Processing tree models for discrete and continuous variables

Heck, Daniel W.

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URL:	https://ub-madoc.bib.uni-mannheim.de/42815
URN:	urn:nbn:de:bsz:180-madoc-428151
Document Type:	Doctoral dissertation
Year of publication:	2017
Place of publication:	Mannheim
University:	Universität Mannheim
Evaluator:	Erdfelder, Edgar
Date of oral examination:	5 September 2017
Publication language:	English
Institution:	School of Social Sciences > Kognitive Psychologie u. Differentielle Psychologie (Erdfelder 2002-2019) Außerfakultäre Einrichtungen > Graduate School of Economic and Social Sciences- CDSS (Social Sciences)
Subject:	150 Psychology
Subject headings (SWD):	Mathematische Psychologie , Modellierung , Kognitiver Prozess
Keywords (English):	Cognitive modeling , multinomial processing tree models , decision making , mathematical psychology
Abstract:	In psychology, multinomial processing tree (MPT) models explain how qualitatively different processes determine observed response behavior. Even though they have successfully been used in many applications, MPT models are inherently limited to discrete data such as choice frequencies. In my thesis, I therefore propose two new approaches that extend MPT models to continuous variables such as response times (RTs), ﬁne-grained response scales, or process-tracing measures. Both approaches assume that continuous variables follow a ﬁnite mixture distribution with mixture weights determined by the processing tree structure and state-speciﬁc, continuous component distributions. In the ﬁrst approach, RT-extended versions of MPT models are obtained by categorizing continuous observations into a ﬁnite number of intervals. Thereby, the RT component distributions can be estimated by histograms, allowing researchers to test the relative speed of different latent processes as demonstrated for the two-high-threshold model of recognition memory. In a theoretical paper, the new method is used to develop an RT-extended MPT model of recognition-based decisions and test competing process models. Even though the two theoretical accounts under consideration differ strongly and assume serial and parallel information integration, respectively, empirical tests have proved to be difﬁcult without the new measurement model. As a second approach, I developed the class of generalized processing tree (GPT) models that assume parametric families instead of histograms for the continuous component distributions. The main advantages of GPT models are that they reduce the ﬂexibility of the component distributions, can result in more precise estimates for the processing-tree parameters compared to MPT models, and allow for modeling one or more continuous variables jointly. In a ﬁrst empirical application, a GPT model provided a good account of mouse-tracking data in a semantic-categorization paradigm. In sum, my thesis lays the foundations for new empirical tests of discrete-state theories of cognition by jointly modeling discrete and continuous variables.