Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 19, Iss. 3, July, 2015, pp. 229-248 @2015 Society for Chaos Theory in Psychology & Life Sciences Detecting Nonlinearity and Edge-of-Chaos Phenomena in Ordinal Data Abstract: Some but not all algorithms for detecting nonlinearity in experimental data,
such as prediction methods and Lyapunov spectra, require a much larger amount of
stable continuous data than is generally available from individual human participants.
A new method for detecting nonlinearity in relatively short data sets,
Monotonic Ectropy, computes the change in Shannon information as ordinal scale values evolve
over time by comparing runs of various lengths and directions. This method compares
two successive ordinal scale changes with similar monotonic changes for
three successive ordinal scale values. The resulting index discriminates a
chaotic Henon series from both Gaussian noise and phase-randomised surrogate series,
the latter containing the stochastic structure of the Henon series but without the
nonlinearity. The empirical utility of the technique is illustrated using mood rating data
obtained from two participants, one suffering from chronic depression, the
other showing no signs of the disorder. Although Monotonic Ectropy discriminated
between the mood ratings of the depressed and nondepressed subjects, evidence
for nonlinearity was only obtained using Lempel-Ziv complexity, a measure based
on symbolic dynamics. This was probably due to Monotonic Ectropy”s unique sensitivity
to edge-of-chaos phenomena. Keywords: entropy, symbolic dynamics, mood ratings, order, depression, complexity |