Testing the Within-State Distribution in Mixture Models for Responses and Response Times

Mixture models have been developed to enable detection of within-subject differences in responses and response times to psychometric test items. To enable mixture modeling of both responses and response times, a distributional assumption is needed for the within-state response time distribution. Since violations of the assumed response time distribution may bias the modeling results, choosing an appropriate within-state distribution is important. However, testing this distributional assumption is challenging as the latent within-state response time distribution is by definition different from the observed distribution. Therefore, existing tests on the observed distribution cannot be used. In this article, we propose statistical tests on the within-state response time distribution in a mixture modeling framework for responses and response times. We investigate the viability of the newly proposed tests in a simulation study, and we apply the test to a real data set

Burgerschap in het basisonderwijs:Technisch rapport Peil.Burgerschap 2020

Ruimte voor verbetering burgerschapscompetentiesHet niveau van burgerschapscompetenties, burgerschapskennis en -houdingen van groep 8-leerlingen blijkt anno 2020 niet onverdeeld gunstig. Zo beantwoordde een kwart van de leerlingen driekwart van de kennisvragen fout. Een kwart de leerlingen beantwoordde ten minste de helft van de kennisvragen goed. Het niveau van burgerschapskennis van leerlingen blijkt vergeleken met 2009 wat lager. De meerderheid van de leerlingen scoort relatief laag op burgerschapshoudingen.Omvangrijk onderzoek in het basisonderwijsDit blijkt uit Peil.burgerschap, een omvangrijk onderzoek, uitgevoerd door de afdeling Pedagogische en Onderwijswetenschappen van de Universiteit van Amsterdam, het Kohnstamm Instituut, het GION van de Rijksuniversiteit Groningen en het Cito. Aan het onderzoek deden 2.237 groep 8-leerlingen mee van 94 basisscholen. Gegevens zijn verzameld onder leerlingen, leerkrachten en schoolleiders. Peil.burgerschap geeft inzicht in de burgerschapscompetenties van leerlingen en het burgerschapsonderwijs aan het einde van het basisonderwijs. Het maakt onderdeel uit van Peil.onderwijs: een serie periodieke onderzoeken onder de regie van de Inspectie van het Onderwijs naar domeinen van onderwijskwaliteit

Standard errors and confidence intervals for scalability coefficients in Mokken scale analysis using marginal models

Mokken scale analysis is a popular method for scaling dichotomous and polytomous items. Whether or not items form a scale is determined by three types of scalability coefficients: (1) for pairs of items, (2) for items, and (3) for the entire scale. It has become standard practice to interpret the sample values of these scalability coefficients using Mokken’s guidelines, which have been available since the 1970s. For valid assessment of the scalability coefficients, the standard errors of the scalability coefficients must be taken into account. So far, standard errors were not available for scales consisting of Likert items, the most popular item type in sociology, and standard errors could only be computed for dichotomous items if the number of items was small. This study solves these two problems. First, we derived standard errors for Mokken’s scalability coefficients using a marginal modeling framework. These standard errors can be computed for all types of items used in Mokken scale analysis. Second, we proved that the method can be applied to scales consisting of large numbers of items. Third, we applied Mokken scale analysis to a set of polytomous items measuring tolerance. The analysis showed that ignoring standard errors of scalability coefficients might result in incorrect inferences. Keywords: Mokken scale analysis, standard errors, scalability coefficients, marginal models

Testing hypotheses involving Cronbach's alpha using marginal models

We discuss the statistical testing of three relevant hypotheses involving Cronbach's alpha: one where alpha equals a particular criterion; a second testing the equality of two alpha coefficients for independent samples; and a third testing the equality of two alpha coefficients for dependent samples. For each of these hypotheses, various statistical tests have been proposed. Over the years, these tests have depended on progressively fewer assumptions. We propose a new approach to testing the three hypotheses that relies on even fewer assumptions, is especially suited for discrete item scores, and can be applied easily to tests containing large numbers of items. The new approach uses marginal modelling. We compared the Type I error rate and the power of the marginal modelling approach to several of the available tests in a simulation study using realistic conditions. We found that the marginal modelling approach had the most accurate Type I error rates, whereas the power was similar across the statistical tests