Test theory without an answer key

A general model is presented for homogeneous, dichotomous items when the answer key is not known a priori. The model is structurally related to the two-class latent structure model with the roles of respondents and items interchanged. For very small sets of respondents, iterative maximum likelihood estimates of the parameters can be obtained by existing methods. For other situations, new estimation methods are developed and assessed with Monte Carlo data. The answer key can be accurately reconstructed with relatively small sets of respondents. The model is useful when a researcher wants to study objectively the knowledge possessed by members of a culturally coherent group that the researcher is not a member of.This research was supported by NSF Grant No. SES-8320173 to the authors. We gratefully acknowledge comments and suggestions from John Boyd, Tarow Indow, and Kathy Maher as well as the editor and several anonymous referees.     

COVARIATION WITHIN FUNCTIONAL RESPONSE CLASSES: IMPLICATIONS FOR TREATMENT OF SEVERE PROBLEM BEHAVIOR

Two studies examined the effects of a reductive treatment versus instruction-based treatments on the generalized reduction of problem behaviors. Each study involved a detailed analysis of multiple problem behaviors performed by school-aged youth with severe intellectual disabilities. The analysis examined the contrasting effects of one of two different positive intervention procedures (teaching a positive alternative behavior or providing additional teacher assistance during instruction) versus blocking and/or verbally reprimanding a problem behavior. The focus of each analysis was on the covariation of multiple problem behaviors within functional response classes. Results of the investigation indicated that when only one member of the response class was blocked, a collateral increase was observed in one or more different problem behaviors from the same response class. Alternatively, when 1 participant was taught a functionally equivalent mand response, all problem behaviors in the response class were reduced. Problem behaviors also were reduced for the remaining participant by presenting antecedent teacher assistance. Implications of the research extend to analysis of covariation within response classes and to procedures that result in generalized reduction of problem behaviors within a response class.     

Examining differential item functioning due to item difficulty and alternative attractiveness

A method for analyzing test item responses is proposed to examine differential item functioning (DIF) in multiple-choice items through a combination of the usual notion of DIF, for correct/incorrect responses and information about DIF contained in each of the alternatives. The proposed method uses incomplete latent class models to examine whether DIF is caused by the attractiveness of the alternatives, difficulty of the item, or both. DIF with respect to either known or unknown subgroups can be tested by a likelihood ratio test that is asymptotically distributed as a chi-square random variable.     

Reflections upon charitable giving: A comparison of individuals from business, ‘manual’ and professional backgrounds

This paper compares three groups of individuals in their beliefs about charitable giving. Focusing upon their preferences for different kinds of needy recipients, the paper compares the views of 49 people from (a) business, (b) professional and (c) ‘manual’ backgrounds. Their justifications of need provided the basis for comparisons on the basic themes of emotional response to requests for funds, to local versus overseas aid and to the relative roles of charity and state provision. It is argued that distinctions between the groups show the need to examine specific beliefs as well as generally held ideologies about charity. In addition, a further comparison of the groups is used to argue that they exemplify differences in the actual form of the gift relationship. These differences in form show the importance of examining charitable giving within specific social contexts, as well as with reference to the various ways of raising funds.     

Units of analysis and kinetic structure of behavioral repertoires

It is suggested that molar streams of behavior are constructed of various arrangements of three elementary constituents (elicited, evoked, and emitted response classes). An eight-cell taxonomy is elaborated as a framework for analyzing and synthesizing complex behavioral repertoires based on these functional units. It is proposed that the local force binding functional units into a smoothly articulated kinetic sequence arises from temporally arranged relative response probability relationships. Behavioral integration is thought to reflect the joint influence of the organism's hierarchy of relative response probabilities, fluctuating biological states, and the arrangement of environmental and behavioral events in time.     

A maximum likelihood method for latent class regression involving a censored dependent variable

The standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored. This model is generalized by developing a conditional mixture, maximum likelihood method for latent class censored regression. The proposed method simultaneously estimates separate regression functions and subject membership in K latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The proposed method is illustrated via a consumer psychology application.     

Category discrimination by pigeons using five polymorphous features

Eight pigeons were trained to discriminate between sets of color photographs of natural scenes. The scenes differed along five two-valued dimensions (site, weather, camera distance, camera orientation, and camera height), and all combinations of the feature values were used. One value of each dimension was designated as positive, and slides containing three or more positive feature values were members of the positive stimulus set. Thus, each feature had an equal, low, correlation with reinforcement, and all features had zero correlations with each other. Seven of the 8 pigeons learned this discrimination, and their responding came under the control of all five features. Within the positive and negative stimulus sets, response rates were higher to stimuli that contained more positive feature values. Once discrimination had been achieved, reversal training was given using a subset of the slides. In this subset, only a single feature was correlated with reinforcement. All pigeons learned this reversal successfully and generalized it to additional photographs with the same feature content. After reversal, the original reinforcement contingencies were reinstated, and training was continued using all the slides except those that had been used in reversal. Reversal generalized to these slides to some extent. Analysis of the response rates to individual slides showed that, compared with prereversal training, only the feature that had been subjected to reversal contingencies showed a reversed correlation with response rate. The remaining features showed the same correlation with response rate as they had before reversal training. Thus, reversal on some members of a category following category discrimination training led to generalization to stimuli within the category that were not involved in the reversal, but not to features that were not reversed. It is therefore inappropriate to refer to the pigeons as learning a concept.     

New lower and upper bounds for communality in factor analysis

We derive several relationships between communalities and the eigenvalues for ap ×p correlation matrix under the usual factor analysis model. For suitable choices ofj, _j (), where _j () is thej-th largest eigenvalue of , provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 - _p () improves on the use of squared mulitiple correlation coefficient as a lower bound.This research was done while the second author was at Tokyo Institute of Technology.     

Continuous and discrete latent structure models for item response data

Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.