Investigating Dimensionality Dimensionality Dimensionality with - PowerPoint PPT Presentation

Investigating Investigating Investigating Dimensionality Dimensionality Dimensionality with with Investigating Dimensionality Mokken Analysis Mokken Analysis and CFA and CFA by means of Nader et al. Nader et al. Mokken Analysis Introduction Introduction Investigating Dimensionality Investigating Dimensionality Most common methods: Mokken Analysis Mokken Analysis and Automated Item Selection Automated Item Selection ◮ Principal Component Analysis (PCA) Procedure Procedure Confirmatory Factor Analysis Practical Example Practical Example ◮ Exploratory Factor Analysis (EFA) Attitudes Toward Suicide Attitudes Toward Suicide Results ◮ Confirmatory Factor Analysis (CFA) Results Mokken Analysis Mokken Analysis Confirmatory Factor Confirmatory Factor Ingo W. Nader, Ulrich S. Tran, Analysis Analysis Less common methods: Patricia Baranyai, Martin Voracek Discussion Discussion Conclusion Conclusion ◮ DIMTEST (Stout, Nandakumar, Junker, Chang, & Steidinger, 1992) University of Vienna ◮ DETECT (Zhang & Stout, 1999) ingo.nader@univie.ac.at ◮ Mokken Analysis (Mokken, 1971; Sijtsma & Molenaar, 2002) Psychoco 2012: International Workshop on Psychometric Computing University of Innsbruck, Austria February 10, 2012 1 / 27 2 / 27 Investigating Investigating Mokken Analysis Mokken Analysis Dimensionality Dimensionality with with Mokken Analysis Mokken Analysis and CFA and CFA Nader et al. Nader et al. A lot of favorable properties: Has already been used conjointly with PCA: Introduction Introduction ◮ has been around for some time Investigating Dimensionality Investigating Dimensionality ◮ unsurprisingly, by researchers from the Netherlands Mokken Analysis Mokken Analysis (Mokken, 1971; Sijtsma & Molenaar, 2002) Automated Item Selection Automated Item Selection Procedure (Wismeijer, Sijtsma, van Assen, & Vingerhoets, 2008) Procedure ◮ in the framework of nonparametric item response theory Practical Example Practical Example ◮ combined use was found to be beneficial ◮ can be applied to dichotomous or polytomous (ordinal) data Attitudes Toward Suicide Attitudes Toward Suicide in terms of these methods complementing each other Results Results ◮ empirically testable assumptions Mokken Analysis Mokken Analysis Confirmatory Factor Confirmatory Factor Analysis Analysis Can also be used conjointly with CFA: Discussion Discussion But hardly ever used: ◮ CFA offers well-established benchmarks to assess the fit of Conclusion Conclusion ◮ still rather unknown (except in the Netherlands) factor models (e.g., Hu & Bentler, 1999) ◮ sounds complicated – item response functions of unknown ◮ can make results comparable to prior research form? ◮ Mokken Analysis offers an“additional dimension”over ◮ results not easily comparable to“standard research” (exploratory/confirmatory) factor analysis ◮ no (commonly known) benchmarks for model fit 3 / 27 4 / 27

Investigating Investigating Mokken Analysis Automated Item Selection Procedure Dimensionality Dimensionality with with Mokken Analysis Mokken Analysis and CFA and CFA 1. select the two items to form a scale Nader et al. Nader et al. ◮ based on the Monotone Homogeneity Model (MHM; Mokken & ◮ that have the highest pairwise scalability coefficient H ij Introduction Introduction ◮ which has to be higher than a user-specified minimum value c Lewis, 1982; Sijtsma & Molenaar, 2002) Investigating Dimensionality Investigating Dimensionality Mokken Analysis Mokken Analysis (scalability criterion) ◮ assumptions: Automated Item Selection Automated Item Selection Procedure Procedure 2. from the remaining items, select the item ◮ unidimensional latent trait(s) Practical Example Practical Example ◮ that correlates positively with all items already in the scale ◮ monotonicity Attitudes Toward Suicide Attitudes Toward Suicide ◮ that has a pairwise scalability coefficient H ij > c with all ◮ local independence of responses Results Results Mokken Analysis Mokken Analysis items in the scale Confirmatory Factor Confirmatory Factor ◮ that maximizes the scale’s scalability coefficient H Analysis Analysis ◮ Mokken Analysis can be used to select items to scales in Discussion Discussion order to satisfy the MHM 3. repeat step 2 until no item satisfies these conditions Conclusion Conclusion ◮ by calculating scalability coefficients 4. start at step 1 to construct a second/third/. . . scale ◮ H ij for item pairs ◮ H i for single items in relation to their common scale ◮ repeat this procedure for increasing scalability criteria c ◮ H for the complete scale ◮ resulting in an increasing number of more and more clear-cut ◮ and using an automated item selection procedure scales (and more unscalable items) ◮ thereby revealing the dimensionality of the questionnaire 5 / 27 6 / 27 Investigating Investigating Practical Example Attitudes Toward Suicide Dimensionality Dimensionality with with Mokken Analysis Mokken Analysis and CFA and CFA Attitudes Toward Suicide Scale (Eskin, 2004) Nader et al. Nader et al. measures different factors (EFA): Introduction Introduction Practical/clinical relevance ◮ acceptability of suicide Investigating Dimensionality Investigating Dimensionality Mokken Analysis Mokken Analysis ◮ suicide as a sign of mental illness Especially the factor acceptability of suicide is important for Automated Item Selection Automated Item Selection Procedure Procedure suicide prevention, as higher acceptability . . . ◮ the belief that persons who commit suicide will be punished Practical Example Practical Example ◮ moderates the relationship between hopelessness and suicidal Attitudes Toward Suicide Attitudes Toward Suicide after death Results Results ideation (in men; Gibb, Andover, & Beach, 2006) ◮ the opinion that suicidal people should communicate their Mokken Analysis Mokken Analysis Confirmatory Factor Confirmatory Factor ◮ is linked to increased planning of suicidal actions in problems Analysis Analysis adolescents (Joe, Romer, & Jamieson, 2007) Discussion Discussion ◮ the intention to hide past suicidal behavior Conclusion Conclusion ◮ may be associated with higher suicide rates (Salander Renberg, ◮ the opinion that suicide should be discussed and reported Hjelmeland, & Koposov, 2008) openly among friends or in the news ◮ although findings remain debated (Beautrais, Horwood, & Fergusson, and maybe 2004; Salander Renberg et al., 2008) ◮ the view of suicide as a solution to one’s problems as found by another study using EFA (Eskin, Voracek, Stieger, & Altinyazar, 2011) . 7 / 27 8 / 27