![]() In MPT modeling, it is often of interest to estimate correlations between various MPT parameters or to relate MPT parameters to external covariates (e.g., Arnold et al., 2015, Calanchini et al., 2014, Heck and Moshagen, 2018, Heck, Thielmann, Moshagen, and Hilbig, 2018, Klein et al., 2017, Müller and Moshagen, 2018). As such, his contributions and more recent extensions of basic MPT models allow for the assessment of individual differences in cognitive processes. Batchelder played a pioneering role by early identifying the potential of MPT models with respect to the assessment of individual differences and made major contributions to the application of MPT models in the field of cognitive psychometrics (e.g., Batchelder, 2010, Batchelder and Riefer, 2007, Riefer et al., 2002). Such models are popular in psychology and beyond because their statistical properties are thoroughly understood (Riefer & Batchelder, 1988), they can easily be adapted to various research paradigms (for reviews, see Batchelder and Riefer, 1999, Erdfelder et al., 2009), and can be used as a measurement device to obtain information about latent processes and states that cannot be observed otherwise (Riefer & Batchelder, 1988). Multinomial processing tree (MPT) models are stochastic models that aim at explaining observed categorical data in terms of a finite number of underlying latent processes (Batchelder, 1998). However, adequately recovering correlations of MPT parameters generally requires a sufficiently large number of observations and sufficient heterogeneity. The results indicate the smallest bias regarding parameter–parameter correlations for the latent-trait approach and the corrected individual-model approach and the smallest bias regarding parameter-covariate correlations for the latent-trait regression and the corrected individual-model approach. Recovery performance was determined via a Monte Carlo simulation varying sample size, number of items, extent of heterogeneity, and magnitude of the true correlation. Regarding parameter-covariate correlations, we additionally considered the latent-trait regression. For parameter–parameter correlations, we considered two Bayesian hierarchical MPT models – the beta-MPT approach and the latent-trait approach – and two frequentist approaches that fit the data of each participant separately, either involving a correction for attenuation or not (corrected and uncorrected individual-model approach). ![]() The present study compares different approaches regarding their ability to estimate both types of correlations. These extensions enable the estimation of correlations among model parameters and correlations between model parameters and external covariates. Multinomial processing tree (MPT) models are a class of stochastic models for categorical data that have recently been extended to account for heterogeneity in individuals by assuming separate parameters per participant.
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