The crqa, R package, allows users to conduct a wide range of recurrence-based analyses on single (e.g., auto-recurrence) and multivariate time series (e.g., multidimensional cross-recurrence quantification), examine coupling properties underlying leader-follower relationships (i.e., diagonal-profile methods), as well as, track the evolution of recurrence rate over the time course (i.e., windowed methods).

crqa comes with some data that can be used to test and study the different functions therein.

First, specify the arguments that will be used in the crqa, core function.

```
## parameter setting
delay = 1; embed = 1; rescale = 0; radius = 0.0001;
normalize = 0; mindiagline = 2; minvertline = 2;
tw = 1; whiteline = FALSE; recpt = FALSE;
side = "both"; method = 'rqa'; metric = 'euclidean';
datatype = "categorical"
```

Then, run crqa on a nursery rhyme “The wheels on the bus” by Verna Hills: a vector of 120 strings (i.e., the words of the song),

```
ans = crqa(text, text, delay, embed, rescale, radius, normalize,
mindiagline, minvertline, tw, whiteline, recpt, side, method, metric,
datatype)
```

Have a look at the output, which contains different measures extracted from the recurrence plot (RP), and the RP itself, which can be plotted using the plotRP function.

Cross-recurrence extends univariate recurrence analysis into a bivariate analysis that allows quantification of the temporal coupling properties of two time series. We use eye-tracking data, 2,000 observations of six possible screen locations that are looked at by a dyad engaged into a joint task.

```
listener = eyemovement$listener[1:500]
narrator = eyemovement$narrator[1:500]
delay = 1; embed = 1; rescale = 0; radius = .01;
normalize = 0; mindiagline = 2; minvertline = 2;
tw = 0; whiteline = FALSE; recpt = FALSE; side = "both"
method = 'crqa'; metric = 'euclidean';
datatype = "categorical"
ans = crqa(narrator, listener, delay, embed, rescale, radius, normalize,
mindiagline, minvertline, tw, whiteline, recpt, side, method, metric,
datatype)
```

From cross-recurrence plots is possible to extract the diagonal cross-recurrence profiles (DCRPs) and use them to capture leader-follower-relationships.

```
timecourse = round( seq(-3300,3300,33)/1000, digit = 2) ## construct the time-course for the diagonal profile
res = drpfromts(narrator, listener, windowsize = 100,
radius = 0.001, delay = 1, embed = 1, rescale = 0,
normalize = 0, mindiagline = 2, minvertline = 2,
tw = 0, whiteline = F, recpt = F, side = 'both',
method = 'crqa', metric = 'euclidean',
datatype = 'continuous')
## visualise the diagonal-profile
profile = res$profile*100 ## extract it from the res object
plot(timecourse, profile, type = "l", lwd = 2.5, xlab = "Lag (seconds)",
ylab = "Recurrence Rate %")
```

Multidimensional cross-recurrence quantification analysis allows for the computation of cross-recurrences between two multidimensional time-series. We use hand-movement data from a complex LEGO joint construction task. The dataframe comprises of 5,799 observations.

```
# reduce the dimensionality of the time series to make the computation faster
# handset = handmovement[1:3000, ]
handset = handmovement[1:500, ]
P1 = cbind(handset$P1_TT_d, handset$P1_TT_n)
P2 = cbind(handset$P2_TT_d, handset$P2_TT_n)
delay = 5; embed = 2; rescale = 0; radius = .1;
normalize = 0; mindiagline = 10; minvertline = 10;
tw = 0; whiteline = FALSE; recpt = FALSE; side = "both"
method = 'mdcrqa'; metric = 'euclidean';
datatype = "continuous"
ans = crqa(P1, P2, delay, embed, rescale, radius, normalize,
mindiagline, minvertline, tw, whiteline, recpt, side, method, metric,
datatype)
RP = ans$RP
results = unlist(ans[1:10])
print(results)
```