Item response theory (IRT) model applications extend well beyond cognitive ability testing, and various patient-reported outcomes (PRO) measures are among the more prominent examples. PRO (and like) constructs differ from cognitive ability constructs in many ways, and these differences have model fitting implications. With a few notable exceptions, however, most IRT applications to PRO constructs rely on traditional IRT models, such as the graded response model. We review some notable differences between cognitive and PRO constructs and how these differences can present challenges for traditional IRT model applications. We then apply two models (the traditional graded response model and an alternative log-logistic model) to depression measure data drawn from the Patient-Reported Outcomes Measurement Information System project. We do not claim that one model is “a better fit” or more “valid” than the other; rather, we show that the log-logistic model may be more consistent with the construct of depression as a unipolar phenomenon. Clearly, the graded response and log-logistic models can lead to different conclusions about the psychometrics of an instrument and the scaling of individual differences. We underscore, too, that, in general, explorations of which model may be more appropriate cannot be decided only by fit index comparisons; these decisions may require the integration of psychometrics with theory and research findings on the construct of interest.

Given a Masters partial credit item with n known step difficulties, conditions are stated for the existence of a set of (locally) independent Rasch binary items such that their raw score and the partial credit raw score have identical probability density functions. The conditions are those for the existence of n positive values with predetermined elementary symmetric functions and include the requirement that the n step difficulties form an increasing sequence.

This paper concerns items that consist of several item steps to be responded to sequentially. The item scoreX is defined as the number of correct responses until the first failure. Samejima's graded response model states that each step h=1,...,m is characterized by a parameter bh, and, for a subject with ability θ, Pr(X ≥ h; θ) = F(θ − bh). Tutz's general sequential model associates with each step a parameterdh, and it states that Pr(X≥h;θ)=Πr=1hG(θ−dr). Tutz's (1991, 1997) conjectures that the models are equivalent if and only ifF(x)=G(x) is an extreme value distribution. This paper presents a proof for this conjecture.

The Graded Response Model (GRM; Samejima, Estimation of ability using a response pattern of graded scores, Psychometric Monograph No. 17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, θ, to underlie the ordinal item scores (Takane & de Leeuw in Psychometrika, 52:393–408, 1987). Traditionally, a normal distribution is specified for Z implying homoscedastic error variances and a normally distributed θ. In this paper, we present the Heteroscedastic GRM with Skewed Latent Trait, which extends the traditional GRM by incorporation of heteroscedastic error variances and a skew-normal latent trait. An appealing property of the extended GRM is that it includes the traditional GRM as a special case. This enables specific tests on the normality assumption of Z. We show how violations of normality in Z can lead to asymmetrical category response functions. The ability to test this normality assumption is beneficial from both a statistical and substantive perspective. In a simulation study, we show the viability of the model and investigate the specificity of the effects. We apply the model to a dataset on affect and a dataset on alexithymia.

A comprehensive class of models is proposed that can be used for continuous, binary, ordered categorical and count type responses. The difficulty of items is described by difficulty functions, which replace the item difficulty parameters that are typically used in item response models. They crucially determine the response distribution and make the models very flexible with regard to the range of distributions that are covered. The model class contains several widely used models as the binary Rasch model and the graded response model as special cases, allows for simplifications, and offers a distribution free alternative to count type items. A major strength of the models is that they can be used for mixed item formats, when different types of items are combined to measure abilities or attitudes. It is an immediate consequence of the comprehensive modeling approach that allows that difficulty functions automatically adapt to the response distribution. Basic properties of the model class are shown. Several real data sets are used to illustrate the flexibility of the models

Knowledge space theory (KST) structures are introduced within item response theory (IRT) as a possible way to model local dependence between items. The aim of this paper is threefold: firstly, to generalize the usual characterization of local independence without introducing new parameters; secondly, to merge the information provided by the IRT and KST perspectives; and thirdly, to contribute to the literature that bridges continuous and discrete theories of assessment. In detail, connections are established between the KST simple learning model (SLM) and the IRT General Graded Response Model, and between the KST Basic Local Independence Model and IRT models in general. As a consequence, local independence is generalized to account for the existence of prerequisite relations between the items, IRT models become a subset of KST models, IRT likelihood functions can be generalized to broader families, and the issues of local dependence and dimensionality are partially disentangled. Models are discussed for both dichotomous and polytomous items and conclusions are drawn on their interpretation. Considerations on possible consequences in terms of model identifiability and estimation procedures are also provided.

Samejima (Psychometrika 65:319–335, 2000) proposed the logistic positive exponent family of models (LPEF) for dichotomous responses in the unidimensional latent space. The objective of the present paper is to propose and discuss a graded response model that is expanded from the LPEF, in the context of item response theory (IRT). This specific graded response model belongs to the general framework of graded response model (Samejima, Psychometrika Monograph, No. 17, 1969 and No. 18, 1972; Handbook of modern item response theory, Springer, New York, 1997; Encyclopedia of Social Measurement, Academic Press, San Diego, 2004), and, in particular to the heterogeneous case (Samejima, Psychometrika Monograph, No. 18, 1972). Thus, the model can deal with any number of ordered polytomous responses, such as letter grades (e.g., A, B, C, D, F), etc.

For brevity, hereafter, the model will be called the LPEF graded response model, or LPEFG. This model reflects the opposing two principles contained in the LPEF for dichotomous responses, with the logistic model (Birnbaum, Statistical theories of mental test scores, Addison Wesley, Reading, 1968) as their transition, which provide a reasonable rationale for partial credits in LPEFG, among others.

We present a class of finite mixture multilevel multidimensional ordinal IRT models for large scale cross-cultural research. Our model is proposed for confirmatory research settings. Our prior for item parameters is a mixture distribution to accommodate situations where different groups of countries have different measurement operations, while countries within these groups are still allowed to be heterogeneous. A simulation study is conducted that shows that all parameters can be recovered. We also apply the model to real data on the two components of affective subjective well-being: positive affect and negative affect. The psychometric behavior of these two scales is studied in 28 countries across four continents.

For each Rasch (Masters) partial credit item, there exists a set of independent Rasch binary and indecomposable trinary items for which the sum of the scores and the partial credit score have identical probability density functions. If each indecomposable trinary item is further expressed as the sum of two binary items, then the binary items are positively dependent and cannot be both of the Rasch type.

Samejima’s graded response model (GRM) has gained popularity in the analyses of ordinal response data in psychological, educational, and health-related assessment. Obtaining high-quality point and interval estimates for GRM parameters attracts a great deal of attention in the literature. In the current work, we derive generalized fiducial inference (GFI) for a family of multidimensional graded response model, implement a Gibbs sampler to perform fiducial estimation, and compare its finite-sample performance with several commonly used likelihood-based and Bayesian approaches via three simulation studies. It is found that the proposed method is able to yield reliable inference even in the presence of small sample size and extreme generating parameter values, outperforming the other candidate methods under investigation. The use of GFI as a convenient tool to quantify sampling variability in various inferential procedures is illustrated by an empirical data analysis using the patient-reported emotional distress data.

The item response function (IRF) for a polytomously scored item is defined as a weighted sum of the item category response functions (ICRF, the probability of getting a particular score for a randomly sampled examinee of ability θ). This paper establishes the correspondence between an IRF and a unique set of ICRFs for two of the most commonly used polytomous IRT models (the partial credit models and the graded response model). Specifically, a proof of the following assertion is provided for these models: If two items have the same IRF, then they must have the same number of categories; moreover, they must consist of the same ICRFs. As a corollary, for the Rasch dichotomous model, if two tests have the same test characteristic function (TCF), then they must have the same number of items. Moreover, for each item in one of the tests, an item in the other test with an identical IRF must exist. Theoretical as well as practical implications of these results are discussed.

The limitations for self-reporting of dietary patterns are widely recognised as a major vulnerability of FFQ and the dietary screeners/scales derived from FFQ. Such instruments can yield inconsistent results to produce questionable interpretations. The present article discusses the value of psychometric approaches and standards in addressing these drawbacks for instruments used to estimate dietary habits and nutrient intake. We argue that a FFQ or screener that treats diet as a ‘latent construct’ can be optimised for both internal consistency and the value of the research results. Latent constructs, a foundation for item response theory (IRT)-based scales (e.g. Patient Reported Outcomes Measurement Information System) are typically introduced in the design stage of an instrument to elicit critical factors that cannot be observed or measured directly. We propose an iterative approach that uses such modelling to refine FFQ and similar instruments. To that end, we illustrate the benefits of psychometric modelling by using items and data from a sample of 12 370 Soldiers who completed the 2012 US Army Global Assessment Tool (GAT). We used factor analysis to build the scale incorporating five out of eleven survey items. An IRT-driven assessment of response category properties indicates likely problems in the ordering or wording of several response categories. Group comparisons, examined with differential item functioning (DIF), provided evidence of scale validity across each Army sub-population (sex, service component and officer status). Such an approach holds promise for future FFQ.