Statistical Models of Cognitive and Perceptual Processes
Most students and researchers are familiar with linear statistical models such as those instantiated in ANOVA. The advantage of linear models is that they are flexible and can be used for inference across many disciplines. They are, however, often poor models of cognitive and psychological processes. For example, memory researchers may be interested in assessing the roles of storage and retrieval processes in a mnemonic task. The relationship between storage and retrieval is surely not linear.
The proposed course is about a different class of models for psychology: Psychological Process Models. These models are concerned with a detailed, substantive, and formal accounts of specific mental processes. For example, storage and retrieval may be modeled as sequential processes with retrieval of an item contingent on successful storage of that item. The course is designed to cover a limited number of models in depth. In doing so, important general concepts in modeling are introduced. Examples of these concepts include parameter estimation, goodness-of-fit, and measurement of latent processes. The following themes will be used throughout:
- The unification of models. Models, be they statistical (say ANOVA) or psychological (say, Signal Detection Theory), can be treated in a unified framework.
- Likelihood: Maximizing likelihood is a general, all-purpose approach to analyzing any model. I will teach how to express the likelihoods of various models and then how to use computational techniques to maximize these likelihoods. Understanding likelihood and how to maximize it is critical in analysis of realistic models of cognition.
- Model selection: Model selection, the art of rejecting or accepting one hypothesis over another, is one of the trickiest elements of statistics. My goal is to teach you a range of techniques. Perhaps the most under-utilized techniques are graphical. We focus on finding the appropriate transforms of data so that inference may be performed by inspection. Other techniques include nested likelihood, AIC, and BIC.
- Simulation: Simulation is the surest means of developing insight about how models account for phenomena. We will use simulations extensively in this regard.
I am requesting that you have taken graduate-level regression and ANOVA. I am, however, treating the class as if you don't remember too much of the experience. I will start at the beginning and keep the course as self-contained as possible.
We will be using R. R is available for free at http://cran.r-project.org. R is a great program. I find it to be indispensable because it is more flexible than SPSS, SAS, or Systat. It is a programming language rather than a menu-driven system (much like SAS). The big advantage over SAS is its ability to work interactively. R is so cool that it has spawned a number of R evangelists. It is a lifelong tool that will be around for many decades. The main drawback is that the learning curve is nontrivial. You will have to work a bit at it.
Your grade will be based exclusively and entirely on your homework performance. Almost all of your homework will be based on simulation and analysis of problems. Homework will be assigned weekly or biweekly. I give three grades: A means at or above expectation; B means below expectation; C means greatly below expectations. You can ask/consult/help each other with homework to some reasonable degree (it does nobody any good if some of you turn into doers and others turn into scribes). Contact me if you are having persistent or deep problems with a homework. Homework is due at the start of class on the due date (no exceptions), and you will self grade your homework in class and turn it in.
I am currently preparing a book on this class (in fact, I have a
contract, so it will eventually be published ). Please make comments to help me improve the book. Thanks.
We will do the class totally electronic and has no paper components. Readings, lectures, hoework assignments, and homework submissions will be done over the internet at http://pcl.missouri.edu/jeff
- I would greatly prefer an interactive, fun class. Please
attend, share, and help shape the class.
- I do take the material fairly seriously so I might shout ``wrong'' at you. Don't take it too personally, its part of my New York heritage. I will try not to swear too much; but don't be surprised if I use cuss words to convey subtle points.
- Disabilities/Academic-Honesty/Intellectual-Pluralism/Recording Statements: The Provost requests certain statements in a syllabus and you have seen them before. DISABILITIES: If you have any issue or concern that affects your ability to get the most out of my course, including those of disability, injury, or illness, then please come see me. ACADEMIC HONESTY: this class is a collaborative effort. It is more like group research than a class. We are all responsible that everybody learns. So, do your best to help you and your fellow classmates. Do engage the material, however, as best you can before seeking help. INTELLECTUAL PLURALISM: The University, in its limited wisdom, has a web site where you may complain if you think there is not sufficient intellectual pluralism in a course (http://osrr.missouri.edu/intellectualpluralism/concerns.html). AUDIO/VIDEO RECORDINGS: University of Missouri System Executive Order No. 38 lays out principles regarding the sanctity of classroom discussions at the university. The policy is described fully in Section 200.015 of the Collected Rules and Regulations. In this class, students may not make audio or video recordings of course activity, except students permitted to record as an accommodation under Section 240.040 of the Collected Rules. All other students who record and/or distribute audio or video recordings of class activity are subject to discipline in accordance with provisions of Section 200.020 of the Collected Rules and Regulations of the University of Missouri pertaining to student conduct matters. Those students who are permitted to record are not permitted to redistribute audio or video recordings of statements or comments from the course to individuals who are not students in the course without the express permission of the faculty member and of any students who are recorded. Students found to have violated this policy are subject to discipline in accordance with provisions of Section 200.020 of the Collected Rules and Regulations of the University of Missouri pertaining to student conduct matters.
- Basics: experiments, sets, sample spaces, events, random variables, parameters, estimators, properties of estimators, convergence
- Likelihood: likelihood functions, binomial, log-likelihood, likelihood ratio tests.
- High Threshold Model, Double High Threshold Model, Process Dissociation, Cowan's K, ROC curves
- Signal Detection Models: continuous random variables, quantiles, signal detection,
- Three Parameter Models of Choice: Generalized High-Threshold Model, Unequal Variance Signal Detection, Other Detection Models, Low-Threshold Model
- Multinomial Models: Confidence Ratings and ROC, Tree Models, Storage and Retrieval Model, Similarity Choice Models, Generalized Context Model, Introduction to multidimnesional scaling.
- Normal Models: The normal distribution, t-test/ANOVA, graphing CIs in realistic designs, regression, ANCOVA, inspecting for misspecification
- RT Models: various distributional models (gamma, Weibull, lognormal, ex-Gaussian, inverse-Gaussian), delta and QQ plots, Logan's Race Model, Additive Factors, Ratcliff's Diffusion Model
- The Bayesian Approach: Subtopics to be determined