The Best of Both Worlds: Factor Analysis of Dichotomous Data Using Item Response Theory and Structural Equation Modeling

Glöckner-Rist, Angelika; Hoijtink, Herbert

doi:10.1207/s15328007sem1004_4

Cited by 124 publications

(79 citation statements)

References 33 publications

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“…This suggests that using polychoric correlations in factor analysis may be a substantial improvement, but may not fully overcome the base rate dependence of using dichotomous data. Item Response Theory and Structural Equation Modelling for dichotomous data have also been proposed as alternative approaches for factor analysis of dichotomous items (Glockner-Rist & Hoijtink, 2003;Yang, Lu, & Qiao, 2014).…”

Section: Recommendationsmentioning

confidence: 99%

The influence of base rates on correlations: An evaluation of proposed alternative effect sizes with real-world data

Babchishin

Helmus²

2015

Behav Res

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Correlations are the simplest and most commonly understood effect size statistic in psychology. The purpose of the current paper was to use a large sample of real-world data (109 correlations with 60,415 participants) to illustrate the base rate dependence of correlations when applied to dichotomous or ordinal data. Specifically, we examined the influence of the base rate on different effect size metrics. Correlations decreased when the dichotomous variable did not have a 50 % base rate. The higher the deviation from a 50 % base rate, the smaller the observed Pearson's point-biserial and Kendall's tau correlation coefficients. In contrast, the relationship between base rate deviations and the more commonly proposed alternatives (i.e., polychoric correlation coefficients, AUCs, Pearson/Thorndike adjusted correlations, and Cohen's d) were less remarkable, with AUCs being most robust to attenuation due to base rates. In other words, the base rate makes a marked difference in the magnitude of the correlation. As such, when using dichotomous data, the correlation may be more sensitive to base rates than is optimal for the researcher's goals. Given the magnitude of the association between the base rate and point-biserial correlations (r = −.81) and Kendall's tau (r = −.80), we recommend that AUCs, Pearson/Thorndike adjusted correlations, Cohen's d, or polychoric correlations should be considered as alternate effect size statistics in many contexts.

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Section: Recommendationsmentioning

confidence: 99%

The influence of base rates on correlations: An evaluation of proposed alternative effect sizes with real-world data

Babchishin

Helmus²

2015

Behav Res

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“…Previous studies on the relationship between the FA and IRT frameworks showed that the unidimensional two-parameter normal ogive IRT model is equivalent to a onefactor FA model when binary manifest variables are predicted by a continuous latent variable (e.g., Brown 2006;Ferrando and Lorenzo-Seva 2005;Glöckner-Rist and Hoijtink 2003;MacIntosh and Hashim 2003;Takane and de Leeuw 1987). The two-parameter normal ogive IRT model can be written as…”

Section: Irt and Factor Analysismentioning

confidence: 99%

“…As Brown (2006) noted, the use of the FA model provides greater analytic flexibility than the IRT framework because traditional IRT models can be embedded within a larger model that includes additional variables to explain the item parameters as well as the latent trait (e.g., Glöckner-Rist and Hoijtink 2003;Lu et al 2005). Using the structural equation modeling (SEM) framework, an IRT model can be defined as a measurement model in which there is a latent trait (e.g., reading ability) underlying a set of manifest variables (e.g., dichotomous items in a reading assessment).…”

Section: Modeling Position Effectsmentioning

confidence: 99%

A structural equation modeling approach for examining position effects in large-scale assessments

Bulut

Quo

Gierl

2017

Large-scale Assess Educ

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“…All the methods discussed in this study were applied to dichotomous data. The majority of the IRT models handle dichotomous data (Hambleton & Swaminathan, 1985, p.34): 1 for correct response and 0 for incorrect response (Glöckner-Rist & Hoijtink, 2003).…”

Section: Common Assumptions and Data Descriptionmentioning

confidence: 99%

Are all the item response functions monotonically increasing?

Wang¹

2012

PsycEXTRA Dataset

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Item response functions of the parametric logistic IRT models follow the logistic form which is monotonically increasing. However, item response functions of some real items are nonmonotonic which might lead to examinees with lower proficiency levels receiving higher scores. This study compared three nonparametric IRF estimation methods-the nonparametric smooth regression method, the item-ability regression method, and the B-spline nonparametric IRF method-to determine whether they could detect the nonmonotonic IRF accurately using simulated data. In addition, these methods were used to identify items with nonmonotonic IRFs on real assessments. Results present that three nonparametric methods can detect the nonmonotonic IRF equally and each real assessment has some items with nonmonotonic IRFs.Investigations on the reasons for and the consequences of the nonmonotonicity were conducted for several items and indicate that the nonmonotonicity can affect the fairness and comparability of the test score. Thus, the nonmonotonicity should be checked before applying the parametric logistic models.iv Acknowledgments

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The Best of Both Worlds: Factor Analysis of Dichotomous Data Using Item Response Theory and Structural Equation Modeling

Cited by 124 publications

References 33 publications

The influence of base rates on correlations: An evaluation of proposed alternative effect sizes with real-world data

The influence of base rates on correlations: An evaluation of proposed alternative effect sizes with real-world data

A structural equation modeling approach for examining position effects in large-scale assessments

Are all the item response functions monotonically increasing?

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