Abstract
Schrepp (2005) points out and builds upon the connection between knowledge space theory (KST) and latent class analysis (LCA) to propose a method for constructing knowledge structures from data. Candidate knowledge structures are generated, they are considered as restricted latent class models and fitted to the data, and the BIC is used to choose among them. This article adds additional information about the relationship between KST and LCA. It gives a more comprehensive overview of the literature and the probabilistic models that are at the interface of KST and LCA. KST and LCA are also compared with regard to parameter estimation and model testing methodologies applied in their fields. This article concludes with an overview of KST-related publications addressing the outlined connection and presents further remarks about possible future research arising from a connection of KST to other latent variable modeling approaches.
References
forthcoming, 2011). Knowledge spaces: Applications to education. Berlin, Germany: Springer.
(1999). Knowledge spaces: Theories, empirical research, and applications. Mahwah, NJ: Erlbaum.
(1982). Latent structure analysis: A survey. Scandinavian Journal of Statistics, 9, 1–12.
(1975). Discrete multivariate analysis: Theory and practice. Cambridge, MA: MIT Press.
(1973). Algorithms for minimization without derivatives. Englewood Cliffs, NJ: Prentice Hall.
(1991). Investigating Mokken scalability of dichotomous items by means of ordinal latent class analysis. British Journal of Mathematical and Statistical Psychology, 44, 315–331.
(1998). Latent class scaling analysis. Thousand Oaks, CA: Sage.
(1976). A probabilistic model for the validation of behavioral hierarchies. Psychometrika, 41, 189–204.
(1985). Spaces for the assessment of knowledge. International Journal of Man-Machine Studies, 23, 175–196.
(1999). Knowledge spaces. Berlin, Germany: Springer.
(1981). Finite mixture distributions. London, UK: Chapman and Hall.
(1989). A latent trait theory via a stochastic learning theory for a knowledge space. Psychometrika, 54, 283–303.
(2006). The assessment of knowledge, in theory and in practice. In , Formal Concept Analysis, 4th International Conference, ICFCA 2006, Dresden, Germany, Lecture Notes in Artificial Intelligence (pp. 61–79). Berlin, Heidelberg, and New York, NY: Springer.
(2010). Learning spaces. Berlin, Germany: Springer.
(1990). Introduction to knowledge spaces: How to build, test and search them. Psychological Review, 97, 201–224.
(1992). PRAXIS: Brent’s algorithm for function minimization. Behavior Research Methods, Instruments, and Computers, 24, 560–564.
(1978). Analysing qualitative/categorical variables: Loglinear models and latent structure analysis. Cambridge, MA: Cambridge University Press.
(1944). A basis for scaling qualitative data. American Sociological Review, 9, 139–150.
(1950). The basis for scalogram analysis. In , Measurement and prediction (pp. 60–90). Princeton, NJ: Princeton University Press.
(1979). Analysis of qualitative data. New developments, Vol. 2, New York, NY: Academic Press.
(1990). Categorical longitudinal data – Loglinear analysis of panel, trend and cohort data. Newbury Park, CA: Sage.
(1993). Loglinear models with latent variables. Newbury Park, CA: Sage.
(2002). Applied latent class analysis. Cambridge, MA: Cambridge University Press.
(1996). Latent class and discrete latent trait models: Similarities and differences. Thousand Oaks, CA: Sage.
(1968). Latent structure analysis. Boston, MA: Houghton Mifflin.
(1997). Hidden Markov models and other types of models for discrete-valued time series. London, UK: Chapman and Hall.
(2001). Latent class factor and cluster models, bi-plots and related graphical displays. Sociological Methodology, 31, 223–264.
(1987). Latent class analysis. Newbury Park, CA: Sage.
(1988). Mixture models: Inference and application to clustering. New York, NY: Marcel Dekker.
(2000). Finite mixture models. New York, NY: Wiley.
(1964). An efficient method for finding the minimum of a function in several variables without calculating derivatives. Computer Journal, 7, 155–162.
(1970). A probabilistic formulation and statistical analysis of Guttman scaling. Psychometrika, 35, 73–78.
(1988). Goodness-of-fit statistics for discrete multivariate data. New York, NY: Springer.
(2005). About the connection between knowledge structures and latent class models. Methodology, 1, 93–103.
(2004). Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. Boca Raton, FL: Chapman and Hall.
(2006). A logistic approach to knowledge structures. Journal of Mathematical Psychology, 50, 545–561.
(2009). Recovering a probabilistic knowledge structure by constraining its parameter space. Psychometrika, 74, 83–96.
(1985). Statistical analysis of finite mixture distributions. New York, NY: Wiley.
(2006). Estimation of careless error and lucky guess probabilities for dichotomous test items: A psychometric application of a biometric latent class model with random effects. Journal of Mathematical Psychology, 50, 309–328.
(2007). Nonparametric item response theory axioms and properties under nonlinearity and their exemplification with knowledge space theory. Journal of Mathematical Psychology, 51, 383–400.
(1997). Log-linear models for event histories. Thousand Oaks, CA: Sage.
(2000). Latent GOLD 2.0 user’s guide. Belmont, CA: Statistical Innovations.
(2004). Latent class analysis. In , The Sage encyclopedia of social science research methods (pp. 549–553). Thousand Oaks, CA: Sage.
(2001). A nonparametric random-coefficients approach: The latent class regression model. Multilevel Modelling Newsletter, 13, 6–13.
(