Theory change in immunology part II: The clonal selection theory

This two-part article examines the competition between the clonal selection theory and the instructive theory of the immune response from 1957–1967. In Part I the concept of a temporally extended theory is introduced, which requires attention to the hitherto largely ignored issue of theory individuation. Factors which influence the acceptability of such an extended theory at different temporal points are also embedded in a Bayesian framework, which is shown to provide a rational account of belief change in science. In Part II these factors, as elaborated in the Bayesian framework, are applied to the case of the success of the clonal selection theory and the failure of the instructive theory.     

Ordinal consistency and ordinal true scores

This paper argues that test data are ordinal, that latent trait scores are only determined ordinally, and that test data are used largely for ordinal purposes. Therefore it is desirable to develop a test theory based only on ordinal assumptions. A set of ordinal assumptions is presented, including an ordinal version of local independence. From these assumptions it is first shown that the gamma-correlation between two tests is the product of their gamma-correlations with the true latent order. The theory is generalized to allow for heterogeneous tests by defining a weighted average local independence. The tau-correlations between total score and the latent order can be found in both homogeneous and heterogeneous cases, and a system of differential item weighting to maximize the tau-correlation between weighted items and the latent order is provided. Thus a purely ordinal test theory seems possible.Part of this work was done while the author was a Visiting Fellow at Macquarrie University. The paper has benefitted from discussions with Professors Thomas J. Reynolds and Roderick P. McDonald and from the comments of several anonymous reviewers.     

Criterion-related construct validity

Established results on latent variable models are applied to the study of the validity of a psychological test. When the test predicts a criterion by measuring a unidimensional latent construct, not only must the total score predict the criterion, but the joint distribution of criterion scores and item responses must exhibit a certain pattern. The presence of this population pattern may be tested with sample data using the stratified Wilcoxon rank sum test. Often, criterion information is available only for selected examinees, for instance, those who are admitted or hired. Three cases are discussed: (i) selection at random, (ii) selection based on the current test, and (iii) selection based on other measures of the latent construct. Discriminant validity is also discussed.This work was supported in part by Grant SES-87-01890 from the Measurement Methods and Data Improvement Program of the U.S. National Science Foundation.     

Influential observations in principal factor analysis

We propose a method for detecting influential observations in iterative principal factor analysis. For this purpose we derive the influence functionsI(x; LL ^T ) andI(x; ) for the common variance matrixT =LL ^T and the unique variance matrix , respectively, in the common factor decomposition =LL ^T + . A numerical example is given for illustration.The authors are grateful to Tomoyuki Tarumi and Atsuhiro Hayashi for their kind permission to use their software Seto/B for drawing Figures 1 and 2 and to anonymous reviewers for comments on the paper.     

Using item-specific instructional information in achievement modeling

The problem of detecting instructional sensitivity (item basis) in test items is considered. An illustration is given which shows that for tests with many biased items, traditional item bias detection schemes give a very poor assessment of bias. A new method is proposed instead. This method extends item response theory (IRT) by including item-specific auxiliary measurement information related to opportunity-to-learn. Item-specific variation in measurement relations across students with varying opportunity-to-learn is allowed for.This paper was presented at the 1987 AERA meeting in Washington, DC. This research was supported by grant OERI-G-86-003 from the Office of Educational Research and Improvement, Department of Education. The author thanks Michael Hollis and Chih-fen Kao for valuable research assistance, and appreciates valuable comments made by an anonymous reviewer.     

A NEUROBIOLOGICAL ALTERNATIVE TO THE PERCEPTUAL REINFORCEMENT HYPOTHESIS OF STEREOTYPED BEHAVIOR: A COMMENTARY ON “SELF-STIMULATORY BEHAVIOR AND PERCEPTUAL REINFORCEMENT”

A perceptual reinforcement theory of stereotyped movements is advanced by Lovaas, Newsom, and Hickman (1987) in an effort to integrate a number of diverse observations about the origins and maintenance of this behavior. We, in turn, argue that the theory, as presented, is logically flawed and fails to take into account important biological findings and theory concerning pathological stereotyped acts. An alternative theory, derived primarily from neurological concepts, is briefly described.     

A nonparametric approach for assessing latent trait unidimensionality

Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.The referees' comments were remarkably detailed and greatly enhanced the writeup and sensitized the author to certain pertinent issues. Discussions with Fritz Drasgow, Lloyd Humphreys, Dennis Jennings, Brian Junker, Robert Linn, Ratna Nandakumar, and Robin Shealy were also very useful.This research was supported by the Office of Naval Research under grant N00014-84-K-0186; NR 150-533, and by the National Science Foundation under grant DMS 85-03321.     

Reliability of test scores in nonparametric item response theory

Three methods for estimating reliability are studied within the context of nonparametric item response theory. Two were proposed originally by Mokken (1971) and a third is developed in this paper. Using a Monte Carlo strategy, these three estimation methods are compared with four classical lower bounds to reliability. Finally, recommendations are given concerning the use of these estimation methods.The authors are grateful for constructive comments from the reviewers and from Charles Lewis.     

Latent trait models and dichotomization of graded responses

This paper discusses thecompatibility of the polychotomous Rasch model with dichotomization of the response continuum. It is argued that in the case of graded responses, the response categories presented to the subject are essentially an arbitrary polychotomization of the response continuum, ranging for example from total rejection or disagreement to total acceptance or agreement of an item or statement. Because of this arbitrariness, the measurement outcome should be independent of the specific polychotomization applied, for example, presenting a specific multicategory response format should not affect the measurement outcome. When such is the case, the original polychotomous model is called compatible with dichotomization.A distinction is made between polychotomization or dichotomization before the fact, that is, in constructing the response format, and polycho- or dichotomization after the fact, for example in dichotomizing existing graded response data.It is shown that, at least in case of dichotomization after-the-fact, the polychotomous Rasch model is not compatible with dichotomization, unless a rather special condition of the model parameters is met. Insofar as it may be argued that dichotomization before the fact is not essentially different from dichotomization after the fact, the value of the unidimensional polychotomous Rasch model is consequently questionable. The impact of our conclusion on related models is also discussed.