group will have embed columns and N - ((embed - 1) * tau) rows. If any group has less than (tau + 1 + ((embed - 2) * tau)) elements then that group will not appear in the time delay embedding matrix since there is not sufficient data in the time series to compose 1 row.

Missing values are retained in the output time delay embedded matrix. This is useful for methods such as latent differential equations where full information maximum likelihood can account for the missingness, but will result in missing valued rows in the output of Generalized Local Linear Approximation as calculated using the wccGLLAWMatrix function.

Time delay embedding is a technique that represents a time series in a state space that contains both the instantaneous state of a system and its local dynamics. Takens (1981) showed that time delay embedding captures all of the dynamics in a system if the embedding dimension is sufficient. Choosing the appropriate embedding dimension for representing the dynamics of a system is something of an art (Sauer, Yorke, and Casdagli, 1991). For calculating time series deriviatives using Generalized Local Linear Approximation, the minimum embedding dimension is recommended to be two plus the order of the highest derivative to be calculated. Higher embedding dimensions than required will perform smoothing on the time series, which may be useful, but will also attenuate the values of the derivatives calculated.

Value

Returns a time delay embedding matrix. Optionally this includes a column of ID numbers representing the group to which each row belongs.

References

Boker, S. M., Rotondo, J. L., Xu, M., & King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological methods, 7(3), 338.

Boker, S. M., Deboeck, P. R., Edler, C., & Keel, P. K. (2010) Generalized Local Linear Approximation of Derivatives from Time Series. In Statistical Methods for Modeling Human Dynamics: An Interdisciplinary Dialogue, S.-M. Chow & E. Ferrar (Eds). Boca Raton, FL: Taylor & Francis, pp 179–212.

Sauer, T., Yorke, J., & Casdagli, M. (1991). Embedology. Journal of Statistical Physics, 65(3,4), 95-116.

Takens, F. (1981). Detecting strange attractors in turbulence. In D. Rand & L.-S. Young(Eds.), Dynamical systems and turbulence, warwick 1980: Proceedings of a symposium held at the University of Warwick (pp. 366-381). Berlin: Springer-Verlag.

See Also

wccGLLAWMatrix for the definition of the matrix required to estimate derivatives using Generalized Local Linear Approximation.

Examples

# Create a time delay embedding matrix from a single time series.
theSeries <- sin((1:20)/10)
length(theSeries)
embeddedMatrix <- wccGLLAEmbed(theSeries, embed=4, tau=1, label="x", idColumn=FALSE)
dim(embeddedMatrix)
# Calculate derivatives for the series
embeddedMatrix %*% wccGLLAWMatrix(embed=4, tau=1, deltaT=1, order=2)


theFrame <- data.frame(theSeries=c(sin((1:20)/10)), sin((1:20)/15),theGroups=c(rep(1,20),rep(2,20)))
dim(theFrame)
embeddedMatrix <- wccGLLAEmbed(theFrame$theSeries, embed=4, tau=1, label="x", 
     groupby=theFrame$theGroups, idColumn=TRUE)
dim(embeddedMatrix)
# Calculate derivatives for the series
embeddedMatrix[,2:5] %*% wccGLLAWMatrix(embed=4, tau=1, deltaT=1, order=2)

W Matrix

Description

This function returns a matrix, W, which when premultiplied by a time delay embedded matrix will calculate the time derivatives of the time series in the time delay embedded matrix.

Usage

wccGLLAWMatrix(embed=NA, tau=NA, deltaT=1, order=2)

Arguments

Details

The W matrix is defined by the Generalized Local Linear Approximation method for calculating derivatives of time series. First time delay embed the time series using ‘wccGLLAEmbed’ . Then call ‘wccGLLAWMatrix’ to return the appropriate W matrix for that embedding. Finally postmultiply the time delay embedding matrix by the W matrix, which creates an output matrix whose rows match the rows of the time delay embedded matrix and whose columns are the calculated derivatives of the time series.

Value

Returns the W matrix that can postmultiply a time delay embedded matrix to calculate derivatives.

References

Boker, S. M., Deboeck, P. R., Edler, C., & Keel, P. K. (2010) Generalized Local Linear Approximation of Derivatives from Time Series. In Statistical Methods for Modeling Human Dynamics: An Interdisciplinary Dialogue, S.-M. Chow & E. Ferrar (Eds). Boca Raton, FL: Taylor & Francis, pp 179–212.

See Also

wccGLLAEmbed for creating a time delay embedding matrix.

Examples

# Create a time delay embedding matrix from a single time series.
theSeries <- sin((1:20)/10)
length(theSeries)
embeddedMatrix <- wccGLLAEmbed(theSeries, embed=4, tau=1, label="x", idColumn=FALSE)
dim(embeddedMatrix)
# Calculate derivatives for the series
embeddedMatrix %*% wccGLLAWMatrix(embed=4, tau=1, deltaT=1, order=2)

wccHeatmap

Description

This function plots a heatmap of a chosen aggregate statistic from the results of wccFindDyadParam

Usage

wccHeatmap(xparam=NA, yparam=NA, aggstat=NA, xlabel=NA, ylabel=NA, pdffile=NA)

Arguments

Details

This function produces a heat map plot of selected aggregated statistics returned by ‘wccFindDyadParam’ for combinations of selected parameter values. First run ‘wccFindDyadParam’ using two or more parameter vectors for a grid search. Next select two colums of parameters and one aggregated statistic to plot and send it to wccHeatmap. If the optional parameter pdffile exists, then a publication quality pdf file will be saved. Otherwise the heatmap will be displayed on the default device.

Value

Returns nothing.

References

Boker, S. M., Rotondo, J. L., Xu, M., & King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological methods, 7(3), 338.

See Also

wccFindDyadParam for the definition of the dataframe columns used by ‘wccHeatmap’.

Examples

# Create two arrays of timeseries with dyadic dependence
array1 <- matrix(NA, nrow=10, ncol=500)
array2 <- matrix(NA, nrow=10, ncol=500)
for(i in 1:10) {
    array1[i,] <- sin(c(1:500)/runif(1, min=5, max=20)) + rnorm(500, mean=0, sd=.5)
    array2[i,] <- array1[i,] + rnorm(500, mean=0, sd=.5)
}
# Select parameters to explore
wMaxVec <- c(50,100)
tMaxVec <- c(25,50)
wccFDPout <- wccFindDyadParam(inArray1=array1, inArray2=array2, wMaxvector=wMaxVec,
    tMaxvector=tMaxVec, nSurrogates=30, samplespersecond=1, windcross=FALSE)
# Plot the heatmap
wccHeatmap(xparam=wccFDPout$wMax, yparam=wccFDPout$tMax, aggstat=wccFDPout$maxMean,
    xlabel="Window Max", ylabel="Max Lag")

wccPeakPick

Description

This function finds the maximum or minimum correlation peak nearest to zero lag for each row in a windowed crosscorrelation matrix.

Usage

wccPeakPick(tAllCor=NA, Lsize=8, pspan=.25, type="Max")

Arguments

Details

This function operates on the result of ‘wccCalc’, a windowed crosscorrelation matrix in order to find the peak correlation closest to a lag of zero. The lag and the value of the peak correlation are returned for each row of the windowed crosscorrelation matrix, i.e., for the elapsed time of each window calculated by ‘wccCalc’. The wccCalc windows are sampled at time lagged intervals from one another so that the association between the time series can be estimated even though the time lag of maximum association between the two time series may be itself time varying. For instance, when two individuals converse, their body motions may be associated such that the leader and follower take turns as the two individuals swap roles as speaker and listener.

This same kind of nonstationary association has been observed between many physiological time series. At any particular elapsed time, the maximum correlation closest to a lag of zero (whether a positive or negative lag) is taken to be the lagged offset between the two time series. For series that have oscillatory structure (such as head nodding in conversation) the maximum correlation closest to a lag of zero can be interpreted as the phase lag between the series. The variability in the lag is one measure of the degree of nonstationarity present in the association between two time series.

Value

Returns a list with two vectors: ‘maxIndex’ is the lag of the peak for each window and ‘maxValue’ is the calculated correlation at that peak. If ‘wccPeakPick’ is called with ‘type = Min’ then the returned vectors are named ‘minIndex’ and ‘minValue’

References

Boker, S. M., Rotondo, J. L., Xu, M., & King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological methods, 7(3), 338.

See Also

wccCalc for the definition of the windowed crosscorrelation matrix.

Examples

#Calculate windowed cross correlation between two time series
tSeries1 <- sin(c(1:1000)/10) + rnorm(1000, mean=0, sd=.5)
tSeries2 <- sin(c(1:1000)/15) + rnorm(1000, mean=0, sd=.5)
wccCalcOut <- wccCalc(inSeries1=tSeries1, inSeries2=tSeries2, wMax=50, tMax=50, wInc=1,
     tInc=1, windcross=FALSE)

#Calculate the peak picking vectors
wccPeakPick(wccCalcOut, Lsize=8, pspan=.25, type="Max")

wccPlot

Description

This function plots a Windowed Cross Correlation heatmap.

Usage

wccPlot(inSeries1=NA, inSeries2=NA, startwindow=1, endwindow=200, wMax=50, tMax=50, 
    wInc=1, tInc=1, Lsize=8, pspan=.25, type="Max", samplespersecond=1, windcross=TRUE) 

Arguments

Details

This function runs wccCalc and wccPeakPick using the arguments passed in and plots a heatmap of a selected section of windows. The vertical axis is labeled with the lags in the units of seconds. Each calculated window is plotted as a vertical slice of the heat map and correlations near 1 are plotted in yellow and correlations near -1 are plotted in red. Lags of inSeries1 are plotted as positive and lags of inSeries2 are plotted as negative lags. The horizontal black line in the middle of the plot represents a lag of zero. The result of wccPeakPick is overlayed as a black line that traces the peak correlation closest to a lag of zero. The horizontal axis is labeled with the elapsed time to the right edge of two windows when they are at zero lag.

It is recommended that the plot includes no more than 1000 windows since if a large number of windows are plotted, the resulting heatmap will overwrite one window with the next window.

Value

Returns nothing.

References

Boker, S. M., Rotondo, J. L., Xu, M., & King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological methods, 7(3), 338.

See Also

wccCalc and wccPeakPick for the calculation of the wccCalc matrix and wccPeakPick timeseries that are used by this function.

Examples

#Create a windowed cross correlation plot for two simulated time series with a phase offset
tSeries1 <- sin(c(1:1000)/10) + rnorm(1000, mean=0, sd=.5)
tSeries2 <- sin(1+c(1:1000)/10) + rnorm(1000, mean=0, sd=.5)
wccPlot(inSeries1=tSeries1, inSeries2=tSeries2, startwindow=1, endwindow=500, 
    wMax=100, tMax=100, wInc=1, tInc=1, Lsize=8, pspan=.25, type="Max", 
    samplespersecond=10)
    

wccSurrogateDyads

Description

This function randomly pairs timeseries and creates a distribution of the null hypothesis that the pairing of dyads does not matter.

Usage

wccSurrogateDyads(inArray1=NA, inArray2=NA, wMax=50, tMax=50, wInc=1, tInc=1, Lsize=8,
     pspan=.25, type="Max", nSurrogates=NA, windcross=TRUE, embedD=9) 

Arguments

Details

This function generates and returns a distribution of aggregated statistics from running Windowed Cross Correlation and peakpicking (Boker, Rotondo, Xu, & King 2002) on pairs of timeseries that conform to the null hypothesis that the true pairing of the timeseries does not matter. This is called a surrogate analysis (Moulder, Boker, Ramsayer, & Tschacher 2018) and is a nonparametric way of estimating whether the observed association between timeseries is due to dyadic interactions occuring while the timeseries were measured or simply due to the distributions of scores within all the timeseries. This is important to consider since the timeseries may be measurements of individual processes that are constrained in some way. For instance, consider dyadic timeseries of head motions. All persons' heads are constrained in the motions they can perform due to similarities in skeletal and muscular dynamics that are shared by most humans. One does not want these shared constraints to show up as significant associations within dyads when they are actually due to similarities between individuals.

The function returns a dataframe whose columns contain different ways of aggregating the associations and each row contains results from one random pairing of dyads. The randomization allows reuse of dyads, so it is best if the number of possible random pairings is large relative to the number of surrogates requested. If there are N rows in inArray1 and inArray2, the maximum number of unique surrogates that can be generated is N*(N-1)/2. With that constraint, we recommend at least N = 10 dyads as a source pool since that allows 45 unique surrogates to be generated. The only exclusion to the random pairing of dyads is that if the random pairing results in an actual dyad, it is not included.

Value

Returns a dataframe whose columns are defined in wccAggregate and whose rows are the results of each random pairing of dyads.

References

Boker, S. M., Rotondo, J. L., Xu, M., & King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological methods, 7(3), 338.

Moulder, R., Boker, S., Ramseyer, F., & Tschacher, W. (2018). Determining synchrony between behavioral time series: An application of surrogate data generation for establishing falsifiable null-hypotheses. Psychological Methods. 23:4 pp 757–773

See Also

wccAggregate for the definition of the columns of the returned dataframe.

Examples

#Create two arrays of timeseries with dyadic dependence
array1 <- matrix(NA, nrow=10, ncol=500)
array2 <- matrix(NA, nrow=10, ncol=500)
for(i in 1:10) {
    array1[i,] <- sin(c(1:500)/runif(1, min=5, max=20)) + rnorm(500, mean=0, sd=.5)
    array2[i,] <- array1[i,] + rnorm(500, mean=0, sd=.5)
}
wccSurrogateDyads(inArray1=array1, inArray2=array2, wMax=50, tMax=50, wInc=1, tInc=1, 
    Lsize=8, pspan=.25, type="Max", nSurrogates=20, windcross=TRUE)