On What Empiricism Cannot Be

Bas C. van Fraassen, in his Terry Lectures at Yale University (subsequently published as The Empirical Stance), is concerned to elucidate what empiricism is, and could be, given past and current failures of characterization. He contends that naïve empiricism—the metaphilosophical position that characterizes empiricism in terms of a thesis—is self‐refuting, and he offers a reductio ad absurdum to substantiate this claim. Moreover, in place of naïve empiricism, van Fraassen endorses stance empiricism: the metaphilosophical position that characterizes empiricism in terms of certain attitudes and commitments. The present article, however, argues that van Fraassen begs the question in his reductio of naïve empiricism, and thus that his primary defense of stance empiricism is inadequate.     

A model-based approach to multivariate principal component regression: Selecting principal components and estimating standard errors for unstandardized regression coefficients

Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model-based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed.     

Marginal maximum likelihood estimation for a psychometric model of discontinuous development

Item response theory models posit latent variables to account for regularities in students' performances on test items. Wilson's “Saltus” model extends the ideas of IRT to development that occurs in stages, where expected changes can be discontinuous, show different patterns for different types of items, or even exhibit reversals in probabilities of success on certain tasks. Examples include Piagetian stages of psychological development and Siegler's rule-based learning. This paper derives marginal maximum likelihood (MML) estimation equations for the structural parameters of the Saltus model and suggests a computing approximation based on the EM algorithm. For individual examinees, empirical Bayes probabilities of learning-stage are given, along with proficiency parameter estimates conditional on stage membership. The MML solution is illustrated with simulated data and an example from the domain of mixed number subtraction. The authors' names appear in alphabetical order. We would like to thank Karen Draney for computer programming, Kikumi Tatsuoka for allowing us to use the mixed-number subtraction data, and Eric Bradlow, Chan Dayton, Kikumi Tatsuoka, and four anonymous referees for helpful suggestions. The first author's work was supported by Contract No. N00014-88-K-0304, R&T 4421552, from the Cognitive Sciences Program, Cognitive and Neural Sciences Division, Office of Naval Research, and by the Program Research Planning Council of Educational Testing Service. The second author's work was supported by a National Academy of Education Spencer Fellowship and by a Junior Faculty Research Grant from the Committee on Research, University of California at Berkeley. A copy of the Saltus computer program can be obtained from the second author.     

General estimators for the reliability of qualitative data

We study a proportional reduction in loss (PRL) measure for the reliability of categorical data and consider the general case in which each ofN judges assigns a subject to one ofK categories. This measure has been shown to be equivalent to a measure proposed by Perreault and Leigh for a special case when there are two equally competent judges, and the correct category has a uniform prior distribution. We consider a general framework where the correct category is assumed to have an arbitrary prior distribution, and where classification probabilities vary by correct category, judge, and category of classification. In this setting, we consider PRL reliability measures based on two estimators of the correct category—the empirical Bayes estimator and an estimator based on the judges' consensus choice. We also discuss four important special cases of the general model and study several types of lower bounds for PRL reliability.Bruce Cooil is Associate Professor of Statistics, and Roland T. Rust is Professor and area head for Marketing, Owen Graduate School of Management, Vanderbilt University. The authors thank three anonymous reviewers and an Associate Editor for their helpful comments and suggestions. This work was supported in part by the Dean's Fund for Faculty Research of the Owen Graduate School of Management, Vanderbilt University.     

Within-session changes in the VI response function: separating food density from elapsed session time.

Previous studies examining the relationship between response rate and reinforcement rate on variable-interval schedules (the variable-interval response function) have confounded elapsed session time with within-session changes in food density. The present experiments attempted to manipulate these factors independently and thus isolate their effects on responding. In Experiment 1, 7 rats pressed a bar for food on a series of four variable-interval schedules (7.5 s, 15 s, 30 s, and 480 s). Elapsed session time was held constant while food density was manipulated via a presession feeding. Changes in food density altered the form of the variable-interval response function, independently of elapsed session time. In Experiment 2, 8 rats responded on the same series of variable-interval schedules as in Experiment 1, but food density was held constant and elapsed session time was manipulated via the use of timeout periods. The results revealed no evidence for an effect of elapsed session time independent of food density. The present results extend a recent analysis of the variable-interval response function by Dougan, Kuh, and Vink (1993) by identifying food density as an important factor determining the form of the function. The present results also help clarify the controversy over the correct empirical form of the variable-interval response function by further defining the variables responsible for differences in the form of that function.     

HOW EMPIRICAL IS WIEMAN'S THEOLOGY?

Abstract. The essay is a response to the papers written by Nancy Frankenberry and Charley Hardwick in the March 1987 issue of Zygon. Questions are raised about whether Wieman's theology is functionalist in the way described by Frankenberry and whether Hardwick's proposal to establish the logical possibility of naturalism as a framework for an existential interpretation of the Christian message is satisfactory. The most basic question raised by both papers is whether Wieman's theology is fully empirical when viewed from the point of view of the radical empiricist.     

Estimating latent distributions in recurrent choice data

This paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data. These choice models are derived by specifying elements of the choice process at the individual level. Probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior. Due to the explicit consideration of random effect sources, the choice models are parsimonious and readily interpretable. An easy to implement EM algorithm is presented for parameter estimation. Two applications illustrate the proposed approach.     

Contributions of empirical research to medical ethics

Empirical research pertaining to cardiopulmonary resuscitation (CPR), clinician behaviors related to do-not-resuscitate (DNR) orders and substituted judgment suggests potential contributions to medical ethics. Research quantifying the likelihood of surviving CPR points to the need for further philosophical analysis of the limitations of the patient autonomy in decision making, the nature and definition of medical futility, and the relationship between futility and professional standards. Research on DNR orders has identified barriers to the goal of patient involvement in these life and death discussions. The initial data on surrogate decision making also points to the need for a reexamination of the moral basis for substituted judgment, the moral authority of proxy decision making and the second-order status of the best interests standard. These examples of empirical research suggest that an interplay between empirical research, ethical analysis and policy development may represent a new form of interdisciplinary scholarship to improve clinical medicine.     

A comparison of three simple test theory models

In very simple test theory models such as the Rasch model, a single parameter is used to represent the ability of any examinee or the difficulty of any item. Simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available, and are themselves of real practical value for small or even medium samples. They can also serve a normative role in test design.As an alternative to the Rasch model, or the Rasch model with a correction for guessing, a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference. This model provides a natural account of guessing, and has other useful things to contribute as well. It also offers an alternative to the Rasch model with the usual correction for guessing. The three models are compared in terms of statistical properties and fits to actual data. The goal of the paper is to widen the range of minimal models available to test analysts.This research was supported by grant AP320 from the Natural Sciences and Engineering Research Council of Canada. The author is grateful for discussions with M. Abrahamowicz, I. Molenaar, D. Thissen, and H. Wainer.