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.     

An eyewitness paradox

Two methods of analysing data from an identification parade give rise to seemingly contradictory outcomes, both of which reach statistical significance. The traditional method is based on the first choices of eyewitnesses, whereas the paired-comparison method takes account of each eyewitness's full rank ordering of the lineup participants. The person that most eyewitnesses pick out as the perpetrator of an offence (according to the first-choice method) may in fact be the person that those same eyewitnesses as a group regard as least likely to have committed the act (according to the paired-comparison method). Implications of the paradox for the analysis of lineup data are considered.     

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.     

Determination of a behavioral transfer function: White-noise analysis of session-to-session response-ratio dynamics on concurrent VI VI schedules

Six pigeons were exposed to concurrent variable-interval schedules in which the programmed reinforcer ratios changed from session to session according to a pseudorandom binary sequence. This procedure corresponded to the stochastic identification paradigm (“white-noise experiment”) of systems theory and enabled the relation between log response ratios in the current session and log reinforcer ratios in all previous sessions to be determined. Such dynamic relations are called linear transfer functions. Both nonparametric and parametric representations of these, in the form of “impulse-response functions,” were determined for each bird. The session-to-session response ratios resulting from the session-to-session pseudorandom binary variations in reinforcer ratios were well predicted by the impulse-response functions identified for each pigeon. The impulse-response functions were well fitted by a second-order dynamic model involving only two parameters: a time constant and a gain. The mean time constant was 0.67 sessions, implying that the effects of abrupt changes in log reinforcer ratios should be 96% complete within about five sessions. The mean gain was 0.53, which was surprisingly low inasmuch as it should equal the sensitivity to reinforcement ratio observed under steady-state conditions. The same six pigeons were subjected to a similar experiment 10 months following the first. Despite individual differences in impulse-response functions between birds within each experiment, the impulse-response functions determined from the two experiments were essentially the same.     

Molecular maximizing characterizes choice on Vaughan's (1981) procedure

Pigeons keypecked on a two-key procedure in which their choice ratios during one time period determined the reinforcement rates assigned to each key during the next period (Vaughan, 1981). During each of four phases, which differed in the reinforcement rates they provided for different choice ratios, the duration of these periods was four minutes, duplicating one condition from Vaughan's study. During the other four phases, these periods lasted six seconds. When these periods were long, the results were similar to Vaughan's and appeared compatible with melioration theory. But when these periods were short, the data were consistent with molecular maximizing (see Silberberg & Ziriax, 1982) and were incompatible with melioration, molar maximizing, and matching. In a simulation, stat birds following a molecular-maximizing algorithm responded on the short- and long-period conditions of this experiment. When the time periods lasted four minutes, the results were similar to Vaughan's and to the results of the four-minute conditions of this study; when the time periods lasted six seconds, the choice data were similar to the data from real subjects for the six-second conditions. Thus, a molecular-maximizing response rule generated choice data comparable to those from the short- and long-period conditions of this experiment. These data show that, among extant accounts, choice on the Vaughan procedure is most compatible with molecular maximizing.     

Choice between reliable and unreliable outcomes: mixed percentage-reinforcement in concurrent chains.

Pigeons' choices between alternatives that provided different percentages of reinforcement in mixed schedules were studied using the concurrent-chains procedure. In Experiment 1, the alternatives were terminal-link schedules that were equal in delay and magnitude of reinforcement, but that provided different percentages of reinforcement, with one schedule providing, reinforcement twice as reliably as the other. All pigeons preferred the more reliable schedule, and their level of preference was not systematically affected by variation in the absolute percentage values, or in the magnitude of reinforcement. In Experiment 2, preference for a schedule providing 100% reinforcement over one providing 33% reinforcement increased systematically with increases in the duration of the terminal links. In contrast, preference decreased systematically with increases in the duration of the initial links. Experiment 3 examined choice with equal percentages of reinforcement but unequal delays to reinforcement. Preference for the shorter delay to reinforcement was not systematically affected by variation in the absolute percentage of reinforcement. The overall pattern of results supported predictions based on an extension of the delay-reduction hypothesis to choice procedures involving mixed schedules of percentage reinforcement.     

Reply to silberberg and ziriax

Silberberg and Ziriax (1985) report that a modification of Vaughan's (1981) procedure produces results inconsistent with melioration (the position advocated by Vaughan) but consistent with a process they term molecular maximizing. Here it is argued that the theory of molecular maximization is not sufficiently unambiguous that researchers other than the developers can test its predictions, and that in any case none of the data presented by Silberberg and Ziriax are both clearly consistent with molecular maximization and inconsistent with melioration.     

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.