Ida Marais

Quantifying Local, Response Dependence Between Two Polytomous Items Using the Rasch Model

Models of modern test theory imply statistical independence among responses, generally referred to as local independence. One violation of local independence occurs when the response to one item governs the response to a subsequent item. Expanding on a formulation of this kind of violation as a process in the dichotomous Rasch model, this article generalizes the dependence process to the case of the unidimensional, polytomous Rasch model. It then shows how the magnitude of this violation can be estimated as a change in the location of thresholds separating adjacent categories in the second item caused by the response dependence on the first. As in the dichotomous model, it is suggested that this index is relatively more tangible in interpretation than other indices of dependence that are either a weight in the interaction term in a model or a correlation coefficient. One function of this method of assessing dependence is likely to be in the development of tests and assessment formats where evidence of the magnitude of dependence of one item on another in a pilot study can be used as part of the evidence in deciding which items will be retained in a final version of a test or which formats might need to be reconstructed. A second function might be to identify the magnitude of response dependence that may then need to be taken into account in some other way, perhaps by applying a model that takes account of the dependence.

Using a Theorem by Andersen and the Dichotomous Rasch Model to Assess the Presence of Random Guessing in Multiple Choice Items

Andersen (1995, 2002) proves a theorem relating variances of parameter estimates from samples and subsamples and shows its use as an adjunct to standard statistical analyses. The authors show an application where the theorem is central to the hypothesis tested, namely, whether random guessing to multiple choice items affects their estimates in the Rasch model. Taking random guessing to be a function of the difficulty of an item relative to the proficiency of a person, the authors describe a method for creating a subsample of responses, which is least likely to be affected by guessing. Then using Andersen’s theorem, the authors assess the difference in difficulty estimates between responses from the whole sample and the subsample for each item. To demonstrate the effectiveness of the procedure, data are simulated according to a class of models in which random guessing is a function of the proficiency of a person relative to the difficulty of an item. The procedure is also applied to an empirical data set from Raven’s Advanced Progressive Matrices, with the results indicating that guessing is present in a substantial number of items. It is noted that one especially important application in which estimating the correct relative difficulty of items is required is where the items will form part of an item bank and where on subsequent occasions the items will be administered interactively. In this case, items too difficult for a person are not administered and therefore unlikely to attract random guessing.

Patterns of graffiti offending: towards recognition that graffiti offending is more than ‘kids messing around’

Graffiti is often viewed as a nuisance ‘kids’ crime, an act of youthful resistance and, as such, it is sometimes given a lower policing prioritisation level than more ‘serious’ crimes. In this study, the three-year offending histories of 798 graffitists were extracted from the Western Australian Police Information Management System database. To address the studys aim of determining whether age-differentiated patterns of offending exist among three age-cohorts of offenders (i.e. preteens, adolescents and adults), the number of offences, the number of contacts with police, the type of offences and the rank category of each offence for each of the three age-cohort were calculated. The findings reveal that while 96 graffiti offenders had only one recorded graffiti offence, the majority of graffitists (n=702) were recidivist offenders involved in multiple crimes. The most prevalent crime among the recidivist preteen and early adolescent cohort of graffiti offenders was burglary; however, the recidivist late-adolescent and adult cohorts of graffiti offenders committed more violent and drug-related crimes.

A Rasch Model Analysis of the Mindful Attention Awareness Scale

The Mindful Attention Awareness Scale was developed to measure individual differences in the tendency to be mindful. The current study examined the psychometric properties of the Mindful Attention Awareness Scale in a heterogeneous sample of 565 nonmeditators and 612 meditators using the polytomous Rasch model. The results showed that some items did not function the same way for these two groups. Overall, meditators had higher mean estimates than nonmeditators. The analysis identified a group of items as highly discriminating. Using a different model, Van Dam, Earleywine, and Borders in 2010 identified the same group of items as highly discriminating, and concluded that they were the items with the most information. Multiple pieces of evidence from the Rasch analysis showed that these items discriminate highly because of local dependence, hence do not supply independent information. We discussed how these different conclusions, based on similar findings, result from two very different paradigms in measurement.

Person Proficiency Estimates in the Dichotomous Rasch Model When Random Guessing Is Removed From Difficulty Estimates of Multiple Choice Items

Andrich, Marais, and Humphry showed formally that Waller’s procedure that removes responses to multiple choice (MC) items that are likely to be guessed eliminates the bias in the Rasch model (RM) estimates of difficult items and makes them more difficult. The former did not study any consequences on the person proficiency estimates. This article shows that when the procedure is applied, the more proficient persons who are least likely to guess benefit by a greater amount than the less proficient, who are most likely to guess. This surprising result is explained by appreciating that the more proficient persons answer difficult items correctly at a greater rate than do the less proficient, even when the latter guess some items correctly. As a consequence, increasing the difficulty of the difficult items benefits them more than the less proficient persons. Analyses of a simulated and real example are shown illustratively. To not disadvantage the more proficient persons, it is suggested that Waller’s procedure be used when the RM is used to analyze MC items.

Not in my back schoolyard: schools and skate-park builds in Western Australia

Abstract Skate-parks serve as hang-out hubs for juveniles engaged in both lawful leisure pursuits (e.g. skateboarding, inline skating, bike/scooter riding and urban artistry) and illegal activities (e.g. graffiti-writing, underage drinking or substance abuse). Thus, proposed skate-park builds often can produce polarized community debate. Such debate typically focuses on issues relating to the potentiality for increased graffiti-tagging, noise, litter, and antisocial behaviour and the resultant fear that such actions might engender in the communitys more vulnerable members. This places city planners in the difficult position of having to decide whether to approve or not approve skate-park builds. This study reports on a common concern regarding skate-park builds namely whether their placement in close proximity to schools will increase the likelihood of graffiti attack. Correlation analysis of the annual removal costs for 355 schools located within Western Australia revealed that this graffiti-attack concern is unfounded as, regardless of school size or SES Index, there is no strong linear relationship between distance from skate-parks and number of graffiti incidents or yearly graffiti removal costs.

Making the grade: describing inherent requirements for the initial teacher education practicum

ABSTRACT This study explores the development, description, and illustration of inherent requirement (IR) statements to make explicit the requirements for performance on an initial teacher education (ITE) practicum. Through consultative group processes with stakeholders involved in ITE, seven IR domains were identified. From interviews with academics, first-person narratives (vignettes) were developed to illustrate pre-service teachers’ performance in complex professional practice scenarios. The narratives were rated by university staff and pre-service teachers in relation to three of the IR domains: self-awareness, social awareness, and sustained professional conduct. Narratives were placed along a continuum of performance using Rasch-model statistical analysis. The findings suggest that the IR domains and the narratives illustrating them could be valuable resources for making explicit required performance standards. The findings suggest that the development of explicit IR statements has the potential to improve all stakeholders’ awareness of professional practice requirements and enhance course outcomes for all ITE students.

Positive Mental Well-Being A Validation of a Rasch-Derived Version of the Warwick-Edinburgh Mental Well-Being Scale

This study presents a Rasch-derived short form of the Warwick-Edinburgh Mental Well-Being Scale for use as a screening tool in the general population. Data from 2,005 18- to 69-year-olds revealed problematic discrimination at specific thresholds. Estimation of model fit also deviated from Rasch model expectations. Following deletion of 4 items, the 10 remaining items indicated the data fitted the model. No items showed differential item functioning, thereby making comparisons of overall positive mental well-being for the different age, gender, and income groups valid and accurate. Cronbach’s alpha and Rasch Person Separation Index indicated a strong degree of reliability. Overall, the 10-item scale challenges researchers and clinicians to reconsider the assessment of positive mental well-being.

Controlling Guessing Bias in the Dichotomous Rasch Model Applied to a Large-Scale, Vertically Scaled Testing Program

Recent research has shown how the statistical bias in Rasch model difficulty estimates induced by guessing in multiple-choice items can be eliminated. Using vertical scaling of a high-profile national reading test, it is shown that the dominant effect of removing such bias is a nonlinear change in the unit of scale across the continuum. The consequence is that the proficiencies of the more proficient students are increased relative to those of the less proficient. Not controlling the guessing bias underestimates the progress of students across 7 years of schooling with important educational implications.

Differences between Mothers' and Fathers' Ratings of Family Functioning with the Family Assessment Device: The Validity of Combined Parent Scores.

The psychometric properties of the General Functioning subscale of the McMaster Family Assessment Device were examined using the Rasch Model (N = 237 couples). Mothers’ and fathers’ ratings of the General Functioning subscale of the McMaster Family Assessment Device are recommended, provided these are analyzed separately. More than a quarter of couples differed significantly in their ratings.