A note on monotonicity of item response functions for ordered polytomous item response theory models

A monotone relationship between a true score (τ) and a latent trait level (θ) has been a key assumption for many psychometric applications. The monotonicity property in dichotomous response models is evident as a result of a transformation via a test characteristic curve. Monotonicity in polytomous models, in contrast, is not immediately obvious because item response functions are determined by a set of response category curves, which are conceivably non-monotonic in θ. The purpose of the present note is to demonstrate strict monotonicity in ordered polytomous item response models. Five models that are widely used in operational assessments are considered for proof: the generalized partial credit model (Muraki, 1992, Applied Psychological Measurement, 16, 159), the nominal model (Bock, 1972, Psychometrika, 37, 29), the partial credit model (Masters, 1982, Psychometrika, 47, 147), the rating scale model (Andrich, 1978, Psychometrika, 43, 561), and the graded response model (Samejima, 1972, A general model for free-response data (Psychometric Monograph no. 18). Psychometric Society, Richmond). The study asserts that the item response functions in these models strictly increase in θ and thus there exists strict monotonicity between τ and θ under certain specified conditions. This conclusion validates the practice of customarily using τ in place of θ in applied settings and provides theoretical grounds for one-to-one transformations between the two scales.     

A precursor to the relational evaluation procedure: searching for the contextual cues that control equivalence responding.

The precursor to the relational evaluation procedure (pREP) is a go/no-go successive discrimination procedure for examining stimulus equivalence. Previous research has shown that it does not readily produce equivalence responding unless some matching-to-sample (MTS) procedures are incorporated into the experimental sequence. Two experiments attempted to identify contextual cues that would generate equivalence responding on the pREP. Experiment 1 examined the effects of using abstract symbols or various verbal labels as response options on the pREP. Only the words same and different, when used as response options, reliably produced equivalence responding across 4 subjects. Experiment 2 examined different pretraining preparations designed to attach the functions of the words same and different to abstract symbols that could then be used as response options on the pREP. The most effective pretraining procedure involved multiple-exemplar training during which subjects were trained to respond to abstract symbols in the presence of pairs of stimuli that were either formally the same or different. The abstract symbols were subsequently used as response options with the pREP, and all subjects reliably demonstrated equivalence responding. The findings suggest that the relations of same and different may be fundamental to equivalence responding. These findings are discussed in terms of what they suggest about the nature of the equivalence phenomenon specifically and derived relational responding more generally.     

The person response function as a tool in person-fit research

Item responses that do not fit an item response theory (IRT) model may cause the latent trait value to be inaccurately estimated. In the past two decades several statistics have been proposed that can be used to identify nonfitting item score patterns. These statistics all yieldscalar values. Here, the use of the person response function (PRF) for identifying nonfitting item score patterns was investigated. The PRF is afunction and can be used for diagnostic purposes. First, the PRF is defined in a class of IRT models that imply an invariant item ordering. Second, a person-fit method proposed by Trabin & Weiss (1983) is reformulated in a nonparametric IRT context assuming invariant item ordering, and statistical theory proposed by Rosenbaum (1987a) is adapted to test locally whether a PRF is nonincreasing. Third, a simulation study was conducted to compare the use of the PRF with the person-fit statistic ZU3. It is concluded that the PRF can be used as a diagnostic tool in person-fit research.The authors are grateful to Coen A. Bernaards for preparing the figures used in this article, and to Wilco H.M. Emons for checking the calculations.     

Marginal maximum likelihood estimation of item response theory (IRT) equating coefficients for the common-examinee design

A method of estimating item response theory (IRT) equating coefficients by the common-examinee design with the assumption of the two-parameter logistic model is provided. The method uses the marginal maximum likelihood estimation, in which individual ability parameters in a common-examinee group are numerically integrated out. The abilities of the common examinees are assumed to follow a normal distribution but with an unknown mean and standard deviation on one of the two tests to be equated. The distribution parameters are jointly estimated with the equating coefficients. Further, the asymptotic standard errors of the estimates of the equating coefficients and the parameters for the ability distribution are given. Numerical examples are provided to show the accuracy of the method.     

品牌态度强度与品牌态度可达性的关系性质

运用态度量表和反应时实验比较了品牌态度强度与品牌态度可达性的关系性质。研究发现,女性被试对保健品品牌要素的态度评价越肯定,态度通达和提取的时间就越快,两者之间形成有规律的函数关系;但在否定性态度条件下,没有出现类似的规律性;当要求被试把模糊性态度明确为肯定或否定态度时,67％的被试明确为否定态度,但所用时间显著慢于明确为肯定态度所用的时间     

Perfectionism and psychological distress: evidence of the mediating effects of rumination

Three studies investigated the role of ruminative tendencies in mediating the effects of multidimensional perfectionism (Hewitt & Flett, 1991) on psychological distress. Study 1 (Sample 1, N = 279; Sample 2, N = 224) and Study 2 (N = 205) found evidence, cross‐sectionally and prospectively, that brooding ruminative response style either fully or partially mediated the effects of socially prescribed and self‐oriented perfectionism on psychological distress, depression and hopelessness levels. In addition, Study 3 (N = 163) confirmed these mediation effects for socially prescribed perfectionism in relation to depression and hopelessness, 2 months later, after initial levels of distress were controlled. Overall, these findings provide evidence that brooding ruminative response style is an important mechanism that can explain, in part, the relationship between perfectionism and distress. Copyright © 2006 John Wiley & Sons, Ltd.     

Assessing and treating vocal stereotypy in children with autism

Previous research implies that stereotypic behavior tends to be maintained by the sensory consequences produced by engaging in the response. Few investigations, however, have focused on vocal stereotypy. The current study examined the noncommunicative vocalizations of 4 children with an autism spectrum disorder. First, functional analyses were conducted in an attempt to identify the function of each child's behavior. For each of the participants, it was found that vocal stereotypy was likely not maintained by the social consequences. Following assessment, response interruption and redirection (RIRD) was implemented in an ABAB design to determine whether vocal stereotypy could be successfully redirected. RIRD involved a teacher issuing a series of vocal demands the child readily complied with during regular academic programming. Vocal demands were presented contingent on the occurrence of vocal stereotypy and were continuously presented until the child complied with three consecutively issued demands without emitting vocal stereotypy. For each child, RIRD produced levels of vocal stereotypy substantially lower than those observed in baseline. For 3 of the children, an increase in appropriate communication was also observed. The children's teachers were trained to implement RIRD. Brief follow-up probes and anecdotal information implied that the treatment had a positive impact in the natural environment.     

Response induction during the acquisition and maintenance of lever pressing with delayed reinforcement

The acquisition of lever pressing by rats and the occurrence of unreinforced presses at a location different from that of the reinforced response were studied using different delays of reinforcement. An experimental chamber containing seven identical adjoining levers was used. Only presses on the central (operative) lever produced food pellets. Groups of 3 rats were exposed to one of seven different tandem random-interval (RI) fixed-time (FT) schedules. The average RI duration was the complement of the FT duration such that their sum yielded a nominal 32-s interreinforcement interval on average. Response rate on the operative lever decreased as the FT value was lengthened. The spatial distribution of responses on the seven levers converged on the operative lever when the FT was 0 or 2 s and spread across the seven levers as the FT value was lengthened to 16 or 32 s. Presses on the seven levers were infrequent during the FT schedule. Both operative- and inoperative-lever pressing intertwined in repetitive patterns that were consistent within subjects but differed between subjects. These findings suggest that reinforcer delay determined the response-induction gradient.     

Aging and intraindividual variability in performance: analyses of response time distributions

It has been suggested that older adults are more variable in their performance because they are more prone to lapses of either attention or intention. In the present experiment, 9 young and 9 older adults each performed nearly 2000 trials of a same-different judgment task. As expected, older adults were slower and more variable than young adults. When the age-related difference in speed was taken into account, however, the older adults were, if anything, less variable than the young adults. When younger and older adults' RT distributions were analyzed using quantile-quantile plots and by fitting ex-Gaussian and Weibull functions, there was no consistent evidence that older adults' distributions were more skewed than young adults', as would be predicted by age-related increases in lapses of attention or intention. Importantly, there was a positive, linear relation between RT and intraindividual variability, and the same relation was observed both within subjects (practice increased speed and reduced variability) as well as between subjects (regardless of age, slower individuals were more variable). Thus, the present results suggest that there may be a general law governing the relation between average RT and variability, and that the greater performance variability of older adults primarily reflects their greater average RTs.