###### Georg Rasch

- The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between (a) the respondent's abilities, attitudes, or personality traits and (b) the item difficulty. (wikipedia.org)
- A central aspect of this divide relates to the role of specific objectivity, a defining property of the Rasch model according to Georg Rasch, as a requirement for successful measurement. (wikipedia.org)
- David Andrich spent time working with Georg Rasch in Denmark and Australia. (wikipedia.org)
- In 1977 he spent 6 months as a fellow of the Danish Institute for Educational Research working with the late Danish Mathematician [Georg Rasch], and he spent another six months as a research fellow at The University of Chicago working with Professor Benjamin Wright. (wikipedia.org)
- Three of the pioneers were the Educational Testing Service psychometrician Frederic M. Lord, the Danish mathematician Georg Rasch, and Austrian sociologist Paul Lazarsfeld, who pursued parallel research independently. (wikipedia.org)

###### Estimation

- Estimation of a Rasch model is used to estimate the parameters of the Rasch model. (wikipedia.org)
- Some kind of expectation-maximization algorithm is used in the estimation of the parameters of Rasch models. (wikipedia.org)
- Estimation methods for Rasch measures. (wikipedia.org)
- When each individual in the person sample is parameterized for item estimation, it is Rasch. (rasch.org)
- As a senior author, Formann also showed that the common assumption that the EM estimation of the two-parameter logistic model is not influenced by initial values is incorrect. (wikipedia.org)
- Real-world applications of the model include estimation of the influence of statistical journals, or ranking documents by relevance in machine-learned search engines. (wikipedia.org)
- Wright's seminal contributions to measurement continued until 2001, and included articulation of philosophical principles, production of practical results and applications, software development, development of estimation methods and model fit statistics, vigorous support for students and colleagues, and the founding of professional societies and new publications. (wikipedia.org)
- The standard errors are normally produced as a by-product of the estimation process (see Rasch model estimation). (wikipedia.org)

###### methods

- IRT methods include the Rasch, partial credit, and rating scale models. (wikipedia.org)
- He is renowned for his contributions to item response theory (Rasch models), latent class analysis, the measurement of change, mixture models, categorical data analysis, and quantitative methods for research synthesis (meta-analysis). (wikipedia.org)
- With later developments in psychometric theory, it has become possible to employ direct methods of scaling such as application of the Rasch model or unfolding models such as the Hyperbolic Cosine Model (HCM) (Andrich & Luo, 1993). (wikipedia.org)

###### 1977

- The polytomous Rasch model was derived by Andrich (1978), subsequent to derivations by Rasch (1961) and Andersen (1977), through resolution of relevant terms of a general form of Rasch's model into threshold and discrimination parameters. (wikipedia.org)
- Empirical research papers advocating the use of the Rasch model (Rasch, 1960) typically emphasize the unique properties of Rasch measurement, for example, specific objectivity (Rasch, 1977), invariance, sample independence or raw score sufficiency, which are, in fact, closely related. (rasch.org)
- Several probabilistic models of Guttman implicatory scales were developed by Krus (1977) and Krus and Bart (1974). (wikipedia.org)
- Krus and Kennedy (1977) elaborated the paired comparison scaling within their domain-referenced model. (wikipedia.org)
- Krus, D.J., & Kennedy, P.H. (1977) Normal scaling of dominance matrices: The domain-referenced model. (wikipedia.org)
- 1977. 'Monitoring Educational Standards: an inappropriate model' Bull. (wikipedia.org)

###### specific objectivity

- Specific Objectivity 1 is the requirement that the measures produced by a measurement model be sample-free for the agents (test items) and test-free for the objects (people). (rasch.org)

###### dichotomous data

- In this more general form of the Rasch model for dichotomous data, the score on a particular item is defined as the count of the number of threshold locations on the latent trait surpassed by the individual. (wikipedia.org)
- The polytomous Rasch model specialises to the model for dichotomous data when responses are classifiable into only two categories. (wikipedia.org)

###### responses

- Data analysed using the model are usually responses to conventional items on tests, such as educational tests with right/wrong answers. (wikipedia.org)
- It is a measurement model that has potential application in any context in which the objective is to measure a trait or ability through a process in which responses to items are scored with successive integers. (wikipedia.org)
- 2005, p.26) state that "Rasch measurement assumes responses on an ordinal level", Salzberger and Sinkovics (2006, p.412) point out that "[t]he manifest responses are assumed to be ordinal and need not be interval-scaled. (rasch.org)
- CTT relies on the observed scores (possibly weighted sum of patients items' responses) that are assumed to provide a good representation of a "true" score, while IRT relies on an underlying response model relating the items responses to a latent trait, interpreted as the true individual quality of life (QoL) for instance. (biomedcentral.com)
- The results of Rasch model analysis can highlight aspects for scale improvement, such as gap, duplicate items or scale responses. (biomedcentral.com)
- Moreover, model fit indices depend on a variety of factors, including the number of response options and the spread of responses across categories. (biomedcentral.com)
- An important property of Guttman's model is that a person's entire set of responses to all items can be predicted from their cumulative score because the model is deterministic. (wikipedia.org)
- The Rasch model requires a probabilistic Guttman structure when items have dichotomous responses (e.g. right/wrong). (wikipedia.org)
- Rasch model scaling - respondents interact with items and comparisons are inferred between items from the responses to obtain scale values. (wikipedia.org)
- Formann criticized the established method of dichotomizing water-level responses by the subjects into "right" versus "wrong" - he showed that this method was inappropriate because it ignored the heterogeneity of the task difficulties - and instead recommended using latent class models or Rasch models. (wikipedia.org)

###### Thurstone

- Thurstone used the normal distribution in applications of the model. (wikipedia.org)

###### Logistic Test Model

- Formann was probably the first researcher to practically apply Fischer's linear logistic test model (LLTM) for test development. (wikipedia.org)
- Application of the Linear Logistic Test Model in Psychometric Research. (wikipedia.org)

###### invariance

- Psychometric measurement models are only valid if measurement invariance holds between test takers of different groups. (uzh.ch)
- Global model tests, such as the well-established likelihood ratio (LR) test, are sensitive to violations of measurement invariance, such as differential item functioning and differential step functioning. (uzh.ch)

###### parameters

- However, there are important differences in the interpretation of the model parameters and its philosophical implications that separate proponents of the Rasch model from the item response modeling tradition. (wikipedia.org)
- In the Rasch model, the probability of a specified response (e.g. right/wrong answer) is modeled as a function of person and item parameters. (wikipedia.org)
- In most contexts, the parameters of the model characterize the proficiency of the respondents and the difficulty of the items as locations on a continuous latent variable. (wikipedia.org)
- In particular, the familiar statistical assumption of a normal (or any known) distribution of model parameters is not required. (rasch.org)
- The model is a general probabilistic measurement model which provides a theoretical foundation for the use of sequential integer scores, in a manner that preserves the distinctive property that defines Rasch models: specifically, total raw scores are sufficient statistics for the parameters of the models. (wikipedia.org)
- The objective was to explore the impact of the parameters used for study design on the RATIO and to identify the most relevant to provide a simple method for sample size determination for Rasch modelling. (biomedcentral.com)
- A linear regression model explaining the RATIO and including all the former parameters as covariates was fitted. (biomedcentral.com)
- These models require two crucial assumptions including unidimensionality and local independence to estimate the model parameters. (biomedcentral.com)
- The following algorithm computes the parameters pi of the basic version of the model from a sample of observations. (wikipedia.org)

###### 1960

- 1960) Probabilistic models for some intelligence and attainment tests. (rasch.org)
- In the wake of what Rasch referred to as Wright's "almost unbelievable activity in this field" in the period from 1960 to 1972, Rasch's ideas entered the mainstream in high-stakes testing, professional certification and licensure examinations, and in research employing tests, and surveys and assessments across a range of fields. (wikipedia.org)

###### Probabilistic Models

- Thus, decisions need not be deterministically transitive in order to apply probabilistic models. (wikipedia.org)

###### quantitative

- However, the model is a general one, and can be applied wherever discrete data are obtained with the intention of measuring a quantitative attribute or trait. (wikipedia.org)
- The participants were assessed with the ESS, which was tested through a quantitative analysis based on the classical measurement theory (CMT) or the Rasch model (RM) conventions. (springer.com)
- Based on a solid theoretical definition of a latent variable, fit of the data to the model assures us of having successfully measured a quantitative variable. (rasch.org)
- The objective of quantitative research is to develop and employ mathematical models, theories and hypotheses pertaining to phenomena. (wikipedia.org)
- Approaches to quantitative psychology were first modeled on quantitative approaches in the physical sciences by Gustav Fechner in his work on psychophysics, which built on the work of Ernst Heinrich Weber. (wikipedia.org)

###### approaches

- This book can help readers develop a sound understanding of measurement theories and approaches, particularly Rasch modeling, to using and developing measurement instruments for science education research. (booktopia.com.au)
- Psychological Test Calibration using the Rasch Model - Some Critical Suggestions on Traditional Approaches. (wikipedia.org)

###### probability

- Specifically, in the original Rasch model, the probability of a correct response is modeled as a logistic function of the difference between the person and item parameter. (wikipedia.org)
- When a person's location on the latent trait is equal to the difficulty of the item, there is by definition a 0.5 probability of a correct response in the Rasch model. (wikipedia.org)
- These models also assume unidimensionality but posit that the probability of endorsing an item is proportional to the distance between the items standing on the unidimensional trait and the standing of the respondent. (wikipedia.org)
- The Bradley-Terry model is a probability model that can predict the outcome of a comparison. (wikipedia.org)

###### contexts

- The model is also sometimes referred to as the Partial Credit Model, particularly when applied in educational contexts. (wikipedia.org)

###### empirical

- In addition to preserving this property, the model permits a stringent empirical test of the hypothesis that response categories represent increasing levels of a latent attribute or trait, hence are ordered. (wikipedia.org)

###### mathematical

- The mathematical theory underlying Rasch models is a special case of item response theory and, more generally, a special case of a generalized linear model. (wikipedia.org)
- The mathematical form of the model is provided later in this article. (wikipedia.org)
- The Partial Credit Model (Masters, 1982) has an identical mathematical structure but was derived from a different starting point at a later time, and is expressed in a somewhat different form. (wikipedia.org)
- It is based on the application of related mathematical models to testing data. (wikipedia.org)
- Kaplan & Saccuzzo, 2010) Herbart was responsible for creating mathematical models of the mind, which were influential in educational practices in years to come. (wikipedia.org)

###### Wright

- I learned statistics from Kempthorne and Bancroft at Iowa State and measurement from Rasch via Ben Wright at the University of Chicago. (raschmeas.info)

###### item

- For Rasch measurement, irrelevancies include the person and item distributions. (rasch.org)
- This is a multiplicative model, in which we can bring the frames of reference for persons and items into conjunction by choosing the reference item and person such that P00 = 0.5 which makes the constant term 1. (rasch.org)
- The Partial Credit Model was applied to the data and item fit evaluated against published criteria. (springer.com)
- Therefore, the fact that the Rasch model does not depend on interval-scaled item scores is often put forward as an important property of the model. (rasch.org)
- Two main types of analytic strategies are used for PRO data: so-called classical test theory (CTT) and models coming from Item Response Theory (IRT). (biomedcentral.com)
- If the Rasch Model has been introduced to you as the "one-parameter logistic" item response theory model ( 1 PL IRT ), then you haven't been properly introduced. (raschmeas.info)
- This expository paper describes the use of latent variable mixture modeling (LVMM), in conjunction with item response theory (IRT), to examine: (a) whether a sample is homogeneous with respect to a unidimensional measurement model, (b) implications of sample heterogeneity with respect to model-predicted scores (theta), and (c) sources of sample heterogeneity. (springer.com)
- The Rasch partial credit model (PCM) was used to investigate item statistics and ordering of response categories. (biomedcentral.com)
- Guttman's deterministic model is brought within a probabilistic framework in item response theory models, and especially Rasch measurement. (wikipedia.org)
- The LLTM is a special case of the Rasch model, which allows the construction of items with item difficulties based on the user's demand. (wikipedia.org)
- His main research work focuses on fundamental research of assessment processes and on application and advancement of Item response theory models (Rasch model). (wikipedia.org)
- He is especially known for his work in Item Response Theory, with a particular focus on Rasch models for measurement. (wikipedia.org)
- Thus IRT models the response of each examinee of a given ability to each item in the test. (wikipedia.org)
- Such extraction processes, the Rasch model for instance, are standard practice for item development among professionals. (wikipedia.org)

###### invariant

- By requiring measures to remain the same (invariant) across different tests measuring the same thing, Rasch models make it possible to test the hypothesis that the particular challenges posed in a curriculum and on a test coherently represent the infinite population of all possible challenges in that domain. (wikipedia.org)
- This also implies that Rasch point-estimates are invariant when the data fit the Rasch model. (rasch.org)

###### 1995

- Vollema, Meinte 2004-10-17 00:00:00 This paper will introduce, discuss and illustrate two contemporary extensions of theRasch model: the one parameter logistic model (Verhelst and Glas, 1995) and theMultidimensional Rasch model (Hoijtink et al. (deepdyve.com)

###### respondents

- In practice, actual data from respondents do not closely match Guttman's deterministic model. (wikipedia.org)

###### Comparisons

- However, transitivity will generally hold for a large number of comparisons if models such as the BTL can be effectively applied. (wikipedia.org)

###### psychometric properties

- The objective of this study was to evaluate the psychometric properties of the DASH, with focus on validity evidence using the Rasch measurement model. (biomedcentral.com)

###### Data

- Beyond data, Rasch's equations model relationships we expect to obtain in the real world. (wikipedia.org)
- Models are most often used with the intention of describing a set of data. (wikipedia.org)
- Consequently, the Rasch model is not altered to suit data. (wikipedia.org)
- 1999). Using data with respect tothe measurement of schizotypy (Vollema and Hoijtink, 2000) the most importantfeatures of both models will be illustrated. (deepdyve.com)
- In Rasch measurement, we define measurement as the successful discovery of the structure of quantity in the data (Michell, 1990, 1997), tantamount to data fitting the model. (rasch.org)
- Statements of this sort are permitted regardless of whether the data fit the model or not, as we do not infer anything from the comparison of Mary and John beyond the number of correctly answered items. (rasch.org)
- Justification of study size is hardly provided, especially when a Rasch model is planned for analysing the data in a 2-group comparison study. (biomedcentral.com)
- Using the classical sample size formula adjusted with the proposed RATIO can provide a straightforward and reliable formula for sample size computation for 2-group comparison of PRO data using Rasch models. (biomedcentral.com)
- Consequently, many questionnaires are validated (or revalidated) using IRT along with CTT [ 13 - 15 ] allowing analysing PRO data with IRT models in clinical research. (biomedcentral.com)
- We applied the Rasch model to FKSI-DRS data from a randomized phase 3 trial in which first-line sunitinib therapy showed superiority to interferon-alfa in patients with metastatic renal cell carcinoma. (ovid.com)
- Defective model does not adequately describe the data. (rasch.org)

###### regression

- i ) ) = β i − β j {\displaystyle \operatorname {logit} (P(i>j))=\log \left({\frac {P(i>j)}{1-P(i>j)}}\right)=\log \left({\frac {P(i>j)}{P(j>i)}}\right)=\beta _{i}-\beta _{j}} reducing the model to logistic regression on pairs of individuals. (wikipedia.org)
- Thus if X {\displaystyle X} and Y {\displaystyle Y} are taken to be imperfect measurements of underlying variables X ′ {\displaystyle X'} and Y ′ {\displaystyle Y'} with independent errors, then r x ′ y ′ {\displaystyle r_{x'y'}} estimates the true correlation between X ′ {\displaystyle X'} and Y ′ {\displaystyle Y'} . Regression dilution Errors-in-variables model Jensen, A.R. (1998). (wikipedia.org)

###### hierarchical

- The Guttman model works best for constructs that are hierarchical and highly structured such as social distance, organizational hierarchies, and evolutionary stages. (wikipedia.org)
- He is best known for his development and application of hierarchical linear models (HLM) in the field of education but he has also published on other subjects such as health and crime. (wikipedia.org)
- Hierarchical linear models, which go by many other names, are used to study many natural processes. (wikipedia.org)
- To use an example from education, a three level hierarchical model might account for the fact that students are nested in classrooms which are nested in schools. (wikipedia.org)
- Hierarchical Linear Models (Second Edition). (wikipedia.org)

###### conceptual

- It describes measurement instruments reported in refereed science education research journals, and introduces the Rasch modeling approach to developing measurement instruments in common science assessment domains, i.e. conceptual understanding, affective variables, science inquiry, learning progression, and learning environments. (booktopia.com.au)
- For most practical purposes these models are the same, despite their conceptual differences. (rasch.org)

###### stochastic

- Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance, etc. (iste.co.uk)
- Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. (iste.co.uk)

###### partial credit

- The Partial Credit Model also allows different thresholds for different items. (wikipedia.org)

###### Rasch's

- He is largely responsible for the widespread adoption of Georg Rasch's measurement principles and models. (wikipedia.org)
- He is one of the most prominent advocates of Rasch's probabilistic measurement models. (wikipedia.org)

###### findings

- The findings suggest that the Rasch model can be utilized for measuring the level of sexual risk for HIV/STI infection as a single latent construct and for establishing the relative degree of severity of each type of sexual behavior in HIV/STI transmission and acquisition among MSM. (biomedcentral.com)

###### ordinal level

- This is an ordinal level technique when a measurement model is not applied. (wikipedia.org)

###### research

- In addition to psychometrics and educational research, the Rasch model and its extensions are used in other areas, including the health profession and market research because of their general applicability. (wikipedia.org)
- This resulted in the development of a Rasch-scaled abstract reasoning test (based on Raven's matrices test) which has since been widely used in research and practice. (wikipedia.org)
- His research and work ranges from the philosophy of measurement, through model developments, exposition and interpretation, to software development. (wikipedia.org)

###### outcomes

- A fundamental assumption of patient-reported outcomes (PRO) measurement is that all individuals interpret questions about their health status in a consistent manner, such that a measurement model can be constructed that is equivalently applicable to all people in the target population. (springer.com)

###### contrast

- A class of unidimensional models that contrast with Guttman's model are unfolding models. (wikipedia.org)