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Informative Psychometric Filters

Informative Psychometric Filters

Copyright Date: 2006
Published by: ANU Press
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  • Book Info
    Informative Psychometric Filters
    Book Description:

    This book is a series of case studies with a common theme. Some refer closely to previous work by the author, but contrast with how they have been treated before, and some are new. Comparisons are drawn using various sorts of psychological and psychophysiological data that characteristically are particularly nonlinear, non-stationary, far from equilibrium and even chaotic, exhibiting abrupt transitions that are both reversible and irreversible, and failing to meet metric properties. A core idea is that both the human organism and the data analysis procedures used are filters, that may variously preserve, transform, distort or even destroy information of significance.

    eISBN: 978-1-920942-66-3
    Subjects: Psychology

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-viii)
  3. Chapter 1 Introduction
    (pp. 1-32)

    This monograph is about building models of psychological or psychophysiological data that extend through time, are inherently unstable and, even from the perspective of the applied mathematician, are often intractable. Such instabilities have not gone unnoticed by statisticians and even such patterns as good and bad patches in the performance of sports teams, which are inexplicable to some of their followers, have been modelled. Attempts to address this problem in a diversity of disciplines are legion and it is only data of interest to the psychologist and the constructor of psychological measurements that are our focus. This does not mean...

  4. Chapter 2 Information, Entropy and Transmission
    (pp. 33-52)

    This monograph is mostly about data that can be characteristically intractable in the face of viable methods that are developed in other disciplines. For example, in creating methods to study series of earth tremors that could be used to predict earthquakes, multiscale analyses are proposed (Zaliapin, Gabrielov & Keils-Borok, 2004). A series is chopped into short segments, where it is known from extensive data and experience they will be approximately linear trends, up or down, separated by turning points. The segments thus created are a mix of slow and fast fluctuations; the slow fluctuations have large amplitude and are the part...

  5. Chapter 3 Transients onto Attractors
    (pp. 53-70)

    There are various ways of dealing with transient perturbations of what appears to be an almost regular evolution of dynamics: one can ignore them; one can delete them and replace then by the moving average of adjacent observations; one can treat them as outliers, perhaps generated by errors in measurement; one can treat them as outliers from a non-normal distribution due the the presence of a secondary distribution; or one can treat them as intrinsic to the dynamics and perhaps predicted by chaos theory. We will examine some alternatives. In psychometrics, it is tempting to regard them as errors due...

  6. Chapter 4 Inter- and Intra-level Dynamics of Models
    (pp. 71-104)

    In the period since the early 1980s, the amount of research published on the nonlinear dynamics of systems, including networks, has so expanded that it is impossible, even if one had the necessary erudition, to comprehend and synthesise effectively its implications for the psychologist. Admittedly, only a tiny fraction of this work is specifically addressed to problems which plausibly arise in considering brain and behaviour, but, even then, one has to selectively sift through results to discern what has implications for data analysis and theory construction.

    Historically, one may trace an evolution and a shift in the style of modelling:...

  7. Chapter 5 A Bivariate Entropic Analogue of the Schwarzian Derivative
    (pp. 105-128)

    An analogue expression for the Schwarzian derivative of a series had been previously constructed and used to examine the dynamics of a collection of time series from psychological and psychophysiological data. The derivatives of a function in the Schwarzian expression are replaced by information theory expressions based on absolute successive differences of a time series sample. This work is briefly recapitulated, and then the exploratory analysis of the numerical properties of the index is extended to compare the coupling of two time series in parallel, for series that are variously known to be periodic, random, or nearly chaotic. This requires...

  8. Chapter 6 Tribonacci and Long Memory
    (pp. 129-174)

    There are various ways of constructing systems that jump in their dynamics from one configuration to another. Systems that move from edge-of-chaos into a sort of saturated stability as their complexity increases are considered to be a basis for a new sort of thermodynamics where entropy is not always increasing, but the complexity of both a biological system and its connected potential environment are increasing together (Kauffman, 2000). This chapter uses a completely artificial model whose properties can at least heuristically provide illustrations of qualitative jumps in dynamics, some of which are irreversible, unlike transitions through cusp catastrophes, and identify...

  9. Chapter 7 Rescorla’s Theory of Conditioning
    (pp. 175-188)

    Rescorla and Wagner (1972) published an influential model of classical conditioning, which has been further refined by Rescorla (2001), introducing as necessary an ogival or cubic function which departs from its original linearity. The question of interest is whether this revised model could be subsumed as a special case of nonlinear psychophysical dynamics. The original model, being linear and deterministic, was widely studied and modified in various ways to try and incorporate stochastic ideas and thus cope with the probabilistic nature of competing response behaviour and response measures (Frey & Sears, 1978; Hanson & Timberlake, 1983).

    Alternative models for interaction effects between...

  10. Chapter 8 Nonlinearity, Nonstationarity and Concatenation
    (pp. 189-214)

    A comparison of six time series two from pseudo random generation, two from convoluted theoretical psychophysics, and two from EEG records are compared using a set of four statistics. It is seen that local largest Lyapunov exponents, the entropic analogue of the Schwarzian derivative, higher-order kernel matrices, surrogate random tests for confidence limits on parameters and eigenvalues of the dynamics all yield different information about the local instabilities of the processes. All the time series are, in some way, different from one other.

    Only something that appears to be both orderly and disorderly, regular and irregular, variant and invariant, constant...

  11. Chapter 9 Time Series of Disasters
    (pp. 215-236)

    Disasters in British coal mines between 1851 and 1962 provide a well studied data base, mainly analysed for the shape of the distribution of times between successive disasters. Here the series is treated as one of variations in the local rate of fatalities. Another series, also showing erratic fluctuations, sometimes due to unidentified exogenous factors, is that of the reported monthly sightings of UFOs in the USA over an 18-year period. Both these series raise interesting questions for social psychologists, yet can require quite different methods of analysis to explore their dynamics. There are big differences in temporal scale, and...

  12. Chapter 10 Perron-Frobenius at the Edge of Chaos
    (pp. 237-268)

    From the approach of symbolic dynamics, any psychophysiological time series may be given a square non-negative matrix representation that is then treated as the generator of a Markov chain. This has eigenvalues that, if the matrix is scrambled, that is effectively not degenerate, give a picture of the complexity of the dynamics. That picture is computed for two time series: one theoretical and homogeneous, resembling a Shilnikov attractor, and the other from real physiological data that are very unstable with transient outliers. A comparison is made with indices of entropy and chaos for each of 10 data sub-blocks. No index...

  13. Chapter 11 Appendix: Nonlinear Psychophysical Dynamics
    (pp. 269-278)

    This appendix summarises some algebraic properties used in nonlinear psychophysics with reference to their contextual literature in pure mathematics. It enlarges on some material presented graphically in Chapter 1, and drawn on particularly in Chapters 3, 7, 8 and 10.

    Alternative representations of the dynamics in real time:

    (1) Julia sets of the dynamics, with coordinates the starting points Y (Re, Im)0 of the recursive iterations which yield the trajectories; attractor basins and self-similarities displayed with magnification.

    (2) Dynamic partitions of the system’s parameter space; local regions associated with attractor characteristics. Coordinates are the equation’s fixed parameters, not the internal...

  14. References and Bibliography
    (pp. 279-306)
  15. Subject Index
    (pp. 307-310)