scholarly journals A Graded Response Model Framework for Questionnaires With Uniform Response Formats

2018 ◽  
Vol 43 (4) ◽  
pp. 290-302 ◽  
Author(s):  
Dirk Lubbe ◽  
Christof Schuster
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Factor Model ◽  
General Purpose ◽  
Response Model ◽  
Graded Response Model ◽  
Model Framework ◽  
Response Formats ◽  
Graded Response ◽  
Ordered Categorical

Questionnaires with uniform-ordered categorical response formats are widely applied in psychology. Muraki proposed a modified graded response model accounting for the items’ uniform response formats by assuming identical threshold parameters defining the category boundaries for all items. What is not well known is that there is a set of closely related models, which similarly assume identical thresholds. The present article gives a framework illustrating the differences between these models and their utility for understanding questionnaire responses in detail. The models are explained as constrained cases of a one-dimensional factor model for ordered categorical data. Furthermore, the authors show that the models can be written and fitted as structural equation models, which allows for a very flexible and general purpose use. Instructions on implementing the models in Mplus and SAS PROC NLMIXED are given.

Measuring Variability and Change With an Item Response Model for Polytomous Variables

1998 ◽  
Vol 23 (3) ◽  
pp. 193-215 ◽  
Author(s):  
Michael Eid ◽  
Lore Hoffmann
Keyword(s):  
Latent Variable ◽  
Structural Equation ◽  
Structural Equation Models ◽  
A Priori ◽  
Latent Trait ◽  
Response Model ◽  
Graded Response Model ◽  
Item Response Model ◽  
Interindividual Differences ◽  
Graded Response

An extension of the graded response model of Samejima (1969) for the measurement of variability and change is presented. In this model it is assumed that an occasion-specific latent variable is decomposed into (a) a person-specific variable (a trait variable) and (b) an occasion-specific deviation variable measuring the variability caused by situational and/or interactional effects. Furthermore, it is assumed that interindividual differences in intraindividual trait change occur between a priori specified periods of time. The correlations of the latent trait variables between periods of time indicate the degree of (trait) change. It is shown how the parameters of the model can be estimated and some implications of the model can be tested with structural equation models for ordered variables. Finally, the model is illustrated by an application to the measurement of students’ interest in the topic of radioactivity. Based on the results of a longitudinal study of students over 4’years, it is shown that a model considering two periods of time—one before and one after the incident in Chernobyl—fits well. According to the accepted model, it can be concluded that 30% to 60% of the variance of interest in radioactivity on an occasion of measurement are due to situational and/or interactional effects. The autocorrelations of the latent trait variables between both periods of time (r = .72 and r = .76, respectively) indicate that there are interindividual differences in intraindividual changes on the level of the latent trait variables.

ITEM BANKING FOR AN ADAPTIVE MEASUREMENT OF NEUROTICISM

2020 ◽  
Vol 13 (2) ◽  
pp. 459-485
Author(s):  
Facundo Juan Pablo Abal ◽  
Gabriela Susana Lozzia ◽  
Sofía Esmeralda Auné ◽  
Horacio Félix Attorresi
Keyword(s):  
Item Response ◽  
Metropolitan Area ◽  
Buenos Aires ◽  
Factor Model ◽  
Five Factor Model ◽  
Stopping Rules ◽  
Response Model ◽  
Graded Response Model ◽  
Graded Response ◽  
Adaptive Measurement

The psychometric properties of a bank of 36 items are presented measuring Neuroticism based on the Five-Factor Model. These items pertain to the facets that were identified by the work of McCrae and Costa. The sample was comprised of 1133 adult subjects that reside in the Buenos Aires Metropolitan Area in Argentina. Women accounted for 52.1% of those subjects with an average age of 29.5 years (SD = 11.32). In order to get the items calibrated according to Item Response Theory (Graded Response Model), acquire the bank’s information functions and assess the estimated associations with other instruments, 70% of the cases were randomly selected. An adaptive administration simulation was made with the remaining 30% so as to test two stopping rules: a) using 18 items and b) standard error of ≤ 0.25. Correlations greater than .95 were found between the estimated bank scores and the two adaptive versions. The advantages of using the adaptive Neuroticism measurement over other well-renowned instruments that use conventional large formats, as well as abbreviated ones, are discussed.

IRT Information Function of Polytomously Scored Items under the Graded Response Model

2009 ◽  
Vol 40 (11) ◽  
pp. 1212-1220 ◽  
Author(s):  
Zhao-Sheng LUO ◽  
Xue-Lian OUYANG ◽  
Shu-Qing QI ◽  
Hai-Qi DAI ◽  
Shu-Liang DING
Keyword(s):  
Response Model ◽  
Graded Response Model ◽  
Information Function ◽  
Graded Response

scholarly journals The Monotonic Polynomial Graded Response Model: Implementation and a Comparative Study

2020 ◽  
Vol 44 (6) ◽  
pp. 465-481
Author(s):  
Carl F. Falk
Keyword(s):  
Latent Variable ◽  
Kernel Smoothing ◽  
Marginal Likelihood ◽  
Expectation Maximization Algorithm ◽  
Real Data ◽  
Response Model ◽  
Response Functions ◽  
Graded Response Model ◽  
Graded Response ◽  
Maximum Marginal Likelihood

We present a monotonic polynomial graded response (GRMP) model that subsumes the unidimensional graded response model for ordered categorical responses and results in flexible category response functions. We suggest improvements in the parameterization of the polynomial underlying similar models, expand upon an underlying response variable derivation of the model, and in lieu of an overall discrimination parameter we propose an index to aid in interpreting the strength of relationship between the latent variable and underlying item responses. In applications, the GRMP is compared to two approaches: (a) a previously developed monotonic polynomial generalized partial credit (GPCMP) model; and (b) logistic and probit variants of the heteroscedastic graded response (HGR) model that we estimate using maximum marginal likelihood with the expectation–maximization algorithm. Results suggest that the GRMP can fit real data better than the GPCMP and the probit variant of the HGR, but is slightly outperformed by the logistic HGR. Two simulation studies compared the ability of the GRMP and logistic HGR to recover category response functions. While the GRMP showed some ability to recover HGR response functions and those based on kernel smoothing, the HGR was more specific in the types of response functions it could recover. In general, the GRMP and HGR make different assumptions regarding the underlying response variables, and can result in different category response function shapes.

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