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.

[1]  van der Ark,et al.  Mokken Scale Analysis in R , 2007 .

[2]  Luca Stefanutti,et al.  Recovering a Probabilistic Knowledge Structure by Constraining its Parameter Space , 2009 .

[3]  G. Birkhoff.  Rings of sets , 1937 .

[4]  L. Stefanutti.  A logistic approach to knowledge structures , 2006 .

[5]  Anne Boomsma,et al.  Essays on Item Response Theory , 2000 .

[6]  Dimitrios Rizopoulos.  ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses , 2006 .

[7]  Jean YH Yang,et al.  Bioconductor: open software development for computational biology and bioinformatics , 2004, Genome Biology.

[8]  Martin Schrepp,et al.  About the Connection Between Knowledge Structures and Latent Class Models , 2005 .

[9]  Jean-Claude Falmagne,et al.  Spaces for the Assessment of Knowledge , 1985, Int. J. Man Mach. Stud..

[10]  A. Ünlü.  A Note on the Connection Between Knowledge Structures and Latent Class Models , 2011 .

[11]  Fred S. Roberts,et al.  Applications of combinatorics and graph theory to the biological and social sciences , 1989 .

[12]  M. Petersen,et al.  Introduction to Nonparametric Item Response Theory , 2005, Quality of Life Research.

[13]  R. J. Mokken,et al.  Handbook of modern item response theory , 1997 .

[14]  William M. Bart,et al.  Ordering Theory: A New and Useful Measurement Model. , 1973 .

[15]  L. A. Goodman,et al.  Measures of association for cross classifications , 1979 .

[16]  Ali Ünlü,et al.  Inductive item tree analysis: Corrections, improvements, and comparisons , 2009, Math. Soc. Sci..

[17]  Keam-Claude Falmagne,et al.  A latent trait theory via a stochastic learning theory for a knowledge space , 1989 .

[18]  R. Hambleton,et al.  Handbook of Modern Item Response Theory , 1997 .

[19]  Martin Schrepp,et al.  ITA 2.0: A Program for Classical and Inductive Item Tree Analysis , 2006 .

[20]  Jean-Claude Falmagne,et al.  Knowledge assessment: tapping human expertise by the QUERY routine , 1994, Int. J. Hum. Comput. Stud..

[21]  Georg Rasch,et al.  Probabilistic Models for Some Intelligence and Attainment Tests , 1981, The SAGE Encyclopedia of Research Design.

[22]  Jean-Claude Falmagne,et al.  Knowledge spaces , 1998 .

[23]  Mark Huisman,et al.  Imputation of Missing Scale Data with Item Response Models , 2001 .

[24]  Michael S. Landy,et al.  Knowledge assessment: a comparison between human experts and computerized procedures , 1991 .

[25]  Stan Lipovetsky,et al.  Generalized Latent Variable Modeling: Multilevel,Longitudinal, and Structural Equation Models , 2005, Technometrics.

[26]  Neil Henry.  Latent structure analysis , 1969 .

[27]  WU Wirtschaftsuniversität,et al.  Generalized and Customizable Sets in R , 2009 .

[28]  Dietrich Albert,et al.  Knowledge Spaces: Theories, Empirical Research, and Applications , 1998 .

[29]  F. Krauss.  Latent Structure Analysis , 1980 .

[30]  Emden R. Gansner,et al.  An open graph visualization system and its applications to software engineering , 2000 .

[31]  A. Ünlü.  Nonparametric item response theory axioms and properties under nonlinearity and their exemplification with knowledge space theory , 2007 .

[32]  Jean-Claude Falmagne.  Probabilistic Knowledge Spaces: A Review , 1989 .

[33]  M. Villano,et al.  Introduction to knowledge spaces: How to build, test, and search them , 1990 .

[34]  Martin Schrepp,et al.  A Method for the Analysis of Hierarchical Dependencies between Items of a Questionnaire , 2003 .

[35]  David J. Krus,et al.  An Ordering-Theoretic Method to Determine Hierarchies Among Items , 1971 .

[36]  L. Guttman.  A basis for scaling qualitative data. , 1944 .

[37]  Robert J. Mokken,et al.  A Theory and Procedure of Scale Analysis. , 1973 .

[38]  A. Ünlü.  Estimation of careless error and lucky guess probabilities for dichotomous test items: A psychometric application of a biometric latent class model with random effects , 2006 .

[39]  George B. Macready,et al.  A probabilistic model for validation of behavioral hierarchies , 1976 .

[40]  Charles H. Proctor,et al.  A probabilistic formulation and statistical analysis of guttman scaling , 1970 .

[41]  Paul F. Lazarsfeld,et al.  Latent Structure Analysis. , 1969 .