Two-parameter Logistic Item Response Model Research Articles

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.

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.

Differential item functioning of material deprivation assessment in households with or without children.

Composite multidimensional indices are broadly used to measure child poverty and social exclusion. Many of such indices are based on EU-SILC data or similar large scale complex sampling surveys, with the household as unit of analysis. Indicators related to households with or without children may quantify the intended attribute differently depending on the household structure and characteristics of individuals, potentially compromising the assessment. We conducted statistical modelling and hypotheses tests using a two-parameter logistic item response model (IRM) and the likelihood-ratio test for DIF verification. Methods were applied to 2020 EU-SILC Portuguese data comprising 11,367 households representing a population of 4,099,052. Statistical analysis have allowed for the survey sampling design. Our findings demonstrate differential item functioning in the assessment material deprivation in households with or without children.

A Comparison of Linking Methods for Two Groups for the Two-Parameter Logistic Item Response Model in the Presence and Absence of Random Differential Item Functioning

This article investigates the comparison of two groups based on the two-parameter logistic item response model. It is assumed that there is random differential item functioning in item difficulties and item discriminations. The group difference is estimated using separate calibration with subsequent linking, as well as concurrent calibration. The following linking methods are compared: mean-mean linking, log-mean-mean linking, invariance alignment, Haberman linking, asymmetric and symmetric Haebara linking, different recalibration linking methods, anchored item parameters, and concurrent calibration. It is analytically shown that log-mean-mean linking and mean-mean linking provide consistent estimates if random DIF effects have zero means. The performance of the linking methods was evaluated through a simulation study. It turned out that (log-)mean-mean and Haberman linking performed best, followed by symmetric Haebara linking and a newly proposed recalibration linking method. Interestingly, linking methods frequently found in applications (i.e., asymmetric Haebara linking, recalibration linking used in a variant in current large-scale assessment studies, anchored item parameters, concurrent calibration) perform worse in the presence of random differential item functioning. In line with the previous literature, differences between linking methods turned out be negligible in the absence of random differential item functioning. The different linking methods were also applied in an empirical example that performed a linking of PISA 2006 to PISA 2009 for Austrian students. This application showed that estimated trends in the means and standard deviations depended on the chosen linking method and the employed item response model.

About the Equivalence of the Latent D-Scoring Model and the Two-Parameter Logistic Item Response Model

This article shows that the recently proposed latent D-scoring model of Dimitrov is statistically equivalent to the two-parameter logistic item response model. An analytical derivation and a numerical illustration are employed for demonstrating this finding. Hence, estimation techniques for the two-parameter logistic model can be used for estimating the latent D-scoring model. In an empirical example using PISA data, differences of country ranks are investigated when using different metrics for the latent trait. In the example, the choice of the latent trait metric matters for the ranking of countries. Finally, it is argued that an item response model with bounded latent trait values like the latent D-scoring model might have advantages for reporting results in terms of interpretation.

Local influence analysis of the 2PL IRT model for binary responses

Detecting influence is an important diagnostic stage in every statistical analysis. This paper examines the local influence of minor perturbations of the model and data for the two-parameter logistic item response model for binary data. By applying Cook's approach in the corresponding EM algorithm used to obtain the maximum likelihood estimate of the model parameters, the normal curvature and the conformal normal curvature - building blocks for obtaining the diagnostic measures – are computed. The methodology is illustrated with two real examples and an artificial one.

Psychometric investigation of the French version of the Aberrant Salience Inventory (ASI): differentiating patients with psychosis, patients with other psychiatric diagnoses and non-clinical participants

During the prodromal phase of psychosis, individuals may experience an aberrant attribution of salience to irrelevant stimuli. The concept of aberrant salience has been hypothesized to be a central mechanism in the emergence and maintenance of psychosis. The 29-item Aberrant Salience Inventory (ASI) was designed to measure five aspects of aberrant salience. The aim of this study was to investigate the psychometric properties of the French version of the ASI comparing patients with psychosis, patients with other diagnosis and healthy, non-clinical participants. The French-language ASI was adapted using the back-translation procedure. Two hundred and eighty-two participants issued from the general population and 150 psychiatric patients were evaluated. Internal validity was assessed using a two-parameter logistic item response model. Reliability was estimated using a test–retest procedure. Convergent validity was estimated using correlations between the ASI scores and several other scales. Sensitivity was evaluated by comparing the scores of participants with a diagnosis of psychosis, patients with other diagnoses and the general population. The best model distinguished three factors: Enhanced Interpretation and Emotionality, Sharpening of Senses and Heightened Cognition. Reliability and convergent validity estimates were good in both groups. The Sharpening of Senses factor was able to discriminate between patients and the general population. Only the Heightened Cognition factor was able to discriminate patients with psychosis from the other psychiatric patients. The ASI is a valid and reliable tool to study not only the aberrant salience phenomenon in patients with psychosis, but also with other diagnoses and within the general population.

Escala de Desesperanza de Beck analizada con teoría de respuesta al ítem

Se aplicó el modelo logístico de 2 parámetros (ML2p) de la teoría de respuesta al ítem a la escala de desesperanza de Beck (BHS). La desesperanza es un sistema de expectativas negativas sobre el futuro que ocupa un rol central para diversos trastornos mentales. Colaboraron 390 adultos de población general del área metropolitana de Buenos Aires (65.1% mujeres). Se eliminaron dos ítems originales por presentar funcionamiento inadecuado. Los 18 ítems restantes mostraron un ajuste adecuado al ML2p. Los ítems tendieron a localizarse en los niveles medio-altos del rasgo y mostraron una capacidad discriminativa medio-alta. Se obtuvieron evidencias de validez concurrente con SCL-90-R y facetas del neuroticismo. La función de información del test reveló que la escala es más precisa para niveles altos del rasgo. Los resultados obtenidos son alentadores respecto de la calidad psicométrica de la escala. Los ítems calibrados podrían resultar útiles para implementar test adaptativo informatizado.

Propensity to decide on involuntary hospitalisation in primary medical care: Dispositional or situational determinants?

BackgroundThe incidence of involuntary hospitalisations varies widely among and within countries. One factor that could account for these variations is the local profile of medical doctors deciding on involuntary admissions. The first goal of this study was to test whether to decide on an involuntary hospitalisation was an individual or a situational disposition. The second goal was to explore doctors' characteristics associated with the use of coercion in specific situations. MethodMedical doctors of four French-speaking Swiss cantons with the competence, according to cantonal laws, to decide on an involuntary hospitalisation were invited to take part in an online survey. Respondents were asked whether they would decide on an involuntary hospitalisation or not in seven clinical vignettes. Propensity to decide on involuntary hospitalisation was estimated with a two-parameter logistic item response model and latent class analysis. Univariate logistic regression models were used to test whether individual factors were associated with the use of coercion in each situation. Results192 medical doctors completed the online questionnaire. There was near-zero correlation between vignettes: an involuntary hospitalisation decided on by a doctor in one situation was not related to the use of coercion in another. No subgroup was more prone to generally resort to coercion. However, some individual characteristics were related to the use of coercion in specific situations. ConclusionsMedical doctors' propensity to use coercion for mental health problems was better accounted for by situational rather than dispositional factors. Thus, the use of coercion should be examined as a multidimensional concept.

Negative Binomial Models for Visual Fixation Counts on Test Items.

With the development of technology-enhanced learning platforms, eye-tracking biometric indicators can be recorded simultaneously with students item responses. In the current study, visual fixation, an essential eye-tracking indicator, is modeled to reflect the degree of test engagement when a test taker solves a set of test questions. Three negative binomial regression models are proposed for modeling visual fixation counts of test takers solving a set of items. These models follow a similar structure to the lognormal response time model and the two-parameter logistic item response model. The proposed modeling structures include individualized latent person parameters reflecting the level of engagement of each test taker and two item parameters indicating the visual attention intensity and discriminating power of each test item. A Markov chain Monte Carlo estimation method is implemented for parameter estimation. Real data are fitted to the three proposed models, and the results are discussed.

Perceived coercion in psychiatric hospital admission: validation of the French-language version of the MacArthur Admission Experience Survey

BackgroundThe MacArthur Admission Experience Survey (AES) is a widely used tool to evaluate the level of perceived coercion experienced at psychiatric hospital admission. The French-language AES was prepared using a translation/back-translation procedure. It consists of 16 items and 3 subscores (perceived coercion, negative pressures and voice). This study aimed to assess the psychometric properties of the French-language AES.Methods152 inpatients were evaluated. Reliability was estimated using internal consistency coefficients and a test–retest procedure. Internal validity was assessed using a two-parameter logistic item response model. Convergent validity was estimated using correlations between the AES scores and the Coercion Ladder (CL), the Coercion Experience Scale (CES) and the Global Assessment of Functioning (GAF) scale. Discriminatory power was evaluated by comparing the scores of patients undergoing voluntary or compulsory admission.ResultsThe French-language AES showed good internal consistency and test–retest reliability. Internal validity of the three-factor model was excellent. Correlations between AES and CL, CES and GAF scores suggested good convergent validity. AES scores were significantly higher among patients subject to compulsory psychiatric hospital admission than among those admitted voluntarily.ConclusionsOverall, the French-language version of the AES demonstrated very good psychometric proprieties.

A Speeded Item Response Model: Leave the Harder till Later

A speeded item response model is proposed. We consider the situation where examinees may retain the harder items to a later test period in a time limit test. With such a strategy, examinees may not finish answering some of the harder items within the allocated time. In the proposed model, we try to describe such a mechanism by incorporating a speeded-effect term into the two-parameter logistic item response model. A Bayesian estimation procedure of the current model using Markov chain Monte Carlo is presented, and its performance over the two-parameter logistic item response model in a speeded test is demonstrated through simulations. The methodology is applied to physics examination data of the Department Required Test for college entrance in Taiwan for illustration.

Bayesian inference for an item response model for modeling test anxiety

We develop a Bayesian binary Item Response Model (IRM), which we denote as Test Anxiety Model (TAM), for estimating the proficiency scores when individuals might experience test anxiety. We consider order restricted item parameters conditionally to the examinees’ reported emotional state at the testing session. We consider three test anxiety levels: calm, anxious and very anxious. Using simulated data we show that taking into account test anxiety levels in an IRM help us to obtain fair proficiency estimates as opposed to the ones obtained with three two-parameter logistic IRM (3PM) by Birnbaum (1957, 1968). For the 3PM, the proficiency estimates tend to be positively biased for both, calm and anxious examinees.

Considerations for Measuring Functioning of the Elderly: IRM Dimensionality and Scaling Analysis

Modern measurement methods were applied in this study to examine the properties of a measure of functioning of the elderly. Measures of functioning form an essential element in health services and outcomes research. Several implications for scale development and improved score precision are presented in this case study. This study examined the structure of responses to the Older Americans Resources and Services (OARS) Activities of Daily Living (ADL) and Instrumental Activities of Daily Living (IADL) scales using item response model (IRM) analysis methods. The analysis illustrates the extension of IRM dimensionality and item analysis to health scales in general. Attention is given to the underlying theory and appropriate interpretation of these methods for health measurement. Data were taken from 1364 elderly Canadians participating in the caregiver component of the Canadian Study of Health and Aging (CSHA). The fit of a two-parameter logistic IRM was compared with a one-parameter (Rasch) model for these data. The dimensionality of responses to the scale was evaluated with an approximate χ2 test of residuals after fitting an IRM based on non-linear factor analysis. Results confirm that ADL and IADL item sets differ in the degree of disability they measure and are well represented as separate dimensions using a two-parameter IRM. Implications are drawn concerning the adequacy of the OARS disability measure for health surveys, while more general conclusions cover the precision of IRM based optimal scoring for functional disability measures.

Fitting a two-parameter logistic item response model to clarify the psychometric properties of the Drug Use Screening Inventory for adolescent alcohol and drug abusers.

The suitability of fitting a two-parameter logistic item response model to the Drug Use Screening Inventory (DUSI) was assessed. In a sample of 846 adolescents, each of the 10 domains was found to be unidimensional. Invariance of the item parameters across different groups was also observed. The reliability coefficient, based on item response theory, was found to be superior. The results of these analyses indicate that the DUSI has sound psychometric properties.

An investigation of hierarchical Bayes procedures in item response theory

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item and ability parameters. Simulated data sets were analyzed via two joint and two marginal Bayesian estimation procedures. The marginal Bayesian estimation procedures yielded consistently smaller root mean square differences than the joint Bayesian estimation procedures for item and ability estimates. As the sample size and test length increased, the four Bayes procedures yielded essentially the same result.

Fitting the Two-Parameter Model to Personality Data

The Multidimensional Personality Questionnaire (MPQ; Tellegen, 1982) was parameterized using the two-parameter logistic item response model. This en tailed assessment of the suitability of personality data for item response analyses, including the assessment of dimensionality, monotonicity of item response, and data-model fit. The latter issue received special em phasis. Similarities and differences between maximum performance and typical performance data are dis cussed in relation to item response theory. Results suggest that the two-parameter model fits the MPQ data and that researchers engaged in the assessment of nor mal-range personality processes have much to gain from exploiting item response models. Index terms: item fit, item response theory, Multidimensional Per sonality Questionnaire, personality measurement, two-parameter model.

Symptoms and Diagnosis of Depression in Alcoholics

We examined depressive symptoms, using the Beck Depression Inventory (BDI), in a group of 50 alcoholic patients, diagnosed according to DSM III criteria during active drinking, withdrawal (4 days after their last drink), and abstinence (24 days after their last drink). DSM III diagnoses of major depression were made in 16 (32%) of the patients. The diagnoses were made using the NIMH Diagnostic Interview Schedule (DIS) between the 10th and 24th day after the patients' last drink. Depressive symptoms decreased markedly as the patients progressed from active drinking to abstinence. Alcoholic patients having a diagnosis of major depression had higher BDI scores than those not having a diagnosis of major depression. Analysis of BDI items using a two-parameter logistic item response model confirmed that the BDI measured depressive symptoms in these alcoholics. We conclude that the BDI is valid for screening for depression in alcoholic patients.

Bayesian estimation in the two-parameter logistic model

A Bayesian procedure is developed for the estimation of parameters in the two-parameter logistic item response model. Joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described. Through simulation studies it is shown that Bayesian estimates of the parameters are superior to maximum likelihood estimates in the sense that they are (a) more meaningful since they do not drift out of range, and (b) more accurate in that they result in smaller mean squared differences between estimates and true values.