Modeling Behavior

Psychology 891C
Fall 2004
Wednesday 2:30-5:30, Tobin 304

Name Andrew L. Cohen
Office Location
Tobin 427
Phone Number
Office Hours
M 9:40-10:30, F 2:30-3:30 or by appointment
acohen at psych umass edu

Course Description:  The goals of this course are to demonstrate, first, what mathematical models of behavior are and how to evaluate them in a research context and, second, the basics behind a number of common modeling techniques and how to implement them. The course will begin with an overview of mathematical modeling and a discussion of the role of mathematics for understanding behavioral data.  Rather than focusing on theory, the emphasis of the rest of the course will be on evaluation and applications of and hands-on experience with particular modeling techniques.  Possible topics include: multinomial models, models of choice, models of subjective sensation, signal detection, stimulus sampling theory, Markov models, random walk and diffusion models, multidimensional scaling, model selection, Bayesian models, ACT-R, connectionist models, and dynamic systems.  Students will be assigned weekly readings and mini-projects and a larger group project. Although there are no course prerequisites, basic algebra skills, elementary programming, and undergraduate statistics would be helpful.

Course Goals:

    Primary Goals:
  To learn what mathematical models of behavior are and how to evaluate them in a research context. By the end of the class, you should be able to read a modeling paper critically.

    Secondary Goals: 
To learn the basics behind a number of common modeling techniques and how to implement them.

Prerequisites:  There are no formal prerequisites for this class.  All of the programming, math, and other needed skills will be developed throughout the semester. However, elementary algebra skills, a course in statistics, and some programming experience would be helpful.


  There will be readings for each class.  All students are required to read all of the readings, typically 1 or 2 book chapters or research articles that give an overview of a particular modeling technique and 1 or 2 book chapters or research articles which utilize this technique.  A tentative schedule is given below.  The "technique" papers are marked with a * and it is recommended that you begin with those readings. Copies of the readings will be left a week before they are to be discussed in Tobin Hall 203M. Please return them immediately after use.

  Each week a student will be assigned to give a presentation and lead a group discussion on the papers that utilize the week's technique. The presentation should be a semi-formal talk designed to teach the class about the readings and guide the class through a disscusion evaluating the use of modeling in the research.  Presentation guidelines are provided here.

  There will be a short homework assigment to be turned in each week.  The goal of these assigments is to give the students experience implementing and exploring the modeling technique discussed that week.  A typical assigment will be as follows.  The instructor will implement a simple version of a model discussed that week.  The student's job will be to modify the model in some way and explore its behavior.

    Final project:
  Students will participate in a final group project.  The goal of the project is to give students experience modeling behavioral data "from scratch".  The final project will be presented during the time allocated for the course final.  The presentation time will depend on the size of the class.  No written component of the project will be required.

    Class participation:
  This is a seminar class.  As such, all students are strongly encouraged to ask questions and to provide thoughts and comments during class.

  Attendance is not mandatory and will not be graded except as it pertains to the other assignments (including class participation).  If you know you are going to miss a class, it is your job to make sure any assigments are turned in on time and that you know the material and course logistics discussed during the missed class.  There will be no opportunity to make up an assigment if you miss a class for a non-university sanctioned excuse unless you clear it with the instructor at least a week in advance.  If you miss an assignment turn-in for an unexpected university sanctioned excuse (illness, death, etc), you may either drop that grade from your average or, if applicable, make it up at a later date. If you do miss an assignment, please try to talk to the instructor within a week.

    Tests:  There will be no tests.  There will be no final exam.

  Presentations, class participation, mini-projects, and the final project are each graded out of a total 100 points for a possible course total of 400 points.  Multiple instantiations of the same assignment group are averaged. For example, if you give 2 presentations and get a 90 and a 96, your presentation score is 93. There will be no curve.  There will be no opportunity for extra credit.  Grades will be posted on WebCT ( Your overall course grade will be based on the following chart:

Overall Score
372-400 360-371 348-359 332-347 320-331 308-319 292-307 0-291

Course Structure:  Most classes will be composed of four segments.  First, the instructor will review the basic techniques for the readings.  Second, a student will present research which utilizes these techniques and lead a group discussion.  Third, the instructor will give an overview of the the homework assigment and any needed programming skills. Fourth, the instructor will review any new math needed to understand the next set of readings.  These segments will last roughly 1, 1, 1/2 and 1/2 hours, respectively.

Web Discussions:  Please post any public questions to the appropriate discussion board on the class WebCT site (

Special Needs:  If you have any special academic needs, let me know the first week of class.

  The mini-projects and final project will be implemented in Octave.  Octave is a numerical programming environment that is mostly compatable with Matlab.  The advantage of Octave is that it is free and you may install it on any computer you wish (Windows, UNIX, LINUX, Mac).  If you already have access to Matlab, feel free to use it, but I will not provide "technical support".  Here are instructions for how to install Octave.  Here is a beginning Octave tutorial.  Here is a reference guide for Octave. We will develop proficiency with Octave as the semester progresses so don't worry if you've never used

(Tentative) Schedule
(* = technique readings, read first)
Presenters Assignment Due
W 9/8 What are mathematical models and why?

  Bjork, R. J. (1973). Why mathematical models? American Psychologist, 28, 22-27.
  Chapanis, A. (1961). Men, machines, and models. American Psychologist, 16, 113-131.
  Harris, R. J. (1976). The uncertain connection between verbal theories and research hypotheses in social psychology. Journal of Experimental Social Psychology, 12, 210-219.
  Hintzman, D. L. (1991). Why are formal models useful in psychology? In Hockley, William E. & Lewandowsky, Stephan (Eds).  Relating theory and data: Essays on human memory in honor of Bennet B. Murdock (pp. 39-56).  Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
  Jacobs, A. M. & Grainger, J. (1994). Models of visual word recognition - sampling the state of the art. Journal of experimental psychology: Human perception and performance, 20, 1311-1334.
  Myung, I. J. & Pitt, M. A. (2004). Model comparison methods. Methods in Enzymology, 383, 351-366. 
  Roberts, S. & Pashler, H. (2000). How persuasive is a good fit? A comment on theory testing. Psychological Review, 107, 358-367.
  Rogers J. L. & Rowe, D. C. (2000). Theory development should begin (but not end) with good empirical fits: A comment on Roberts and Pashler (2000). Psychological Review, 109, 599-604.
None None
W 9/15
Multinomial processing tree models
  *Batchelder, W. H. & Riefer, D. M. (1999). Theoretical and empirical review of multinomial process tree modeling.  Psychonomic Bulletin & Review, 6, pp. 57-86. [Skip "Structure of MPT Models"; pick one section from "Application Areas" that interests you; read everything else.]
  Batchelder, W. H. & Riefer, D. M. (1980). Separation of storage and retrieval in free recall of clusterable pairs. Psychological Review, 87, 375-397. [Skip from the paragraph which begins "In the case in which" on page 383 until "Conclusion"; read everything else]
Rebecca Johnson Assignment
W 9/22
  Thurstonian scaling
  Constant-ratio rule
  Luce's choice axiom
  Restle's theory
  *Laming, D. (1973). Mathematical Psychology. New York:  Academic Press, chap 2.
  Rumelhart, D. L. and Greeno, J. G. (1971).  Similarity between stimuli: An experimental test of the Luce and Restle choice models. Journal of Mathematical Psychology, 8, 370-381. [Don't worry too much about the math in the last section.]
Xingshan Li & Barbara Juhasz (jointly) Assignment
W 9/29
Stimulus sampling theory   *Neimark, E. D. & Estes, W. K. (1967). Stimulus sampling theory. San Fransisco: Holden-Day, pp. 25-35.
  Neimark, E. D. & Estes, W. K. (1967). Stimulus sampling theory. San Fransisco: Holden-Day, pp. 274-283.
  *[ might be helpful.]
Tim Slattery Assignment
W 10/6 Markov models   Gray, R. (2002). "Markov at the Bat": A model of cognitive processing in baseball batters. Psychological Science, 13, pp. 542-547.
  *Wickens, T. D. (1982). Models for behavior: Stochastic processes in psychology. San Francisco: W. H. Freeman and Company, chaps. 1-2 and sects. 3.1-3.2 [Skip optional (vertical line) sections].
Ioana Jadic Assignment
W 10/13
No class - Monday schedule.
W 10/20
Multidimensional scaling
  *Borg, I. & Groenen, P. (1997). Modern multidimensional scaling: theory and applications. New York: Springer-Verlag, chaps. 1-3.
  Nosofsky, R. M. (1986).  Attention, similarity, and the identification-categorization relationship.  Journal of Experimental Psychology: General, 115, 39-57.
Min Zeng Assignment
W 10/27
Random walk models   *Atkinson, R. C., Bower, G. H., & Crothers, E. J. (1966). An introduction to mathematical learning theory. New York: John Wiley & Sons, Inc, sect. 4.4.
  Nosofsky, R. M.; Palmeri, T. J. (1997). An exemplar-based random walk model of speeded classification. Psychological Review, 104. pp. 266-300.
  *Wickens, T. D. (1982). Models for behavior: Stochastic processes in psychology. San Francisco: W. H. Freeman and Company, pp. 171-176 (from Chap. 8), 199-208 (from Chap. 9).
Niamh Dundon Assignment
W 11/3
Bayesian models   Steyvers, M., Tenenbaum, J. B., Wagenmakers, E. J., & Blum, B. (2003). Inferring causal networks from observations and interventions. Cognitive Science, 27, 453-489.
  *Durrett, R. (1994). The Essentials of Probability. CA: Duxbury Press, Sects. 2.1, 2.2, & 2.4.
  *Sedlmeier, P. & Gigerenzer, G. (2001). Teaching Bayesian reasoning in less than two hours. Journal of Experimental Psychology: General, 130, pp. 380-382. [Up to the section on Teaching Bayesian Inference.]
Ibrahim Dahlstrom-Hakki Assignment
W 11/10
Model selection

  *Myung, I. J., Pitt, M. A., & Kim, W. (2003). Model Evaluation, Testing, and Selection. In: K. Lamberts and R. Goldstone (Eds.), Handbook of Cognition. London: Sage. [Skip qualitative section.]
 Olsson, H., Wennerholm, P., & Lyxzen, U. (2004). Exemplars, prototypes, and the flexibility of classification models. Journal of Experimental Psychology: Learning, Memory, and Cognition, 30, 936-941.
Michael Stroud Assignment
W 11/17
Connectionist models
  *Rich, E. and Knight, K. (1991). Artificial Intelligence. New York: McGraw Hill, chap. 18.
  Van Rooy, D., Van Overwalle, F., Vanhoomissen, T., Labiouse, C., French, R. (2003). A Recurrent Connectionist Model of Group Biases. Psychological Review, 110, 536-563.
Gordon Anderson Assignment
W 11/24
Constraint satisfaction models   Goldstone, R. L., & Rogosky, B. J. (2002). Using relations within conceptual systems to translate across conceptual systems, Cognition, 84, 295-320.
  Thagard, P. (1989). Explanatory coherence. Behavioral and Brain Sciences, 12, 435-467.
Kathryn Marszalek (Goldstone) & Adrian Staub (Thagard) None
W 12/1 Dynamic system
  *Abraham, F. D., Abraham, R., & Shaw, C. D. (1991). A visual introduction to dynamical systems for psychology. Santa Cruz, CA: Aerial Press, sects. I, II A, B1, B2, F1.
  Haken, H., Kelso, J. A. S., and Bunz, H. (1985). A theoretical model of phase transitions in human hand movement. Biological Cybernetics, 51, 347-356. [Skim the math in Section 3.]
Nicholas Potter Assignment
W 12/1
Signal detection
  Tanner & Swets
  Sequential sampling
  *Wickens, T. D. (2001). Elementary signal detection theory. London: Oxford University Press, pp. 3-44.
  *Laming, D. (1973). Mathematical Psychology. New York:  Academic Press, chap 6.
W 12/8
Class Wrap-up
  *Anderson, J. R., Bothell, D., Byrne M. D. & Lebiere, C. (submitted). An Integrated Theory of the Mind. Psychological Review. pp. 1-28.
  *Understanding Production Systems.
  *Perception and Motor Actions in ACT-R.
  Paper to be selected by presenter from
Simon Buechner None
W 12/15
Group presentations

All Group Project
No final No Class   None
None None