Abstract
A weighted version of the tau-equivalent model of measurement is proposed for overcoming a shortcoming of the original and essential versions of this model resulting from the assumption of equal true scores. Because of this assumption the original version cannot be expected to do well in items with considerably varying variances. The proposed version includes weights reflecting the easiness of items. In a small simulation study the original and weighted versions of the model were applied to items characterized by variances of either equal or varying sizes for demonstrating the usefulness of the weighted version. As expected, only the weighted version of the tau-equivalent model did well in all item sets. Furthermore, the results obtained by the weighted version in combination with maximum likelihood estimation appeared to be closer to the expectations than the results obtained by asymptotic distribution-free estimation and robust estimation.
Highlights
The tau-equivalent model of measurement was proposed in combination with the model of parallel measurements in the context of true-score theory (Lord & Novick, 1968, p. 47-50)
A weighted version of the tau-equivalent model of measurement is proposed for overcoming a shortcoming of the original and essential versions of this model resulting from the assumption of equal true scores
The tau-equivalent model of measurement was considered for confirmatory factor analysis (Alwin & Jackson, 1980), it has not developed into the standard model of measurement of this procedure
Summary
The tau-equivalent model of measurement was proposed in combination with the model of parallel measurements in the context of true-score theory (Lord & Novick, 1968, p. 47-50). G., Chen, West, & Sousa, 2006; Mulaik & Quartelli, 1997; Reise, Morizot, & Hays, 2007) is an important step since it acknowledges that many measures stimulate method effects in addition to the ability or trait of interest This model proved to be especially useful in the investigation of the item wording effect (DiStefano, & Motl, 2006; Vautier, Raufaste, & Cariou, 2003). The position effect is an example of such an overlap since all the items are affected and even worse there is an increasing effect from the first to last items (Hartig, Holzel, & Moosbrugger, 2007; Schweizer, 2012) In this situation the constraint of the factor loadings associated with the true scores can be very useful in separating the components due to the method effect and due to the ability or trait of interest
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Statistics and Probability
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
