Abstract
This paper tries to establish a connection between knowledge structures and latent class models. We will show that knowledge structures can be interpreted as a special type of constrained latent class model. Latent class models offer a well-founded theoretical framework to investigate the connection of a given latent class model to observed data. If we establish a connection between latent class models and knowledge structures, we can also use this framework in knowledge structure theory. We will show that the connection to latent class models offers us a possibility to construct a knowledge structure by exploratory data analysis from observed response patterns. Other possible applications are the empirical comparison of hypothetical knowledge structures and the statistical test of a given knowledge structure.
References
(1974). A new look at the statistical identification model. IEEE Transmission Auto Control,, 19, 716–723.
(1999). Knowledge spaces: Theories, empirical research, and applications. Mahwah, NJ: Erlbaum.
(1994). Construction of knowledge spaces for problem solving in chess. In , Contributions to mathematical psychology, psychometrics, and methodology (pp. 123–135). New York: Springer.
(1937). Rings of sets. Duke Mathematical Journal, 3, 443–454.
(1985). Thermodynamic approach to the traveling salesman problem: An efficient simulation algorithm. Journal of Optimization Theory and Applications, 45(1), 45–51.
(1995). Latent class models. In , Handbook of statistical modeling for the social and behavioral sciences (pp. 311–359). New York: Plenum Press.
(1994). Knowledge spaces and skill assignments. In , Contributions to mathematical psychology, psychometrics, and methodology (pp. 111–121). New York: Springer.
(1985). Spaces for the assessment of knowledge. International Journal of Man-Machine Studies, 23, 175–196.
(1998). Knowledge spaces. Berlin: Springer.
(1993). Applying the basis of a knowledge space for controlling the questioning of an expert. Journal of Mathematical Psychology, 37, 21–48.
(1996). On query procedures to build knowledge structures. Journal of Mathematical Psychology, 40, 160–168.
(1989). A latent trait via a stochastic learning theory for a knowledge space. Psychometrika, 54, 283–303.
(1988a). A class of stochastic procedures for assessing the state of a system. British Journal of Mathematical and Statistical Psychology, 41, 1–23.
(1988b). A Markovian procedure for assessing the state of a system. Journal of Mathematical Psychology, 32(2), 232–258.
(1990). Introduction to knowledge spaces: How to build, test and search them. Psychological Review, 97(2), 201–224.
(1976). L’analyse booleenne de questionaire. Paris: Mouton.
(1974a). The analysis of systems of qualitative variables when some of the variables are unobservable: Part I—A modified latent structure approach. American Journal of Sociology, 79, 1179–1259.
(1974b). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231.
(1978). Analysing qualitative/categorial variables: Loglinear models and latent structure analysis. Cambridge University Press. Cambridge, MA: Abt Books.
(1994). Knowledge assessment: Tapping human expertise by the QUERY routine. International Journal of Human-Computer Studies, 40, 119–151.
(1983). Optimization by simulated annealing. Science, 220, 671–680.
(1993). Extracting human expertise for constructing knowledge spaces: An algorithm. Journal of Mathematical Psychology, 37, 1–20.
(1990). How to build a knowledge space by querying an expert. Journal of Mathematical Psychology, 34, 311–331.
(1996). Kompetenz und Performanz beim Lösen von Geometrie-Aufgaben. Zeitschrift für Experimentelle Psychologie, 43, 279–318.
(1974). Item tree analysis. Nederlands Tijdschrift voor de Psychologie, 29, 475–484.
(2000). Algebraic representations of beliefs and attitudes II: Microbelief models for dichotomous belief data. Soziological Methodology, 30(1), 123–164.
(1987). Latent class analysis. Newbury Park, CA: Sage.
(1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21(6), 1087–1092.
(1970). A probabilistic formulation and statistical analysis of Guttman scaling. Psychometrika, 35, 73–78.
(1985). A note on Bayes factors for log-linear contingency table models with vague prior information. Journal of the Royal Statistical Society, Series B, 48, 249–250.
(1997). Applications of latent trait and latent class models in the social sciences. New York: Waxmann.
(1995). Modeling interindividual differences in solving letter series completion problems. Zeitschrift für Psychologie, 203, 173–188.
(1999a). Extracting knowledge structures from observed data. British Journal of Mathematical and Statistical Psychology, 52(2), 213–224.
(1999b). On the empirical construction of implications on bi-valued test items. Journal of Mathematical Social Sciences, 38(3), 361–375.
(2002). Explorative analysis of empirical data by Boolean analysis of questionnaires. Zeitschrift für Psychologie, 210(2), 99–109.
(2003). A method for the analysis of hierarchical dependencies between items of a questionnaire. Methods of Psychological Research, 8(1), 43–79.
(1995). A simulation study concerning the effect of errors on the establishment of knowledge spaces by querrying experts. Journal of Mathematical Psychology, 39, 376–382.
(1999). Component based construction of surmise relations for chess problems. In , Knowledge spaces: Theories, empirical research, and applications (pp. 41–66). Mahwah, NJ: Erlbaum.
(1978). Estimating the dimensions of a model. Annals of Statistics, 5(2), 461–464.
(1994). A dichotomization method for Boolean analysis of quantifiable co-occurence data. In , Contributions to mathematical psychology, psychometrics, and methodology New York: Springer.
(1998). Building a knowledge space via Boolean analysis of co-occurence data. In , Recent progress in mathematical psychology Hillsdale, NJ: Erlbaum.
(1991). Computerized knowledge assessment: Building the knowledge structure and calibrating the assessment routine Unpublished doctoral dissertation, New York University
(1999). Algebraic representations of beliefs and attitudes: Partial order models for item responses. Sociological Methodology, 29(1), 113–146.
