Imputation of missing categorical data by maximizing internal consistency

This paper suggests a method to supplant missing categorical data by reasonable replacements. These replacements will maximize the consistency of the completed data as measured by Guttman's squared correlation ratio. The text outlines a solution of the optimization problem, describes relationships with the relevant psychometric theory, and studies some properties of the method in detail. The main result is that the average correlation should be at least 0.50 before the method becomes practical. At that point, the technique gives reasonable results up to 10–15% missing data.We thank Anneke Bloemhoff of NIPG-TNO for compiling and making the Dutch Life Style Survey data available to use, and Chantal Houée and Thérèse Bardaine, IUT, Vannes, France, exchange students under the COMETT program of the EC, for computational assistance. We also thank Donald Rubin, the Editors and several anonymous reviewers for constructive suggestions.     

Did Pearson reject the Neyman-Pearson philosophy of statistics?

I document some of the main evidence showing that E. S. Pearson rejected the key features of the behavioral-decision philosophy that became associated with the Neyman-Pearson Theory of statistics (NPT). I argue that NPT principles arose not out of behavioral aims, where the concern is solely with behaving correctly sufficiently often in some long run, but out of the epistemological aim of learning about causes of experimental results (e.g., distinguishing genuine from spurious effects). The view Pearson did hold gives a deeper understanding of NPT tests than their typical formulation as accept-reject routines, against which criticisms of NPT are really directed. The Pearsonian view that emerges suggests how NPT tests may avoid these criticisms while still retaining what is central to these methods: the control of error probabilities.A portion of this research was carried out during tenure of a National Endowment for the Humanities Summer Stipend Fellowship; I gratefully acknowledge that support. A version of this paper was presented at the 1987 meeting of the Society for Exact Philosophy. This paper benefited from discussions and communications with George Barnard and Isaac Levi. I thank Harlan Miller for helpful comments on earlier drafts.     

Revision algebra semantics for conditional logic

The properties of belief revision operators are known to have an informal semantics which relates them to the axioms of conditional logic. The purpose of this paper is to make this connection precise via the model theory of conditional logic. A semantics for conditional logic is presented, which is expressed in terms of algebraic models constructed ultimately out of revision operators. In addition, it is shown that each algebraic model determines both a revision operator and a logic, that are related by virtue of the stable Ramsey test.The author is grateful for a correction and several other valuable suggestions of two anonymous referees. This work was supported by the McDonnell Douglas Independent Research and Development program.     

Partial monotonicity and a new version of the Ramsey test

We introduce two new belief revision axioms: partial monotonicity and consequence correctness. We show that partial monotonicity is consistent with but independent of the full set of axioms for a Gärdenfors belief revision sytem. In contrast to the Gärdenfors inconsistency results for certain monotonicity principles, we use partial monotonicity to inform a consistent formalization of the Ramsey test within a belief revision system extended by a conditional operator. We take this to be a technical dissolution of the well-known Gärdenfors dilemma.In addition, we present the consequential correctness axiom as a new measure of minimal revision in terms of the deductive core of a proposition whose support we wish to excise. We survey several syntactic and semantic belief revision systems and evaluate them according to both the Gärdenfors axioms and our new axioms. Furthermore, our algebraic characterization of semantic revision systems provides a useful technical device for analysis and comparison, which we illustrate with several new proofs.Finally, we have a new inconsistency result, which is dual to the Gärdenfors inconsistency results. Any elementary belief revision system that is consequentially correct must violate the Gärdenfors axiom of strong boundedness (K^*8), which we characterize as yet another monotonicity condition.This work was supported by the McDonnell Douglas Independent Research and Development program.     

An automated test development of parallel tests from a seed test

Binary programming models are presented to generate parallel tests from an itembank. The parallel tests are created to match item for item an existing seed test and match user supplied taxonomic specifications. The taxonomic specifications may be either obtained from the seed test or from some other user requirement. An algorithm is presented along with computational results to indicate the overall efficiency of the process. Empirical findings based on an itembank for the Arithmetic Reasoning section of the Armed Services Vocational Aptitude Battery are given.The Office of Naval Research, Program in Cognitive Science, N00014-87-C-0696 partially supported the work of Douglas H. Jones. The Rutgers Research Resource Committee of the Graduate School of Management partially supported the work of Douglas H. Jones and Ing-Long Wu. A Thomas and Betts research fellowship partially supported the work of Ing-Long Wu. The Human Resources Laboratory, United States Air Force, partially supported the work of Ronald Armstrong. The authors benefited from conversations with Dr. Wayne Shore, Operational Technologies, San Antonio, Texas. The order of authors' names is alphabetical and denotes equal authorship.     

Discrimination learning of rotated faces: a Markov analysis of coding and association processes]

30 subjects participated in a discrimination experiment learning face-letter associations under four rotation conditions (45 degrees, 90 degrees, 135 degrees, 180 degrees). Under each condition two thirds of the faces were presented twice, upright and rotated away from the vertical; the remaining faces were presented once, upright or rotated. Learning is described by a joint Markov model: For faces that are presented twice it assumes a separate association and encoding process (two-stage-model), for faces that are presented once it assumes an association process (all-or-none-model). The Markov model fits the data for all four rotation conditions. The angle of rotation does not affect learning for faces that are presented once. For faces that are presented twice it influences both the association and the encoding process. For the angles employed, the effect of rotation can be approximated linearly. The results suggest that the encoding of a rotated face differs increasingly from an upright face as a function of these angles of rotation. This confirms analogous conclusions from mental rotation experiments.     

Degree of learning,interpolated tests,and rate of forgetting

The purpose of the two experiments reported here was to observe the effects of degree of learning, interpolated tests, and retention interval, primarily on the rate of forgetting of a list of words, and secondarily on hypermnesia for those words. In the first experiment, all the subjects had one study trial on a list of 20 common words, followed by two tests of recall. Half of the subjects had further study and test trials until they had learned the words to a criterion of three correct consecutive recalls. Two days later, half of the subjects under each learning condition returned for four retention tests, and 16 days later, all the subjects returned for four tests. Experiment 2 was similar, except that all the subjects had at least three study trials followed by four recall tests on Day 1, intermediate tests were given 2 or 7 days later, and they all had final tests 14 days later. The results showed that rate of forgetting was attenuated by an additional intermediate set of tests but not by criterion learning. Hypermnesia was generally found over the tests that were given after a retention interval of 2 or more days. The best predictor of the amount of hypermnesia over a set of tests was the difference between overall cumulative recall and net recall on the first test of the set.     

The effects of syntactic structure on letter detection in adjacent function words

In the present study, we examined letter detection in very frequent function-word sequences. It has been claimed that such sequences are processed in a unitized manner, thus preempting access to their constituent letters. In contrast, we showed that letter detection in the words for and the (1) was no more difficult when the words appeared in adjacent locations in a sentence (familiar) than when they appeared apart (less familiar sequence) and (2) was contingent upon the words' syntactic roles within the phrase. Thus, letter detection in for was easier when the sequence was separated by a clause boundary than when the words were part of the same clause. The advantage derived from clause separation was strongest when a comma divided clauses. These results challenge the unitization account of the "missing-letter" effect in common phrases and support a position where this phenomenon is seen to reflect the extraction of phrase structure during reading.