DAKS: An R Package for Data Analysis Methods in Knowledge Space Theory

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.

Statistics and Data with R: An Applied Approach Through Examples

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Inductive item tree analysis: Corrections, improvements, and comparisons

There are various methods in knowledge space theory for building knowledge structures or surmise relations from data. Few of them have been thoroughly analyzed, making difficult to decide which of these methods provide good results and when to apply each of the methods. In this paper, we investigate the method inductive item tree analysis and discuss the advantages and disadvantages of this algorithm. In particular, we introduce some corrections and improvements to it, resulting in two newly proposed algorithms. These algorithms and the original inductive item tree analysis procedure are compared in a simulation study and with empirical data

Mosaics for Visualizing Knowledge Structures

Mosaic plots are state-of-the-art graphics for multivariate categorical data. Knowledge structures are mathematical models that belong to the theory of knowledge spaces in psychometrics. This paper presents an application of mosaic plots to psychometric data arising from underlying knowledge structure models. In simulation trials, the scope of this graphing method in knowledge space theory is investigated

Data Analysis Methods in Knowledge Space Theory

This work deals with data analysis methods in knowledge space theory (KST). In Chapter 2, the main deterministic and probabilistic concepts of KST are introduced. The data analysis methods, Inductive item tree analysis (IITA) and its two enhancements, corrected and minimized corrected IITA, are thoroughly discussed. The IITA algorithms are compared in two simulation studies and with real datasets. We introduce maximum likelihood methodology for the IITA methods. It is shown that these fit measures have several asymptotic quality properties. The R package DAKS is presented, and the use of the package's functions are illustrated with examples. Finally, important directions for future research are presented.Die vorliegende Arbeit beschäftigt sich mit datenanalytischen Verfahren in der Wissensraumtheorie. Es werden die deterministischen und stochastischen Grundlagen der Wissensraumtheorie eingeführt und datenanalytische Verfahren analysiert. Schwerpunkt hierbei sind die drei Inductive Item Tree Analysis (IITA) Algorithmen, wobei zwei im Rahmen dieser Dissertation eingeführt wurden. Die drei IITA-Verfahren werden in Simulationsstudien und anhand von realen Daten verglichen. Es wird Maximum-Likelihood Theorie für die IITA-Verfahren vorgestellt und gezeigt, dass es sich bei den vorliegenden Fit-Maßen um Maximum-Likelihood Schätzer, mit einer Reihe positiver Güteeigenschaften, handelt. Das im Rahmen der Dissertation entwickelte R Paket DAKS wird vorgestellt und analysiert. Abschließend werden mögliche weitere Forschungsrichtungen diskutiert

Interactive visualization of assessment data: The software package Mondrian

Mondrian is state-of-the-art statistical data visualization software featuring modern interactive visualization techniques for a wide range of data types. This paper reviews the capabilities, functionality, and interactive properties of this software package. Key features of Mondrian are illustrated with data from the Programme for International Student Assessment (PISA) and for item analysis applications

Maximum likelihood methodology for diff fit measures for quasi orders

Three inductive item tree analysis algorithms have been proposed for deriving quasi orders from dichotomous data. These procedures have been treated descriptively, without examining theory. In this paper, we introduce maximum likelihood methodology for the inductive item tree analysis methods. The diff fit measures of these methods can be interpreted as maximum likelihood estimators. We show that the estimators are asymptotically efficient, and hence they are asymptotically normal, asymptotically unbiased, and consistent. In simulation studies, the algorithms are compared regarding finite sample consistency, population ranks, and population symmetric differences. The approach to fit measures presented in this paper can be applied to any, sufficiently smooth, coefficient for multinomial count data. In particular, it allows introducing maximum likelihood methodology for measures assessing the fit of general knowledge structures

Inductive item tree analysis: Corrections, improvements, and comparisons

There are various methods in knowledge space theory for building knowledge structures or surmise relations from data. Few of them have been thoroughly analyzed, making it difficult to decide which of these methods provides good results and when to apply each of the methods. In this paper, we investigate the method known as inductive item tree analysis and discuss the advantages and disadvantages of this algorithm. In particular, we introduce some corrections and improvements to it, resulting in two newly proposed algorithms. These algorithms and the original inductive item tree analysis procedure are compared in a simulation study and with empirical data.Inductive item tree analysis Knowledge space theory Deriving surmise relations