DAKS: AnRPackage for Data Analysis Methods in Knowledge Space Theory

Abstract

Knowledge space theory is part of psychometrics and provides a theoretical framework for the modeling, assessment, and training of knowledge. It utilizes the idea that some pieces of knowledge may imply others, and is based on order and set theory. We introduce the R package DAKS for performing basic and advanced operations in knowledge space theory. This package implements three inductive item tree analysis algorithms for deriving quasi orders from binary data, the original, corrected, and minimized corrected algorithms, in sample as well as population quantities. It provides functions for computing population and estimated asymptotic variances of and one and two sample Z tests for the diff fit measures, and for switching between test item and knowledge state representations. Other features are a function for computing response pattern and knowledge state frequencies, a data (based on a finite mixture latent variable model) and quasi order simulation tool, and a Hasse diagram drawing device. We describe the functions of the package and demonstrate their usage by real and simulated data examples.

Untangling comparison bias in inductive item tree analysis based on representative random quasi-orders

“…An explanation of this observation can be found in Sargin and Ünlü (2009) and Ünlü and Sargin (2010).…”

“…This yields a methodologically inconsistent estimate of t ij for some item pairs, especially when longer chains of items are present (for details, see Sargin and Ünlü, 2009;Ünlü and Sargin, 2010).…”

“…As proposed by Ünlü and Sargin (2010), a correct choice of t ij for i ̸ ≤ L j depends on whether j ̸ ≤ L i or j ≤ L i. Thus, a third distinct feature of the estimation of t ij is introduced.…”

“…The fit measure then favors quasi-orders that yield the smallest minimum discrepancies, or equivalently the largest maximum matches, between the observed and expected summaries, b ij and t ij , respectively. This optimum error rate can be expressed in closed analytical form in terms of the data matrix D and the quasi-order ≤ L (for further details, see Ünlü and Sargin, 2010). This can now be used in an alternative IITA procedure, the minimized corrected algorithm, where a minimized diff value is computed for every quasi-order generated according to the inductive construction procedure of the original and corrected algorithms.…”

“…This package was developed by Ünlü and Sargin (2010); see also Sargin and Ünlü (2010). It is available from the Comprehensive R Archive Network CRAN.Rproject.org/package=DAKS.…”