An approximation for the bias function of the maximum likelihood estimate of a latent variable for the general case where the item responses are discrete

Lord developed an approximation for the bias function for the maximum likelihood estimate in the context of the three-parameter logistic model. Using Taylor's expansion of the likelihood equation, he obtained an equation that includes the conditional expectation, given true ability, of the discrepancy between the maximum likelihood estimate and true ability. All terms of orders higher thann ^?1 are ignored wheren indicates the number of items. Lord assumed that all item and individual parameters are bounded, all item parameters are known or well-estimated, and the number of items is reasonably large. In the present paper, an approximation for the bias function of the maximum likelihood estimate of the latent trait, or ability, will be developed using the same assumptions for the more general case where item responses are discrete. This will include the dichotomous response level, for which the three-parameter logistic model has been discussed, the graded response level and the nominal response level. Some observations will be made for both dichotomous and graded response levels.     

On equivalence between a partial credit item and a set of independent Rasch binary items

Given a Masters partial credit item withn known step difficulties, conditions are stated for the existence of a set of (locally) independent Rasch binary items such that their raw score and the partial credit raw score have identical probability density functions. The conditions are those for the existence ofn positive values with predetermined elementary symmetric functions and include the requirement that then step difficulties form an increasing sequence.     

The unique correspondence of the item response function and item category response functions in polytomously scored item response models

The item response function (IRF) for a polytomously scored item is defined as a weighted sum of the item category response functions (ICRF, the probability of getting a particular score for a randomly sampled examinee of ability ). This paper establishes the correspondence between an IRF and a unique set of ICRFs for two of the most commonly used polytomous IRT models (the partial credit models and the graded response model). Specifically, a proof of the following assertion is provided for these models: If two items have the same IRF, then they must have the same number of categories; moreover, they must consist of the same ICRFs. As a corollary, for the Rasch dichotomous model, if two tests have the same test characteristic function (TCF), then they must have the same number of items. Moreover, for each item in one of the tests, an item in the other test with an identical IRF must exist. Theoretical as well as practical implications of these results are discussed.This research was supported by Educational Testing Service Allocation Projects No. 79409 and No. 79413. The authors wish to thank John Donoghue, Ming-Mei Wang, Rebecca Zwick, and Zhiliang Ying for their useful comments and discussions. The authors also wish to thank three anonymous reviewers for their comments.     

A second generation nonlinear factor analysis

Nonlinear common factor models with polynomial regression functions, including interaction terms, are fitted by simultaneously estimating the factor loadings and common factor scores, using maximum-likelihood-ratio and ordinary-least-squares methods. A Monte Carlo study gives support to a conjecture about the form of the distribution of the likelihood-ratio criterion.The research reported in this paper was partly supported by Natural Sciences and Engineering Research Grant No. A6346.     

Additive conjoint isotonic probabilistic models (ADISOP)

The ISOP-model or model of twodimensional or bi-isotonicity (Scheiblechner, 1995) postulates that the probabilities of ordered response categories increase isotonically in the order of subject ability and item easiness. Adding a conventional cancellation axiom for the factors of subjects and items gives the ADISOP model where the c.d.f.s of response categories are functions of an additive item and subject parameter and an ordinal category parameter. Extending cancellation to the interactions of subjects and categories as well as of items and categories (independence axiom of the category factor from the subject and item factor) gives the CADISOP model (completely additive model) in which the parallel c.d.f.s are functions of the sum of subject, item and category parameters. The CADISOP model is very close to the unidimensional version of the polytomous Rasch model with the logistic item/category characteristic(s) replaced by nonparametric axioms and statistics. The axioms, representation theorems and algorithms for model fitting of the additive models are presented.     

Some promising dimensions for behavioral community technology

In recent years, the search for effective and replicable approaches to planned change in communities has escalated. Applied behavior analysts have participated in these efforts to remedy existing community problems and to increase the capacities of community residents to meet their goals. Examples of behavioral technologies for community settings are described and their advantages are noted. Criteria for more contextually appropriate community technologies are suggested and strategies for developing behavioral methods according to these criteria are described. This paper outlines some promising dimensions for behavioral community technology and discusses several possible limitations to a behavioral approach to addressing societal problems.     

Factor structure of the Friends and Family interview

The aim of this study was to specify the latent construct structure of the Friends and Family Interview (FFI: Steele & Steele, 2005) based on its dimensional scale coding protocol. The FFI is a semi-structured interview measuring attachment in middle childhood. We analyzed data from 341 FFI interviews with children aged 7–12 years, recruited in the Scandinavian Öresund Region. Exploratory Factor Analysis revealed a three-component model as best fitting the data. The first component, denoting attachment security, gathered all dimensional scales for evidence of secure base/safe haven regarding mother/father and coherence in the child’s narrative style, along with scales regarding reflective functioning, self-perception, and social functioning. The second component comprised preoccupying feelings of anger, but also derogation. The third component gathered all scales coding idealization. Inter-relations among the components were consistent with attachment theory, and respondents’ scores for all three components differed significantly across the four categorical attachment classifications. Affect regulation of negative emotion through anger and through derogation co-occurred, and was distinct from regulation through maintaining a belief that things are better than they appear (idealization). These two affect regulation strategies appeared commonly when reflective functioning, and an organized self-perception, and positive peer relations were less in evidence. The multi-dimensional FFI coding system appears to measure successfully these diverse features of the child’s narrative provided in response to the interview. Overall, our findings support the construct validity of the FFI and provide further evidence of its usefulness for assessing attachment in middle childhood and early adolescence.     

Commentary: What is the Meaning and Utility of the Psychopathy Concept?

The concept and measurement of psychopathy in young people is discussed with respect to five key issues: (1) the respective merits of self-reports and ratings by others; (2) whether callous/unemotional (CU) features may be more appropriately tapped by physiological measures; (3) the possible utility of genetic studies; (4) the distinctiveness of CU from other risk factors for antisocial behavior; and (5) the homogeneity of CU as a construct.     

Drug discrimination under a concurrent schedule.

Three pigeons were trained to discriminate a 5.0 mg/kg dose of pentobarbital from saline under a two-key concurrent schedule with responding on the key associated with the presession injection, under both stimulus conditions, producing four times as many reinforcers as responding on the other key. This concurrent schedule resulted in approximately 70% responding to the higher reinforcement key under the pentobarbital stimulus and approximately 30% responding to that key under the saline stimulus. During testing, then, the pigeons were able to dose-dependently emit higher (>70%) or lower (<30%) values than were established under the control conditions. Dose-response curves were determined for pentobarbital (twice), methamphetamine, phencyclidine, chlordiazepoxide, and the combination of pentobarbital and the barbiturate antagonist bemegride. The results obtained with pentobarbital and chlordiazepoxide showed that, as the dose increased, pentobarbital-appropriate responding also increased. Methamphetamine produced relatively flat dose--response curves, whereas phencyclidine administration produced inconsistent effects on responding. The combination of the training dose of pentobarbital with increasing doses of bemegride produced a decrease in pentobarbital-appropriate responding. The results also showed that the dose-response curves for pentobarbital and chlordiazepoxide, instead of being all or none, were graded functions of the drug dose.     

Decomposition of a Rasch partial credit item into independent binary and indecomposable trinary items

For each Rasch (Masters) partial credit item, there exists a set of independent Rasch binary and indecomposable trinary items for which the sum of the scores and the partial credit score have identical probability density functions. If each indecomposable trinary item is further expressed as the sum of two binary items, then the binary items are positively dependent and cannot be both of the Rasch type. This paper was written while the author was working with Steve Ferrara and Hillary Michaels on some technical aspects of the Maryland School Performance Assessment Program. The author had been puzzled by the fact that most MSPAP assessment items have three or less score categories. With a psychometric justification now being apparent, this paper is dedicated to both of them.