Application of a multidimensional extension of the two- parameter logistic latent trait model

by McKinley, Robert L.

Publisher: Research and Development Division, American College Testing Program in Iowa City

Written in English
Published: Pages: 40 Downloads: 90
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Subjects:

  • Achievement tests -- Automation.,
  • Educational tests and measurements -- Automation.

Edition Notes

StatementRobert L. McKinley and Mark D. Reckase.
SeriesACT research report -- no. 83-3
ContributionsReckase, Mark D.
The Physical Object
Pagination40, [9] p. :
Number of Pages40
ID Numbers
Open LibraryOL18440641M

The multidimensional extension we consider is called multidimensional 2 parameter logistic (M2PL) model, and has the following expression: P(X ij= xj i;a j;d j) = ex(a0 j i+d) 1+ea0j i+d j (2) where both a jand iare m dimensional vectors, so that the sum in the exponent of e can be rewritten as a0 j i+ d j = P m t=1 a jt it+ d j. This model. 1 more latent traits are simultaneously considered (multidimensionality) 2 these latent traits are represented by a random vector with a discrete distribution common to all subjects (each support point of such a distribution identifies a different latent class of individuals) 3 either a Rasch or a two-parameter logistic (Birnbaum, ). The current study proposes an alternative feasible Bayesian algorithm for the three-parameter logistic model (3PLM) from a mixture-modeling perspective, namely, the Bayesian Expectation-Maximization-Maximization (Bayesian EMM, or BEMM). As a new maximum likelihood estimation (MLE) alternative to the marginal MLE EM (MMLE/EM) for the 3PLM, the EMM can explore the likelihood function much .   Instead of estimating a between-item multidimensional Rasch model, a between-item multidimensional model that allows for varying item discrimination parameters should be used (see, for example, Adams & Wu, ; Muraki, ). Such a model is identified by fixing the variance of both latent dimensions to 1.

Multilevel and multidimensional item response models are two commonly used examples as extensions of the conventional item response models. In this dissertation, I investigate extensions and applications of multilevel and multidimensional item response models, with a primary focus on longitudinal item response data that include students' school switching, classification of examinees . 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. For example, they may be used to estimate a student's reading ability or the. We also consider the three-parameter model that further includes a guessing probability c j, that is, P(y j = 1j ;a j;b j;c j) = c j+ (1 c j)F(Ta j+ b j): (3) By setting c j = 0, the above model recovers (1). In addition, the latent trait vector follows the multivariate normal prior . Extensions of unidimensional linking procedures to multidimensional latent trait models are explored. Adams, Wilson, and Wang discuss the multidimensional random coefficients multinomial logit model. This model generalizes a wide range of Rasch models to the multidimensional case, including the simple APPLIED PSYCHOLOGICAL MEASUREMENT.

The Joe E. Covington Award for Research on Testing for Licensure is intended to provide support for graduate students in any discipline doing research germane to testing and measurement, particularly in a high-stakes licensure setting. View past award recipients and access the Call for Proposals. This paper introduces multilevel extensions for the general diagnostic model (GDM) following recent developments on extensions of latent class analysis (LCA) to hierarchical models. The GDM is based on LCA as well as discrete latent trait models and may be viewed as a general modeling framework for con rmatory multidimensional item response models.   where α c3 and α c4 are latent variables for Attributes 3 and 4, respectively. The logit of the correct response includes the intercept (λ 2,0), a main effect for Attribute 3 (λ 2,1,(3)), a main effect for Attribute 4 (λ 2,1,(4)), and a two-way interaction term between Attributes 3 and 4 (λ 2,2,(3,4)).The second subscript on the item parameters denotes the level of the effect, where 0. The difficulty parameter is called b. the two important assumptions are local independence and unidimensionality. The Item Response Theory has three models. They are one parameter logistic model, two parameter logistic model and three parameter logistic model. In addition, Polychromous IRT Model are also useful (Hambleton & Swaminathan, ).

Application of a multidimensional extension of the two- parameter logistic latent trait model by McKinley, Robert L. Download PDF EPUB FB2

The multidimensional model selected for this study, a multidimensional extension of the two-parameter logistic (M2PL) model, is given by exp(d +a. Pi(6.) =, (2) 1+exp(d i+ai 6.) where Pi(6J) is the probability of a correct response to item i by examinee j, d.

An Application of a Multidimensional Extension of the Two-Parameter Logistic Latent Trait Model. McKinley, Robert L.; Reckase, Mark D. A latent trait model is described that is appropriate for use with tests that measure more than one dimension, and its application to both real and simulated test data is Cited by: 4.

An illustration of an open book. Books. An illustration of two cells of a film strip. Video An illustration of an audio speaker. ERIC ED An Application of a Multidimensional Extension of the Two-Parameter Logistic Latent Trait Model. Item Preview. TITLE An Application of a Multidimensional Extension of the.

Two-Parameter togistic,Latent Trait Model. INSTITUTION American g Program, Iowa City, Iowa. SPONS AGENCY Office of Naval Research, Arlington', Va. Personnel. and Training Research Programs Office. REPORT NO ONR "PUB DATE Aug 83 CONTRACT NK NOTE. An Extension of the Two-Parameter Logistic Model to the Multidimensional Latent Space.

McKinley, Robert L.; Reckase, Mark D. Item response theory (IRT) has proven to be a very powerful and useful measurement by: The two-parameter logistic (2-PL) MIRT model relates the probability of is a transposed vector of latent trait parameters for person.

This model is the multidimensional extension of the unidimensional 2-PL IRT model for dichotomously scored items (Birnbaum, ). Multidimensional latent class item response models for binary and ordinal polytomous items: theory and answer to an item is a function of the person’s position on the latent trait and one or more parameters which characterize the item S.

Bacci (unipg) 3 / two-parameter logistic model (Birnbaum, ) Rasch: Rasch model (Rasch, ). The model, a multidimensional extension of Bock's nominal response model, is shown to allow for the study and control of response style effects in ordered rating scale data so as to reduce bias in.

The model can be contrasted to Embretson's () multicomponent latent trait model (MLTM), which is a partially non-compensatory MIRT model. The IRF for a simplified two-dimensional version of the MLTM, setting component difficulties and the guessing parameter to zero, would be (5) Pr (x v i | θ 1, θ 2) = logit (θ 1) ⋅ logit (θ 2).

Nested logit models have been presented as an alternative to multinomial logistic models for multiple-choice test items (Suh and Bolt in Psychometrika –, ) and possess a mathematical structure that naturally lends itself to evaluating the incremental information provided by attending to distractor selection in scoring.

One potential concern in attending to distractors is the. A Multidimensional Extension of the Two-Parameter Logistic Latent Trait Model [microform] / Robert L. Mc Multidimensional Difficulty as a Direction and a Distance [microform] / Mark D. Reckase and Robert L.

Mc The Use of the General Rasch Model with Multidimensional Item Response Data [microform] / Robert L. McKi. In psychometrics, item response theory (IRT) (also known as latent trait theory, strong true score theory, or modern mental test theory) is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables.

It is a theory of testing based on the relationship between individuals' performances on a test item and. in the unidimensional 3-parameter logistic model.

As a result, the modification of Multidimensional 3-Parameter Logistic model (M3PL) has been a crucial extension of M2PL. In Vietnam, IRT models have been of interest to recent research with Rasch model by Nguyen (), IRT 2PL model by Nguyen () and Nguyen (), and IRT 3PL by Le et al.

parameter rating scale model includes estimates of person latent trait, item difficulty, model fit, person-fit, item-fit, person reliability, item reliability, and step calibration.

A two-parameter model would include estimates for item discrimination, and a three-parameter model would include an. An illustration of a computer application window Wayback Machine. An illustration of an open book. Books. An illustration of two cells of a film strip. Video. An illustration of an audio speaker.

Audio. An illustration of a " floppy disk. An Extension of the Two-Parameter Logistic Model to the Multidimensional Latent Space. A one dimensional latent trait model to infer attitude from non response for nominal data of the Rasch model with the flexibility of the two-parameter logistic model.

In the OPLM, difficulty. McKinley, R.L. (, April). A multidimensional extension of the two-parameter logistic latent trait model. Paper presented at the meeting of the National Council on Measurement in Education, Montreal.

As weighting is much more thorough when carried out by accounting for the dimensionality of a dataset rather than by ignoring it, we suggest to assign weights on the basis of the discrimination parameters estimated through a multidimensional two-parameter logistic IRT model.

Specifically, the procedure is developed through two consecutive steps. A multidimensional extension of the two-parameter logistic latent trait model is presented and some of its characteristics are discussed.

In addition, sufficient statistics for the parameters of the model are derived, as -is the information function. Lawley,Birnbaum,Bock and Aitkin, ].

Here, consider the two-parameter logistic model that specifies the probability of a correct response to item j (Yj = 1) conditional on the ability of subject i (θi)as P(Yij =1| θi)= 1 1 +exp[−aj(θi −bj)] (2) where aj is the slope parameter.

The multidimensional two-parameter logistic model (M2PL; Reckase, ) was chosen as the studied MIRT model to generate item response data. Based on the M2PL model, the probability of responding to item i (i = 1,K) correctly for person j (j = 1,J) with the latent traits θ j = {θ 1 j, θ 2 j } in a two-dimensional test can be.

Item Response Theory vs. Classical Test Theory. IRT Assumptions. 1) Monotonicity – The assumption indicates that as the trait level is increasing, the probability of a correct response also increases2) Unidimensionality – The model assumes that there is one dominant latent trait being measured and that this trait is the driving force for the responses observed for each item in the measure3.

To ensure the identification of the proposed model, some further constraints have to be considered on the model parameters.

As usual in the IRT approach, one item discriminating parameter must be constrained to 1 for each latent trait and one item threshold difficulty parameter to 0 for each latent trait. An Extension of the Two-Parameter Logistic Model to the Multidimensional.

Latent Space. TYPE or RE*ORT 0 PER COVERED Technical Report 6 PERroRNG ORG. REPORT NUMBER 7 AUTh R.) Robert L. McKinley and Mark D. Reckase 6 CONTRACT OR GRANT NUMBER(a) NK 9 pER,NG ORGANIZATION MANE ANO AOOREss American College Testing. that limits the application of MIRT in practice is difficulty in establishing equivalent scales based on multiple traits.

A compensatory multidimensional extension of the two-parameter logistic (2PL) model with m dimensions is (Reckase, ; ) compensatory two-dimensional 2PL model was used as Equation (1).

third paper, a structured constructs model (SCM) for the continuous latent trait is developed to deal with complicated learning progressions, in which relations between levels across multiple constructs are assumed in advance.

Based on the multidimensional Rasch model, discontinuity parameters are incorporated to model the. For example, the formula for the two-parameter logistic latent trait model is given by P x ij = 1 = e a i θ j − b i 1 + e a i θ j − b i where P(x ij = 1) is the probability of a correct response for person j on item i, e is the constant,θ j is the ability of person j, and a i and b i are the item parameters.

The examples demonstrate how to fit many kinds of IRT models, including one- two- and three-parameter logistic models for binary items as well as nominal, ordinal, and hybrid models for polytomous items.

In addition, the authors provide overviews of. An application of a multidimensional extension of the two-parameter logistic latent trait model (ONR (ERIC Document Reproduction Service No.

ED ) Google Scholar. McKinley, R.L., & Reckase, M.D. ( b). MAX-LOG: A computer program for the estimation of the parameters of a multidimensional logistic model.

Abstract. In this chapter, we discuss two extensions to the item response models presented in the first two parts of this book: more than one random effect for persons (multidimensionality) and latent item only consider models with random person weights (following a normal distribution), and with no inclusion of person predictors (except for the constant).

Intercept parameters were drawn from the standard normal distribution. For the multigroup models with two observed groups, the item parameters of all items, except one, were constrained to be equal across the two groups. For the mixture models with two latent groups, no item parameter was constrained to be equal across the two groups.Multidimensional IRT Model for Dichotomous Responses.

Multidimensional Compensatory Three-Parameter Logistic Model (MC3PLM) Whether it is intended or not, when an item or a set of items measures more than one latent trait, the assumption of unidimensionality is violated. An important issue concerns the choice between using latent trait models versus more classical methods.

This question often occurs in the context of developing a scale in survey, behavioral, or health research. In general, my advice is this: it is not necessary to pursue latent trait models in every application.