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.     

A structural model for postpartum responses to the somatic and cognitive items on the Beck Depression Inventory

A distinction can be drawn between those items on the Beck Depression Inventory (BDI) that reflect mainly cognitive and emotional symptoms and those that reflect somatic symptoms. Responses to the BDI were obtained from women at 3, 6, 9, and 24 weeks postpartum. The covariances of cognitive and somatic symptom scores across the four time points were closely fit by a structural equations model referred to as the simplex. The modeling indicates that earlier cognitive scores directly predict later somatic scores but that early somatic scores do not directly predict later cognitive scores. Other data confirm the results.Much of this research was supported while the first author was an NIMH Fellow at the University of Iowa (MH15168).     

Superimposition of response-independent reinforcement

Studies that have superimposed response-independent reinforcement (or reinforcers scheduled by contingencies placed on the absence of responding) upon conventional response-dependent schedules are reviewed. In general, providing alternative sources of reinforcement reduced response rates below the levels observed when alternative reinforcement was absent. However, response-rate elevation was sometimes found, particularly when rates of superimposed response-independent reinforcement were low. Superimposition of schedules providing reinforcers contingent on the absence of responding usually produced more severe response-rate decrements than superimposition of response-independent reinforcement. A variant of Herrnstein's equation, which assumes that some of the alternative reinforcers function as if they were delivered by baseline response-dependent source of reinforcement, is in qualitative agreement with the overall body of results obtained, and can predict both increases and decreases in response rate as resulting from superimposed reinforcers.     

Extending exploratory diagnostic classification models: Inferring the effect of covariates

Diagnostic models provide a statistical framework for designing formative assessments by classifying student knowledge profiles according to a collection of fine-grained attributes. The context and ecosystem in which students learn may play an important role in skill mastery, and it is therefore important to develop methods for incorporating student covariates into diagnostic models. Including covariates may provide researchers and practitioners with the ability to evaluate novel interventions or understand the role of background knowledge in attribute mastery. Existing research is designed to include covariates in confirmatory diagnostic models, which are also known as restricted latent class models. We propose new methods for including covariates in exploratory RLCMs that jointly infer the latent structure and evaluate the role of covariates on performance and skill mastery. We present a novel Bayesian formulation and report a Markov chain Monte Carlo algorithm using a Metropolis-within-Gibbs algorithm for approximating the model parameter posterior distribution. We report Monte Carlo simulation evidence regarding the accuracy of our new methods and present results from an application that examines the role of student background knowledge on the mastery of a probability data set.     

Choice between delayed reinforcers and fixed-ratio schedules requiring forceful responding.

This experiment measured pigeons' choices between delayed reinforcers and fixed-ratio schedules in which a force of approximately 0.48 N was needed to operate the response key. In ratio-delay conditions, subjects chose between a fixed-ratio schedule and an adjusting delay. The delay was increased or decreased several times a session in order to estimate an indifference point--a delay duration at which the two alternatives were chosen about equally often. Each ratio-delay condition was followed by a delay-delay condition in which subjects chose between the adjusting delay and a variable-time schedule, with the components of this schedule selected to match the ratio completion times of the preceding ratio-delay condition. The adjusting delays at the indifference point were longer when the alternative was a fixed-ratio schedule than when it was a matched variable-time schedule, which indicated a preference for the matched variable-time schedules over the fixed-ratio schedules. This preference increased in a nonlinear manner with increasing ratio size. This nonlinearity was inconsistent with a theory that states that indifference points for both time and ratio schedules can be predicted by multiplying the choice response-reinforcer intervals of the two types of schedules by different multiplicative constants. Two other theories, which predict nonlinear increases in preference for the matched variable-time schedules, are discussed.     

自由回忆和线索回忆测验中的系列位置效应

本文以96个中国汉字为材料,使用自由回忆和线索回忆测验方法,对20名被试进行6组分测验和最后所有汉字的总测验。发现自由回忆分测验中存在明显的系列位置效应,总测验出现负近因现象;线索回忆分测验也表现出明显的系列位置效应,但最后的总测验没有出现负近因现象。上述结果验证了Bjork和Whitten（1974）提出的顺序或情景理论。     

Isotonic ordinal probabilistic models (ISOP)

The concept of an ordinal instrumental probabilistic comparison is introduced. It relies on an ordinal scale given a priori and on the concept of stochastic dominance. It is used to define a weakly independently ordered system, or isotonic ordinal probabilistic (ISOP) model, which allows the construction of separate sample-free ordinal scales on a set of subjects and a set of items. The ISOP-model is a common nonparametric theoretical structure for unidimensional models for quantitative, ordinal and dichotomous variables.Fundamental theorems on dichotomous and polytomous weakly independently ordered systems are derived. It is shown that the raw score system has the same formal properties as the latent system, and therefore the latter can be tested at the observed empirical level.I wish to thank 3 reviewers and 2 editors who contributed a lot to the readability and precision of the article.     

Content variations and performance on formal operational tasks by gender,social class and ability1

The role of task content, gender, social class and cognitive ability in performance on two formal operational tasks is explored in this paper. The participants were 110 Icelandic 12-year-olds, early and late developers, males and females from all socio-economic groups. Two tasks of variable isolation (the pendulum and three content versions of the “plant” problem) and two measures of volume conservation (three traditional tasks and three tasks formally identical whose content was pictorial social play) were presented individually in a school setting. The results suggest that content variations have differential consequences for the performance of early and late developers at age 12. Both the nature of logical competence and task content affect solutions, as suggested by Overton and collaborators in 1987. Some social class and gender differences were observed on two Piagetian tasks (pendulum and volume), which was reduced by changing the task content in the case of social class but not in that of gender. As the gender difference in volume conservation was not reflected ins chool achievement nor on other cognitive tasks it was interpreted as a gender bias. The findings are discussed in view of recent literature on the development of cognitive theory with increased emphasis on context and meaning in a post-structural intellectual climate.