State-Trace Analysis

126 Pages·2018·1.919 MB·English

by  John C. Dunn,Michael L. Kalish (auth.)

Computational Approaches to Cognition and Perception
John C. Dunn
Michael L. Kalish
State-Trace
Analysis
Computational Approaches to Cognition
and Perception
Editor-in-chief
AmyH.Criss,DepartmentofPsychology,SyracuseUniversity,Syracuse,
NewYork,USA
Computational Approaches to Cognition and Perception is a series that aims
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Moreinformationaboutthisseriesathttp://www.springer.com/series/15340
John C. Dunn • Michael L. Kalish
State-Trace Analysis
123
JohnC.Dunn MichaelL.Kalish
SchoolofPsychologicalScience DepartmentofPsychology
UniversityofWesternAustralia SyracuseUniversity
Perth,WA,Australia Syracuse,NY,USA
ISSN2510-1889 ISSN2510-1897 (electronic)
ComputationalApproachestoCognitionandPerception
ISBN978-3-319-73128-5 ISBN978-3-319-73129-2 (eBook)
https://doi.org/10.1007/978-3-319-73129-2
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“Whatisthesmallestnumberofsimple
undefinedthingsatthestart,andthesmallest
numberofundemonstratedpremises,outof
whichyoucandefinethethingsthatneedto
bedefinedandprovethethingsthatneedto
beproved?Thatproblem,inanycasethat
youliketotake,isbynomeansasimpleone,
butonthecontraryanextremelydifficultone.
Itisonethatrequiresagreatamountof
logicaltechnique.”
BertrandRussell(1956,p.271)
Preface
Human behavior is complex. One of the aims of experimental psychology is to
accountforthiscomplexitybydevelopingandtestingrelativelysimpletheoretical
models. These models are simpler than the behavior they describe because they
typicallyconsistofasmallnumberoftheoreticalconstructsthatcombineaccording
to a set of rules, sometimes in the form of mathematical equations, to predict
behavior.Adesirablemodelisonethataccountsforthebehaviorinquestionusing
thefewestnumberoftheoreticalconstructs.
Theories of cognition posit a range of hypothetical constructs, often described
in terms of unseen mental processes or processing systems, to account for aspects
of observed behavior. This has been a feature of the “cognitivist” approach to
psychologicalresearchandappearedrelativelyearly—awell-knownexamplebeing
Atkinson and Shiffrin’s division of memory into “short-term” and “long-term”
stores.However,suchproposalshavenotbeenwithoutcontroversyandhaveoften
led to longstanding debates concerning the exact number of constructs that might
be required to explain behavior in a particular domain. For example, researchers
currently debate the number of components underlying recognition memory (one
or two, or perhaps more), the number of processes underlying human reasoning
(again, one or two), working memory (three or more), and the number of systems
underlying perceptual category learning (again, one or two). This small sample is
known to us from our own work—there are likely to be many similar debates in
otherfields.
Perhaps the most basic modeling question is whether observed changes in two
or more, ostensibly distinct, aspects of behavior demand one or more than one
theoretical construct. Yet, despite its centrality, the tools researchers have used to
addressthisquestionareoftenadhoc.Traditionally,therehasbeenstrongreliance
on methods based on functional dissociation—a logic originally borrowed from
neuropsychology—whichhavebeenappliedinvariousways,includingincorpora-
tionintothestatisticalworkhorseofpsychologicalresearch,theanalysisofvariance.
Unfortunatelyforthegreatbulkofresearchthathasreliedonthesemethods,they
are not fit for purpose as they are unable to support the inferential burden placed
upon them. In contrast, state-trace analysis (STA) offers a rigorous procedure for
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viii Preface
achieving this goal that is firmly grounded in mathematics and logic. For this
reason, we believe it is timely to present a comprehensive overview of STA that
willprovideresearchersforthefirsttimewiththemeanstoappreciateandtoapply
thismethodology.
STA supersedes all previous methods for identifying the number of theoretical
constructs or latent variables (as we will refer to them) that mediate the effects of
oneormoreindependentvariablesontwoormoredependentvariables.Itdoesso
becauseitisfirmlybasedonarigorousandexplicitlogic.Ourintentioninthisshort
book is to make the argument for STA, clarifying what it can and cannot do, and
showing that it is the best solution to some of the irreducible difficulties of psy-
chologicalmeasurement.Althoughthereaderwillfindtheoccasionalmathematical
equation, these are presented in the service of clarity rather than obfuscation. Our
aim is to present the basic ideas and techniques of STA in a form that allows the
usertoapplythemimmediately(orasquicklyaspossibleafteralittlestudy).Our
bookisthereforeaimedatgraduatestudentsandourfellowresearchersincognitive
psychology and related fields. It presupposes familiarity with appropriate research
methodologyandstatisticsandsomerelevantmathematicalconcepts.
Ourbook(likeCaesar’sGaul)isdividedintothreemainparts.InPartI,wefocus
on the logical underpinnings of STA. In Chap.1 we outline a general framework
forthinkingabouttherelationshipsbetweenindependentvariables,latentvariables,
and dependent variables. In Chap.2, we explore the implications of the critical
assumptionofmonotonicityinmeasurement,includingmeasurementinpsychology,
and its relevance to STA. In Chap.3, we demonstrate how methods based on
functionaldissociationfailandhowtheyaresupersededbySTA.
In Part II, we turn to practical application of STA. In Chap.4 we show how
to fit and to test the single latent variable model that forms the heart of STA. In
Chap.5 we describe a software package that can be used to fit state-trace models
and to test them within a frequentist perspective. In Chap.6 we apply a modified
versionofthissoftwaretobinarydata,andinChap.7weexplore someadditional
designs.Throughout,wegivenumericalandcomputationalexamplesandshowhow
toperformSTAusingourpubliclyavailablesoftwareinbothMatlabTM andR.
In Part III, we discuss some further topics. In Chap.8 we examine Bayesian
approaches to the analysis of STA designs, and in Chap.9 we discuss potential
extensionsofSTAandaddresssomeadditionalaspectsofitsapplication.
Perth,Australia JohnC.Dunn
Syracuse,NY,USA MichaelL.Kalish
September2017
Acknowledgments
Thisshortbookonstate-traceanalysisistheproductofalongperiodofgestation
that has benefited greatly from the thoughtful input of many colleagues. In the
first instance, we wish to acknowledge the groundbreaking conceptualizations of
psychological measurement developed by Don Bamber and Geoffrey Loftus that
ledtotheinitialformulationanddevelopmentofstate-traceanalysis.Wealsowish
to acknowledge the original contributions by Kim Kirsner and Andrew Heathcote
to the concepts discussed in these pages. And we also would like to thank our
other colleagues, Ben Newell, Brett Hayes, Emily Freeman, Greig de Zubicaray,
LauraAnderson,LukeFinlay,OlegBurdakov,OlegSysoev,RachelStephens,Ralph
James,RikHenson,andSimonDennis,whoseinputhasbeencriticalingettingus
towherewearetoday.
We also wish to acknowledge the generous support of the Australian Research
CouncilandNationalScienceFoundationwhohaveenabledustoconductourwork
andthroughitthepresentdevelopmentofstate-traceanalysis.
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Contents
PartI Theory
1 TheLogicofState-TraceAnalysis ......................................... 3
1.1 Introduction ............................................................. 3
1.2 TheGeneralStructure................................................... 5
1.3 TheDimensionalityoftheState-Trace................................. 9
2 Monotonicity.................................................................. 21
2.1 Introduction ............................................................. 21
2.2 TheProblemofNomicMeasurement.................................. 26
2.3 IsMonotonicityTooRestrictive?....................................... 30
3 FunctionalDissociation...................................................... 33
3.1 Introduction ............................................................. 33
3.2 TheGeneralLinearModel.............................................. 34
3.3 Example ................................................................. 38
PartII Application
4 StatisticalMethodology ..................................................... 43
4.1 Introduction ............................................................. 43
4.2 FittingaLinearModel.................................................. 43
4.3 FittingaMonotonicModel............................................. 46
4.4 FittingaMonotonicModeltoData .................................... 50
4.5 HypothesisTest ......................................................... 53
5 MixedDesignswithContinuousDependentVariables .................. 57
5.1 Introduction ............................................................. 57
5.2 UsingtheSTACMRSoftwarePackage................................ 58
5.3 OnTypeIandTypeIIErrors........................................... 71
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