Biomaterial Database

Multilevel IRT using dichotomous and polytomous response data. 2005

J-P Fox

Department of Research Methodology, Measurement and Data Analysis, University of Twente, The Netherlands. fox@edte.utwente.nl

A structural multilevel model is presented where some of the variables cannot be observed directly but are measured using tests or questionnaires. Observed dichotomous or ordinal polytomous response data serve to measure the latent variables using an item response theory model. The latent variables can be defined at any level of the multilevel model. A Bayesian procedure Markov chain Monte Carlo (MCMC), to estimate all parameters simultaneously is presented. It is shown that certain model checks and model comparisons can be done using the MCMC output. The techniques are illustrated using a simulation study and an application involving students' achievements on a mathematics test and test results regarding management characteristics of teachers and principles.

UI	MeSH Term	Description	Entries
D008390	Markov Chains	A stochastic process such that the conditional probability distribution for a state at any future instant, given the present state, is unaffected by any additional knowledge of the past history of the system.	Markov Process,Markov Chain,Chain, Markov,Chains, Markov,Markov Processes,Process, Markov,Processes, Markov
D008433	Mathematics	The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)	Mathematic
D009010	Monte Carlo Method	In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)	Method, Monte Carlo
D011581	Psychological Tests	Standardized tests designed to measure abilities (as in intelligence, aptitude, and achievement tests) or to evaluate personality traits.	Parenting Stress Index,Trier Social Stress Test,Trier Stress Test,Psychologic Tests,Psychological Test,Test, Psychological,Tests, Psychological,Index, Parenting Stress,Psychologic Test,Stress Index, Parenting,Stress Test, Trier,Test, Psychologic,Test, Trier Stress,Trier Stress Tests
D011594	Psychometrics	Assessment of psychological variables by the application of mathematical procedures.	Psychometric
D011795	Surveys and Questionnaires	Collections of data obtained from voluntary subjects. The information usually takes the form of answers to questions, or suggestions.	Community Survey,Nonrespondent,Questionnaire,Questionnaires,Respondent,Survey,Survey Method,Survey Methods,Surveys,Baseline Survey,Community Surveys,Methodology, Survey,Nonrespondents,Questionnaire Design,Randomized Response Technique,Repeated Rounds of Survey,Respondents,Survey Methodology,Baseline Surveys,Design, Questionnaire,Designs, Questionnaire,Methods, Survey,Questionnaire Designs,Questionnaires and Surveys,Randomized Response Techniques,Response Technique, Randomized,Response Techniques, Randomized,Survey, Baseline,Survey, Community,Surveys, Baseline,Surveys, Community,Techniques, Randomized Response
D004521	Educational Measurement	The assessing of academic or educational achievement. It includes all aspects of testing and test construction.	Assessment, Educational,Graduate Records Examination,Educational Assessment,Examination, Graduate Records,Measurement, Educational,Assessments, Educational,Educational Assessments,Educational Measurements,Examinations, Graduate Records,Graduate Records Examinations,Measurements, Educational
D004522	Educational Status	Educational attainment or level of education of an individual.	Education Level,Educational Achievement,Educational Attainment,Educational Level,Level of Education,Maternal Education Level,Maternal Educational Attainment,Maternal Educational Level,Paternal Education Level,Paternal Educational Attainment,Paternal Educational Level,Achievement, Educational,Educational Status, Maternal,Educational Status, Paternal,Maternal Educational Status,Paternal Educational Status,Status, Educational,Attainment, Educational,Attainment, Maternal Educational,Attainment, Paternal Educational,Education Level, Maternal,Education Level, Paternal,Education Levels,Educational Achievements,Educational Attainment, Maternal,Educational Attainment, Paternal,Educational Attainments,Educational Level, Maternal,Educational Level, Paternal,Educational Levels,Level, Education,Level, Educational,Level, Maternal Education,Level, Maternal Educational,Level, Paternal Education,Level, Paternal Educational,Levels, Maternal Educational,Maternal Education Levels,Maternal Educational Attainments,Maternal Educational Levels,Paternal Education Levels,Paternal Educational Attainments,Paternal Educational Levels,Status, Maternal Educational,Status, Paternal Educational
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000704	Analysis of Variance	A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable.	ANOVA,Analysis, Variance,Variance Analysis,Analyses, Variance,Variance Analyses