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.
Highlights
More than 50 years ago, Louis Guttman introduced his scalogram technique (Guttman 1944)
Three inductive item tree analysis (IITA) algorithms have been proposed for deriving implications from dichotomous data: the original IITA algorithm (Schrepp 2003), and the corrected and minimized corrected IITA algorithms (Sargin and Unlu 2009; Unluand Sargin 2010a)
Inductive item tree analysis algorithms in population values In Unluand Sargin (2010a), we introduce the population analogs of the diff fit measures, interpret the coefficients as maximum likelihood estimators (MLEs) for the corresponding population values, and show for the estimators the quality properties of asymptotic efficiency, asymptotic normality, asymptotic unbiasedness, and consistency
Summary
More than 50 years ago, Louis Guttman introduced his scalogram technique (Guttman 1944). Three inductive item tree analysis (IITA) algorithms have been proposed for deriving implications from dichotomous data: the original IITA algorithm (Schrepp 2003), and the corrected and minimized corrected IITA algorithms (Sargin and Unlu 2009; Unluand Sargin 2010a) These methods constitute the main part of the package DAKS and are implemented in sample and population quantities. Available software implementing the original IITA algorithm is ITA 2.0 by Schrepp (2006) Compared to this stand-alone software that runs only on Windows, the package DAKS is embedded in the comprehensive R computing environment and provides much more functionalities such as more flexible input/output features.
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