Table of Contents
Correct Model Selection Tests
Talk Overview
Examples of Complex Probability Models in the Social and Behavioral Sciences
Economics
Exchange Rate Prediction Problem [Theodossious, 1994; The Financial Review].
Database for Exchange Rate Problem (Episcopos and Davis (1996). Neural Networks in Financial Engineering.)
AR(1)-EGARCH-M(1-1) Model [Nelson (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59]
Autoregressive Back-Propagation Neural Net ([Episcopos and Davis (1996). Neural Networks in Financial Engineering)
Interpretation of Back-Prop Networks as Nonlinear Regression Models (Golden, 1987; Golden, 1988, Biological Cybernetics; White, 1989, Journal of the American Statistical Association)
RESULTS: EXCHANGE RATE PREDICTION (Episcopos and Davis (1996). Neural Networks in Financial Engineering.)
Computational Linguistics
Hidden Markov Models (HMMs) in Computational Linguistics
PPT Slide
Social Network Theory
Idea Regarding Possible Use of Markov Random Fields in Social Network Theory
COGNITIVE SCIENCE
Context Effects
Brain-State-in-a-Box (BSB) Nonlinear Activation Updating Dynamics [Anderson, Silverstein, Ritz, and Jones (1977). Psychological Review, 84, 413-451]
BSB Letter-in-Word Perception Neural Model [Golden, R.M. (1986). Cognitive Science, 10, 241-276]
PPT Slide
PPT Slide
Features and Issues Associated with BSB Model of Letter Perception (also relevant to most “neural net” models)
Assumptions about BSB’s Preferences
BSB Model Attempts to Compute “Most Preferred” Activation Pattern (Golden, 1988; Biological Cybernetics; Golden,1996, Mathematical Methods)
How Can We Check a Complex Probability Model’s Assumptions?
DISCREPANCY RISK MODEL SELECTION TEST (DRMST) THEORY Golden (2000), To be submitted (identically distributed but not independent case, theorems) Golden (2000), Journal of Mathematical Psychology (i.i.d. version, no theorems) Uses approach of White, 1994, to extend Vuong, 1989, Econometrica
Probability Models
Reliable Statistical Inferences with Wrong Probability Models (White, 1982, Econometrica; White, 1994, Estimation, Inference, and Specification Analysis; see Golden, 1995, Journal of Mathematical Psychology; for a review; Golden, 2000)
Formulas for Standard Errors Computed Under False Assumption DGP ? Model are WRONG (Figure 2, Golden, 1995, JMP)
DRMST DGP Assumptions
DRMST Objective Function
DRMST Optimal Estimate
Example DRMST Objective Functions
Model Selection Criterion (MSC) Methods
DRMST Null Hypothesis
Equivalent Loss Functions
THE DRMST
Weighted Chi-Square Distribution (Special case of Sheil and O’Muircheartaigh (1977), Applied Statistics, 26, 92-98)
Gradient and Hessian of DRMST Objective Function
DRMST Stage 1: Variance MST
Sketch of Proof of Variance MST (Golden, 2000; Compare to Vuong, 1989)
DRMST Stage 2: Non-Equivalent Loss MST
Wald MST [Golden (2000). Working paper.]
Wald MST Applications
Limitations of DRMST Theory
EXAMPLE APPLICATIONS OF DRMST THEORY
Logistic Regression Example: Competing Representational Assumptions
Compensated Work Therapy (CWT) Study (“Impact of Therapeutic Work on Homeless Substance Dependent Veterans”; Michael Kashner, UT Southwestern Medical Center, PI; Funded by Dept. VA Affairs)
Database for the Epidemiological Data Analysis Problem [Henley, Dawes, Bodine, Golden, and Kashner (1998). Martingale Research Technical Report]
Logistic Regression Model with Competing Coding Assumptions [Henley, Dawes, Bodine, Golden, and Kashner (1998). Martingale Research Technical Report]
DRMST Results: Epidemiological Data Analysis [Henley, Dawes, Bodine, Golden, and Kashner (1998). Martingale Research Technical Report]
Categorical Time-Series Analysis:
Autoregressive Categorical Time Series: Representative Applications (Fahrmeir and Kaufmann, 1987, Journal of Time Series Analysis; Golden, 1995, Journal of Mathematical Psychology)
Autoregressive Categorical Time Series: Methods
Autoregressive Constrained Categorical Regression (ACCR) Time-Series Model (Golden, 1994, Journal of Biological Systems; Golden, 1995, Journal of Mathematical Psychology; Golden, 1998, Discourse Processes)
?-ACCR Two Parameter Probability Model (Golden, 1995; Journal of Mathematical Psychology; Golden, 1998; Discourse Processes)
PPT Slide
ACCR Beta Weights Vs. Retention Interval (Golden, 1998, Discourse Processes)
CONCLUSIONS
References
References (continued)
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Author: Richard M. Golden
Email: golden@utdallas.edu
Home Page: www.utdallas.edu/~golden
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