Two-parameter Logistic Model Research Articles

Automatic setting optimization for robotic upper-extremity rehabilitation in patients with stroke using ReoGo-J: a cross-sectional clinical trial

Stroke-induced upper-extremity paralysis affects a substantial portion of the population, necessitating effective rehabilitation strategies. This study aimed to develop an automated program, incorporating the item response theory, for rehabilitation in patients with post-stroke upper-extremity paralysis, focusing on the ReoGo-J device, and to identify suitable robot parameters for robotic rehabilitation. ReoGo-J, a training device for upper-extremity disorders including 71 items, was administered to over 300 patients with varying degrees of post-stroke upper-extremity paralysis. Each item was rated on a three-point scale (0, very difficult; 1, adequate; 2, very easy). The results were analyzed using the graded response model, an extension of the two-parameter logistic model within the framework of the item response theory, to grade the training items based on ability of the patients. The relationship between the predicted ability, an indicator of the predicted ability the paralyzed upper-extremity to perform an item in the item response theory analysis (higher numbers indicate higher ability, lower numbers indicate lower ability), and the items in the Fugl–Meyer assessment (FMA), which indicate the degree of paralysis, was analyzed using Pearson’s correlation coefficient. This study included 312 patients with post-stroke upper-extremity paralysis. The predicted ability (θ) of the tasks included in the original ReoGo-J test for forward reaching, reaching for mouth, rotational reaching, radial reaching (2D), abduction reaching, reaching in eight directions, radial reach (3D), and reaching for head ranged from − 2.0 to − 0.8, − 1.3 to − 0.8, − 1.0 to − 0.1, − 0.7 to 0.3, − 0.2 to 0.4, − 0.4 to 0.6, − 0.1 to 0.6, and 0.5 to 0.6, respectively. Significantly high correlations (r = 0.80) were observed between the predicted ability of all patients and the upper-extremity items of shoulder-elbow-forearm in the FMA. We have introduced an automated program based on item response theory and determined the order of difficulty of the 71 training items in ReoGo-J. The strong correlation between the predicted ability and the shoulder-elbow-forearm items in FMA may be used to ameliorate post-stroke upper-extremity paralysis. Notably, the program allows for estimation of appropriate ReoGo-J tasks, enhancing clinical efficiency.Trial registration: https://www.umin.ac.jp/ctr/index-j.htm (UMIN000040127).

A Note on Equivalent and Nonequivalent Parametrizations of the Two-Parameter Logistic Item Response Model

The two-parameter logistic (2PL) item response model is typically estimated using an unbounded distribution for the trait θ. In this article, alternative specifications of the 2PL models are investigated that consider a bounded or a positively valued θ distribution. It is highlighted that these 2PL specifications correspond to the partial membership mastery model and the Ramsay quotient model, respectively. A simulation study revealed that model selection regarding alternative ranges of the θ distribution can be successfully applied. Different 2PL specifications were additionally compared for six publicly available datasets.

Item response theory-based continuous test norming.

In norm-referenced psychological testing, an individual's performance is expressed in relation to a reference population using a standardized score, like an intelligence quotient score. The reference population can depend on a continuous variable, like age. Current continuous norming methods transform the raw score into an age-dependent standardized score. Such methods have the shortcoming to solely rely on the raw test scores, ignoring valuable information from individual item responses. Instead of modeling the raw test scores, we propose modeling the item scores with a Bayesian two-parameter logistic (2PL) item response theory model with age-dependent mean and variance of the latent trait distribution, 2PL-norm for short. Norms are then derived using the estimated latent trait score and the age-dependent distribution parameters. Simulations show that 2PL-norms are overall more accurate than those from the most popular raw score-based norming methods cNORM and generalized additive models for location, scale, and shape (GAMLSS). Furthermore, the credible intervals of 2PL-norm exhibit clearly superior coverage over the confidence intervals of the raw score-based methods. The only issue of 2PL-norm is its slightly lower performance at the tails of the norms. Among the raw score-based norming methods, GAMLSS outperforms cNORM. For empirical practice this suggests the use of 2PL-norm, if the model assumptions hold. If not, or the interest is solely in the point estimates of the extreme trait positions, GAMLSS-based norming is a better alternative. The use of the 2PL-norm is illustrated and compared with GAMLSS and cNORM using empirical data, and code is provided, so that users can readily apply 2PL-norm to their normative data. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Patient feasibility as a novel approach for integrating IRT and LCA statistical models into patient-centric qualitative data-a pilot study.

Clinical research increasingly recognizes the role and value of patient-centric data incorporation in trial design, aiming for more relevant, feasible, and engaging studies for participating patients. Despite recognition, research on analytical models regarding qualitative patient data analysis has been insufficient. This pilot study aims to explore and demonstrate the analytical framework of the "patient feasibility" concept-a novel approach for integrating patient-centric data into clinical trial design using psychometric latent class analysis (LCA) and interval response theory (IRT) models. A qualitative survey was designed to capture the diverse experiences and attitudes of patients in an oncological indication. Results were subjected to content analysis and categorization as a preparatory phase of the study. The analytical phase further employed LCA and hybrid IRT models to discern distinct patient subgroups and characteristics related to patient feasibility. LCA identified three latent classes each with distinct characteristics pertaining to a latent trait defined as patient feasibility. Covariate analyses further highlighted subgroup behaviors. In addition, IRT analyses using the two-parameter logistic model, generalized partial credit model, and nominal response model highlighted further distinct characteristics of the studied group. The results provided insights into perceived treatment challenges, logistic challenges, and limiting factors regarding the standard of care therapy and clinical trial attitudes.

An Item Response Theory Analysis of the Psychosis Screening Questionnaire in Ethiopia.

Few psychosis screening instruments have been tested for use in Africa, yet appropriate tools can increase the detection of self-reported psychotic symptoms, improve the detection of psychosis and impact its prognosis. The construct validity and factor structure of Psychosis Screening Questionnaire (PSQ) were tested with confirmatory factor analysis (CFA) and item response theory (IRT) in a sample of 1928 Ethiopian adults without any history of psychosis. We tested a unidimensional model with and without an item on mania. For IRT, unidimensional latent structure one-parameter logistic (1PL) and two-parameter (2PL) logistic models were tested and compared for relative fit using a likelihood-ratio test. The prevalence of lifetime positive screens was 2.8% in an Ethiopian sample of adults from a general medical setting. A unidimensional model demonstrated good fit for the PSQ, (CFI = 0.993, TLI = 0.986 and RMSEA = 0.025). For IRT, a 2PL model was the best fitting one. IRT tests of item difficulty and discrimination parameters showed that paranoia had the highest discrimination and lowest difficulty ( ), likely to be endorsed at low levels of psychotic features. Thought insertion had the highest item difficulty ( ). Overall, the measure captures the psychosis construct at higher levels of the latent trait and may be suited for detecting moderate to severe levels of psychosis. The PSQ is found to have good construct validity in screening for psychosis among Ethiopian adults. Future studies may focus on the diagnostic validity of the PSQ comparing it with a structured clinical interview.

Myths about suicide - validating the Hungarian version of the Literacy of Suicide Scale (H-LOSS) on a community sample

BackgroundSuicide was exceptionally high in Hungary in the last century. According to Eurostat, Hungary ranks second in the EU in death by suicide and was among the few countries where the suicidal tendencies increased in 2020. Primary tasks of suicide prevention programs are to develop suicide literacy and dispel myths and misconceptions about suicide. Therefore, the goal of our research was the Hungarian validation of the 26-item Literacy of Suicide Scale (LOSS). Methods: 749 people (382 female (51.0%), 364 male (48.6%), 3 identify as non-binary or other (0.4%); 4 identifying as transgender (0.5%)) participated in our online cross-sectional survey with a mean age of 32.4 years (SD = 14.5 years). The H-LOSS questionnaire was adapted using the 2PL (two-parameter logistic) model with WLSE (weighted least squares) estimation in item response theory method, similarly to the original English version.ResultsScale unidimensionality was confirmed. Model fit indices and internal reliability indicators were acceptable. Item infit and outfit values were adequate, item discrimination values were within range, but one item had extremely high and three items had extremely low item difficulty parameters. Few items had differential item functioning by age, gender and own suidice attempt.ConclusionsThe H-LOSS scale deemed to be appropriate for assessing suicide literacy in Hungarian speaking samples.

A person-reported cumulative social risk measure does not show bias by income and education

BackgroundSocial risk such as housing instability, trouble affording medical care and food insecurity are a downstream effect of social determinants of health (SDOHs) and are frequently associated with worse health. SDOHs include experiences of racism, sexism and other discrimination as well as differences in income and education. The collective effects of each social risk a person reports are called cumulative social risk. Cumulative social risk has traditionally been measured through counts or sum scores that treat each social risk as equivalent. We have proposed to use item response theory (IRT) as an alternative measure of person-reported cumulative social risk as IRT accounts for the severity in each risk and allows for more efficient screening with computerized adaptive testing.MethodsWe conducted a differential item functioning (DIF) analysis comparing IRT-based person-reported cumulative social risk scores by income and education in a population-based sample (n = 2122). Six social risk items were analyzed using the two-parameter logistic model and graded response model.ResultsAnalyses showed no DIF on an IRT-based cumulative social risk score by education level for the six items examined. Statistically significant DIF was found on three items by income level but the ultimate effect on the scores was negligible.ConclusionsResults suggest an IRT-based cumulative social risk score is not biased by education and income level and can be used for comparisons between groups. An IRT-based cumulative social risk score will be useful for combining datasets to examine policy factors affecting social risk and for more efficient screening of patients for social risk using computerized adaptive testing.

Personality Measurement of Students Using Item Response Theory Models: Stability Responses from Nigerian Institutions

Item Response Theory (IRT) is utilised to detect bias in assessment tools and address issues such as faked or manipulated responses, enhancing the reliability and stability of conclusions in personality assessment. This article examines the item parameter estimates of a scale and the effectiveness of one-, two-, and three-parameter logistic models in analysing response stability in personality measurement from repeated administration. Three hundred undergraduate students at three tertiary institutions in Nigeria were sampled using a multi-stage sampling procedure. Data was collected using an adapted version of the Big Five Inventory (BFI) with a reliability coefficient of 0.85. The results showed that the item parameter estimates (mean threshold) are within the recommended benchmarks. A comparison of the three IRT models based on the Likelihood ratio (InL), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) values revealed that the two-parameter logistic model best fit the personality data among undergraduates from repeated administration. It is recommended that, rather than relying solely on a statistical decision-making process, IRT fit and model comparison should be applied to gain insight into the functioning of items and tests.

Development and validation of the MultiScent-20 digital odour identification test using item response theory

Although validated and reliable psychophysical tests of olfactory function are available, an easy-to-use and feasible test has yet to be developed. This study aimed to design a digital odour identification test, evaluate its validity, assess its reliability, establish a normative curve, and explore the impact of demographic factors. The odour identification test was presented with the Multiscent-20, a hand-held, tablet-like digital scent device that features an integrated odour digital delivery system. The identification performance on the 20 odours was assessed using item response theory (IRT). The normative curve was established by administering the test to a large sample of participants (n = 1299). The mean identification score was 17.5 (SD = 2.1). The two-parameter logistic IRT model provided the best fit, revealing variation in item discrimination and difficulty parameters. Educational attainment influenced performance, with primary education associated with lower scores. Additionally, sex was not found to be associated with performance. This study provides initial evidence supporting the validity and reliability of use of the Multiscent-20 as a digital odour identification test. The test’s automation and portability enable the standardized delivery of olfactory stimuli and efficient automatic recording and scoring of responses.

Estimation of Standard Error, Linking Error, and Total Error for Robust and Nonrobust Linking Methods in the Two-Parameter Logistic Model

The two-parameter logistic (2PL) item response theory model is a statistical model for analyzing multivariate binary data. In this article, two groups are brought onto a common metric using the 2PL model using linking methods. The linking methods of mean–mean linking, mean–geometric–mean linking, and Haebara linking are investigated in nonrobust and robust specifications in the presence of differential item functioning (DIF). M-estimation theory is applied to derive linking errors for the studied linking methods. However, estimated linking errors are prone to sampling error in estimated item parameters, thus resulting in artificially increased the linking error estimates in finite samples. For this reason, a bias-corrected linking error estimate is proposed. The usefulness of the modified linking error estimate is demonstrated in a simulation study. It is shown that a simultaneous assessment of the standard error and linking error in a total error must be conducted to obtain valid statistical inference. In the computation of the total error, using the bias-corrected linking error estimate instead of the usually employed linking error provides more accurate coverage rates.

The Rank-2PL IRT Models for Forced-Choice Questionnaires: Maximum Marginal Likelihood Estimation with an EM Algorithm

The rank two-parameter logistic (Rank-2PL) item response theory models refer to a set of models applying the 2PL model in a sequential ranking process that occurs in forced-choice questionnaires. The multi-unidimensional pairwise preference with 2PL model (MUPP-2PL) is a Rank-2PL model for items with two statements. Focusing on items with three statements, we develop a maximum marginal likelihood estimation with an expectation-maximization algorithm to estimate item parameters and their standard errors. A simulation study is conducted to check parameter recovery, and then the model is applied to a real dataset. Finally, the findings are summarized and discussed, and future research is suggested.

Differential Item Functioning via Robust Scaling.

This paper proposes a method for assessing differential item functioning (DIF) in item response theory (IRT) models. The method does not require pre-specification of anchor items, which is its main virtue. It is developed in two main steps: first by showing how DIF can be re-formulated as a problem of outlier detection in IRT-based scaling and then tackling the latter using methods from robust statistics. The proposal is a redescending M-estimator of IRT scaling parameters that is tuned to flag items with DIF at the desired asymptotic type I error rate. Theoretical results describe the efficiency of the estimator in the absence of DIF and its robustness in the presence of DIF. Simulation studies show that the proposed method compares favorably to currently available approaches for DIF detection, and a real data example illustrates its application in a research context where pre-specification of anchor items is infeasible. The focus of the paper is the two-parameter logistic model in two independent groups, with extensions to other settings considered in the conclusion.

A neural network paradigm for modeling psychometric data and estimating IRT model parameters: Cross estimation network.

This paper presents a novel approach known as the cross estimation network (CEN) for fitting the datasets obtained from psychological or educational tests and estimating the parameters of item response theory (IRT) models. The CEN is comprised of two subnetworks: the person network (PN) and the item network (IN). The PN processes the response pattern of individual respondent and generates an estimate of the underlying ability, while the IN takes in the response pattern of individual item and outputs the estimates of the item parameters. Four simulation studies and an empirical study were comprehensively and rigorously conducted to investigate the performance of CEN on parameter estimation of the two-parameter logistic model under various testing scenarios. Results showed that CEN effectively fit the training data and produced accurate estimates of both person and item parameters. The trained PN and IN adhered to AI principles and acted as intelligent agents, delivering commendable evaluations for even unseen patterns of new respondents and items.

Identifying Individuals with Highest Social Risk in Adults with Type 2 Diabetes Using Item Response Theory.

The aim of this analysis was to create a parsimonious tool to screen for high social risk using item response theory to discriminate across social risk factors in adults with type 2 diabetes. Cross-sectional data of 615 adults with diabetes recruited from two primary care clinics were used. Participants completed assessments including validated scales on economic instability (financial hardship), neighborhood and built environment (crime, violence, neighborhood rating), education (highest education, health literacy), food environment (food insecurity), social and community context (social isolation), and psychological risk factors (perceived stress, depression, serious psychological distress, diabetes distress). Item response theory (IRT) models were used to understand the association between a participant's underlying level of a particular social risk factor and the probability of that response. A two-parameter logistic IRT model was used with each of the 12 social determinant factors being added as a separate parameter in the model. Higher values in item discrimination indicate better ability of a specific social risk factor in differentiating participants from each other. Rate of crime reported in a neighborhood (discrimination 3.13, SE 0.50; item difficulty - 0.68, SE 0.07) and neighborhood rating (discrimination 4.02, SE 0.87; item difficulty - 1.04, SE 0.08) had the highest discrimination. Based on these findings, crime and neighborhood rating discriminate best between individuals with type 2 diabetes who have high social risk and those with low social risk. These two questions can be used as a parsimonious social risk screening tool to identify high social risk.

Pairwise Likelihood Estimation of the 2PL Model with Locally Dependent Item Responses

The local independence assumption is crucial for the consistent estimation of item parameters in item response theory models. This article explores a pairwise likelihood estimation approach for the two-parameter logistic (2PL) model that treats the local dependence structure as a nuisance in the optimization function. Hence, item parameters can be consistently estimated without explicit modeling assumptions of the dependence structure. Two simulation studies demonstrate that the proposed pairwise likelihood estimation approach allows nearly unbiased and consistent item parameter estimation. Our proposed method performs similarly to the marginal maximum likelihood and pairwise likelihood estimation approaches, which also estimate the parameters for the local dependence structure.

Validating a performance assessment of computational thinking for early childhood using item response theory

Despite growing interest in early childhood computational thinking (CT), there is a lack of validated assessments for children who are emerging readers. This paper presents validity and reliability evidence of a performance-based assessment of CT using item response theory (IRT) from 272 children aged 4–8. Using a two-parameter logistic model IRT model (2PL IRT), we confirmed that model- and item-level fits are acceptable. Item analyses revealed a high discriminability (M = 2.26, SD = 1.12) and a moderate item difficulty (M = −0.21; SD = 0.86), on average, across 19 items. Reliability analysis demonstrated that the assessment was substantially reliable (marginal reliability: rxx = 0.87). Differential item functioning (DIF) analyses indicated that the assessment estimated children's item parameters fairly, regardless of their gender and age. However, we confirmed gaps in latent ability (θ) of CT by gender and age: boys showed higher latent ability of CT than girls, and old children (above 72 months) showed higher latent ability than young children (below 72 months). Findings suggest the assessment is a fair measure that can serve as a reliable and valid tool to assess CT for children who are emerging readers.

Principal goals at school: evaluating construct validity and response scaling format.

The purpose of the present study was to test the efficacy and appropriateness of the 4-point response option of the Principal's Goals Scale of the SASS (1999-2000) survey. Competing dichotomous models with various conceptualizations were constructed and tested against the original polytomous conceptualization. Participants were 8,524 principals from whom 64% were males and 36% females. Principals' goals were assessed using a 6-item scale anchored across points reflecting proximity to achieving a goal. The original polytomous conceptualization was contrasted to a dichotomous two-pole conceptualization using a model with freely estimated discriminations (two-parameter logistic model, 2PL) as well as the Rasch model assuming equal discrimination parameters. Results indicated that the 2PL dichotomous model provided the most optimal model fit. Furthermore, item-related, and person-related estimates pointed to enhanced accuracy and validity for the dichotomous model conceptualization compared to the polytomous model. It is suggested that a dichotomous scaling system is considered in subsequent measurements of the scale as a means of enhancing the accuracy and validity of the measured trait.

Rotation Local Solutions in Multidimensional Item Response Theory Models

We conducted an extensive Monte Carlo study of factor-rotation local solutions (LS) in multidimensional, two-parameter logistic (M2PL) item response models. In this study, we simulated more than 19,200 data sets that were drawn from 96 model conditions and performed more than 7.6 million rotations to examine the influence of (a) slope parameter sizes, (b) number of indicators per factor (trait), (c) probabilities of cross-loadings, (d) factor correlation sizes, (e) model approximation error, and (f) sample sizes on the local solution rates of the oblimin and (oblique) geomin rotation algorithms. To accommodate these design variables, we extended the standard M2PL model to include correlated major factors and uncorrelated minor factors (to represent model error). Our results showed that both rotation methods converged to LS under some conditions with geomin producing the highest local solution rates across many models. Our results also showed that, for identical item response patterns, rotation LS can produce different latent trait estimates with different levels of measurement precision (as indexed by the conditional standard error of measurement). Follow-up analyses revealed that when rotation algorithms converged to multiple solutions, quantitative indices of structural fit, such as numerical measures of simple structure, will often misidentify the rotation that is closest in mean-squared error to the factor pattern (or item-slope pattern) of the data-generating model.

Benefits of the Curious Behavior of Bayesian Hierarchical Item Response Theory Models-An in-Depth Investigation and Bias Correction.

When using Bayesian hierarchical modeling, a popular approach for Item Response Theory (IRT) models, researchers typically face a tradeoff between the precision and accuracy of the item parameter estimates. Given the pooling principle and variance-dependent shrinkage, the expected behavior of Bayesian hierarchical IRT models is to deliver more precise but biased item parameter estimates, compared to those obtained in nonhierarchical models. Previous research, however, points out the possibility that, in the context of the two-parameter logistic IRT model, the aforementioned tradeoff has not to be made. With a comprehensive simulation study, we provide an in-depth investigation into this possibility. The results show a superior performance, in terms of bias, RMSE and precision, of the hierarchical specifications compared to the nonhierarchical counterpart. Under certain conditions, the bias in the item parameter estimates is independent of the bias in the variance components. Moreover, we provide a bias correction procedure for item discrimination parameter estimates. In sum, we show that IRT models create a unique situation where the Bayesian hierarchical approach indeed yields parameter estimates that are not only more precise, but also more accurate, compared to nonhierarchical approaches. We discuss this beneficial behavior from both theoretical and applied point of views.

Revisiting the psychometric properties of the McArthur admission experience survey: Validating the Portuguese version using a bifactor approach

Cultural factors play a significant role in shaping the perception of coercion during psychiatric admissions. The present study aimed to assess the psychometric properties of the Portuguese Admission Experience Survey(P-AES).The study employed a cross-sectional approach in five psychiatric departments in three regions of Portugal. A total of 208 patients participated in the survey. Reliability was assessed through internal consistency and test-retest procedures. Internal validity was analyzed using a two-parameter logistic item response model, exploring three models, including a bifactor model. Convergent validity was determined by correlating AES scores with the Coercion Ladder (CL), Client Assessment of Satisfaction (CAT), and Global Assessment of Functioning (GAF) scale. Discriminatory power was assessed by comparing scores between patients with voluntary and involuntary admission status.The P-AES demonstrated satisfactory internal consistency and test-retest reliability. The bifactor model exhibited superior fit compared to the one-factor and three-factor models. Correlations between P-AES and CL, as well as CAT scores, indicated good convergent validity. Additionally, P-AES scores were notably higher in patients with compulsory psychiatric hospital admission compared to those admitted voluntarily, confirming its discriminatory power.The bifactor model suggests that all three domains of the AES should be used to measure the subjective experience of coercion.