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Evaluating Manifest Monotonicity Using Bayes Factors.

Tijmstra J, Hoijtink H, Sijtsma K - Psychometrika (2015)

Bottom Line: We propose the use of Bayes factors to quantify the degree of support available in the data in favor of manifest monotonicity or against manifest monotonicity.Through the use of informative hypotheses, this procedure can also be used to determine the support for manifest monotonicity over substantively or statistically relevant alternatives to manifest monotonicity, rendering the procedure highly flexible.The performance of the procedure is evaluated using a simulation study, and the application of the procedure is illustrated using empirical data.

View Article: PubMed Central - PubMed

Affiliation: Department of Methodology and Statistics, Faculty of Social and Behavioral Sciences, Tilburg University, PO Box 90153, 5000 LE , Tilburg, The Netherlands. j.tijmstra@uvt.nl.

ABSTRACT
The assumption of latent monotonicity in item response theory models for dichotomous data cannot be evaluated directly, but observable consequences such as manifest monotonicity facilitate the assessment of latent monotonicity in real data. Standard methods for evaluating manifest monotonicity typically produce a test statistic that is geared toward falsification, which can only provide indirect support in favor of manifest monotonicity. We propose the use of Bayes factors to quantify the degree of support available in the data in favor of manifest monotonicity or against manifest monotonicity. Through the use of informative hypotheses, this procedure can also be used to determine the support for manifest monotonicity over substantively or statistically relevant alternatives to manifest monotonicity, rendering the procedure highly flexible. The performance of the procedure is evaluated using a simulation study, and the application of the procedure is illustrated using empirical data.

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Related in: MedlinePlus

The item response functions of the three items that were analyzed.
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Fig1: The item response functions of the three items that were analyzed.

Mentions: To facilitate the comparison of the proposed procedure to that of existing methods for evaluating latent monotonicity, conditions similar to those discussed by Tijmstra et al. (2013) were used in a simulation study. In this way, the decisions that would be made using the proposed method could be compared to those that would be made using the order-constrained hypothesis test discussed by Tijmstra et al. (2013). The procedure was used to assess manifest monotonicity for three items, corresponding to three different relevant scenarios: A ‘normal’ item with a monotone IRF that discriminates well, a weakly discriminating item with a monotone but nearly flat IRF, and an item with a locally nonmonotone IRF (Figure 1). For convenience, we label these three items ‘monotone item’, ‘weak item’, and ‘nonmonotone item’, respectively. The monotone item represents a typical desirable item that provides a useful contribution to the test, the weak item represents an item that contributes little to the reliable ordering of persons but does not violate latent monotonicity, and the nonmonotone item represents a problematic item that should not be included in the test.


Evaluating Manifest Monotonicity Using Bayes Factors.

Tijmstra J, Hoijtink H, Sijtsma K - Psychometrika (2015)

The item response functions of the three items that were analyzed.
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4644216&req=5

Fig1: The item response functions of the three items that were analyzed.
Mentions: To facilitate the comparison of the proposed procedure to that of existing methods for evaluating latent monotonicity, conditions similar to those discussed by Tijmstra et al. (2013) were used in a simulation study. In this way, the decisions that would be made using the proposed method could be compared to those that would be made using the order-constrained hypothesis test discussed by Tijmstra et al. (2013). The procedure was used to assess manifest monotonicity for three items, corresponding to three different relevant scenarios: A ‘normal’ item with a monotone IRF that discriminates well, a weakly discriminating item with a monotone but nearly flat IRF, and an item with a locally nonmonotone IRF (Figure 1). For convenience, we label these three items ‘monotone item’, ‘weak item’, and ‘nonmonotone item’, respectively. The monotone item represents a typical desirable item that provides a useful contribution to the test, the weak item represents an item that contributes little to the reliable ordering of persons but does not violate latent monotonicity, and the nonmonotone item represents a problematic item that should not be included in the test.

Bottom Line: We propose the use of Bayes factors to quantify the degree of support available in the data in favor of manifest monotonicity or against manifest monotonicity.Through the use of informative hypotheses, this procedure can also be used to determine the support for manifest monotonicity over substantively or statistically relevant alternatives to manifest monotonicity, rendering the procedure highly flexible.The performance of the procedure is evaluated using a simulation study, and the application of the procedure is illustrated using empirical data.

View Article: PubMed Central - PubMed

Affiliation: Department of Methodology and Statistics, Faculty of Social and Behavioral Sciences, Tilburg University, PO Box 90153, 5000 LE , Tilburg, The Netherlands. j.tijmstra@uvt.nl.

ABSTRACT
The assumption of latent monotonicity in item response theory models for dichotomous data cannot be evaluated directly, but observable consequences such as manifest monotonicity facilitate the assessment of latent monotonicity in real data. Standard methods for evaluating manifest monotonicity typically produce a test statistic that is geared toward falsification, which can only provide indirect support in favor of manifest monotonicity. We propose the use of Bayes factors to quantify the degree of support available in the data in favor of manifest monotonicity or against manifest monotonicity. Through the use of informative hypotheses, this procedure can also be used to determine the support for manifest monotonicity over substantively or statistically relevant alternatives to manifest monotonicity, rendering the procedure highly flexible. The performance of the procedure is evaluated using a simulation study, and the application of the procedure is illustrated using empirical data.

Show MeSH
Related in: MedlinePlus