Methods Center

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"Representing probabilistic models of knowledge space theory by multinomial processing tree models"

Noventa Stefano and Daniel W. Heck, published in the Journal of Mathematical Psychology a proof of representation of basic probabilisitc models from Knowedge Structure Theory (specifically, the Basic Local Independence Model and the Simple Learning Model) within the general framework of Multinomial Processing Tree models. By highlighting such link and its implications for modeling violations of local stochastic independence in Item Response Theory, the authors hope to facilitate an exchange of theoretical results, statistical methods, and software across these different domains of mathematical psychology and psychometrics.

Heck*, D.W., Noventa*, S. (2020). Representing Probabilistic Models of
Knowledge Space Theory by Multinomial Processing Tree Models. Journal
of Mathematical Psychology, 96. DOI: 10.1016/j.jmp.2020.102329.


*shared co-first authorship

A New Nonlinear Dynamic Latent Variable Framework

Augustin Kelava and Holger Brandt published a new nonlinear dynamic latent class structural equation model (NDLC-SEM) framework in the Structural Equation Modeling Journal. The NDLC-SEM is capable of intra-individual psychological processes (e.g., changes in affective states as trajectories in mathematics studies), which for example could predict a drop-out. These processes are decomposed into parts which include individual-specific components (e.g., vulnerabilities, stable risk factors such as personality factors or cognitive abilities) and time-specific components. The NDLC-SEM acts as a very comprehensive framework that allows to integrate information of different data-levels and flexible relationships between variables (e.g., specific interactions).

Kelava, A. & Brandt, H. (2019). A nonlinear dynamic latent class structural equation model. Structural Equation Modeling: A Multidisciplinary Journal, 26(4), 509-528.  doi: 10.1080/10705511.2018.1555692