Multidimensional Rasch Model Research Articles

A log-linear multidimensional Rasch model for capture-recapture.

In this paper, a log-linear multidimensional Rasch model is proposed for capture-recapture analysis of registration data. In the model, heterogeneity of capture probabilities is taken into account, and registrations are viewed as dichotomously scored indicators of one or more latent variables that can account for correlations among registrations. It is shown how the probability of a generic capture profile is expressed under the log-linear multidimensional Rasch model and how the parameters of the traditional log-linear model are derived from those of the log-linear multidimensional Rasch model. Finally, an application of the model to neural tube defects data is presented.

Perceived accessibility, mobility, and connectivity of public transportation systems

Although public transportation is considered effective at reducing the external cost of driving private vehicles, many urbanites do not use public transportation. This study develops measures employing accessibility, mobility, and seamless connectivity for an entire public transportation service chain as indicators for evaluating public transport services, prioritizes underperforming scenarios from the perspective of urban travelers, and derives various market segmentation strategies that consider different socio-demographic characteristics. A conceptual model is set up herein to assess these latent constructs that describe unobservable and immeasurable characteristics. As a Likert ordinal scale can generate misleading statistical inferences, the Rasch model is used to eliminate bias generated by an ordinal scale when measuring these three latent constructs separately. The Rasch model compares person parameters with item parameters, which are then subjected to logarithmic transformation along a logit scale so as to recognize specific difficulties of service scenarios that cannot be easily eliminated by certain urban travelers. The multidimensional Rasch model also measures the perceptions of urban travelers in terms of the interactions between accessibility, mobility, and seamless connectivity of this public transportation system. While comparing urban travelers of two large cities in Taiwan, Taipei and Kaohsiung, the empirical results demonstrate that perceived accessibility, mobility, and seamless connectivity differ based on travelers’ age, frequency of weekly sports activities, and environmental awareness. This paper also advances appropriate improvement strategies and provides policy suggestions for urban planners, public transportation service operation agencies, and policy makers when they seek to create user-friendly public transportation services. The proposed approach can be generalized in other cities by considering their local context uniqueness and further evaluating their public transport services.

The Multidimensional Testlet-Effect Rasch Model

Testlet design has been widely adopted in educational and psychological assessment. A testlet is a cluster of items that share a common stimulus(e.g., a reading comprehension passage or a figure), and the possible local dependence among items within a testlet is called testlet-effect. Various models have been developed to take into account such testlet effect. Examples included the Rasch testlet model, two-parameter logistic Bayesian testlet model, and higher-order testlet model. However, these existing models all assume that an item is affected by only one single testlet effect. Therefore, they are essentially unidimensional testlet-effect models. In practice, multiple testlet effects may simultaneously affect item responses in a testlet. For example, in addition to common stimulus, items can be grouped according to their domains, knowledge units, or item format, such that multiple testlet effects are involved. In essence, an item measures multiple latent traits, in addition to the target latent trait(s) that the test was designed to measure. Existing unidimensional testlet-effect models become inapplicable when multiple testlet effects are involved. To account for multiple testlet effect, in this study we develop the so-called(within-item) multidimensional testlet-effect Rasch model. The parameters can be estimated with marginal maximum likelihood estimation methods or Bayesian methods with Markov chain Monte Carlo(MCMC) algorithms. In this study, a popular computer program for Rasch models, ConQuest, was used. A series of simulations were conducted to evaluate parameter recovery of the new model, consequences of model misspecification, and the effectiveness of model-data fit statistics. Results show that the parameters of the new model can be recovered fairly well; and ignoring the multiple testlet effects resulted in a biased estimation of item parameters, and an overestimation of test reliability. Additionally, it did little harm on parameter estimation to fit a more complicated model(i.e., the multidimensional testlet-effect Rasch model) to data with a simple structure. In conclusion, the new model is feasible and flexible.

Compare Unidimensional & Multidimensional Rasch Model for Test with Multidimensional Construct and Items Local Dependence

Test in education, generally, constructed based on multi contents. If every contents viewed as a dimension, hence the test also have multi-dimension too, so that the analysis must be done with the multidimensional model. In reality at some selected tests, we can see that dependence exist between items in different contents. Dependence as referred, make assumption about multidimensional test is not valid anymore so that gives us the opportunity to apply unidimensional models in its analysis, including by using Rasch Model. This matter motivated me to do write this paper with aim to: get Unidimensional Rasch Model based on logistics function, get the item parameter estimation and testee parameter estimation together using the Joint Maximum Likelihood Method, and prove that Unidimensional Rasch Model is the better choice than Multidimensional Rasch Model in condition like this.

INTRODUCING MULTIDIMENSIONAL RASCH MODEL IN MEASURING TRAFFIC POLICE OFFICERS’ BEHAVIOR

This study applied a multidimensional item response model to measure police officers’ ability in conducting red-light running enforcement. The ability to conduct red-light running enforcement was found to consist of five component constructs, including ability on mental demands (AMD), on stopping and chasing vehicle (ASC), on psychological demands (APD), on physical demands (APHD), and under abnormal environment (AAE). The multidimensional Rasch model was then applied to assess the perceived enforcement ability of officers and item/task difficulties of conducting traffic law enforcement. The results showed that most participating police offices performed well on AMD, ASC, and APD constructs, but half of them were weak on APHD and AAE constructs. Young officers were more appropriate to conduct red-light running enforcement than the other officers. Finally, some management strategies are suggested to improve performance when conducting red-light running enforcement.

Validating and Improving the Reliability of the EORTC QLQ-C30 Using a Multidimensional Rasch Model

The reliability and validity of the European Organization for Research and Treatment of Cancer Quality of Life Questionnaire (EORTC QLQ-C30) has not been examined while taking into account the correlation between subscales. The reliability of the EORTC QLQ-C30 subscales is modest, thus limiting their utility in both clinical and research settings. The purpose of this study was to validate the factor structure of multiple-item subscales of the EORTC QLQ-C30 and to improve their reliability by means of an item response analysis by using the multidimensional partial credit model. A total of 2295 patients with complete data were used for the analysis. One- and nine-dimensional partial credit models were used to fit the data to validate the construct validity of the multiple-item subscales of the QLQ-C30. The model comparison showed that the nine-dimensional factor structure of multiple-item subscales was satisfactory. The multidimensional partial credit model fit data of the multiple-item subscales of the QLQ-C30 reasonably well. The estimated test reliabilities of each domain obtained from the multidimensional approach were higher than those obtained from the unidimensional approach. The constructs represented by the multiple-item subscales of the QLQ-C30 were validated. The improved reliability of the multiple-item subscales of the QLQ-C30 under the multidimensional approach can facilitate their applications in clinical and research settings.

The Influence of Between-Dimension Correlation, Misfit, and Test Length on Multidimensional Rasch Model Information-Based Fit Index Accuracy

Most research on confirmatory factor analysis using information-based fit indices (Akaike information criterion [AIC], Bayesian information criteria [BIC], bias-corrected AIC [AICc], and consistent AIC [CAIC]) has used a structural equation modeling framework. Minimal research has been done concerning application of these indices to item response models, especially within the framework of multidimensional Rasch analysis with an emphasis of the role of between-dimension correlation on index accuracy. We investigated how sample size, between-dimension correlation, model-to-data misfit, and test length affect the accuracy of these indices in model recovery in dichotomous data using a multidimensional Rasch analysis simulation methodology. Results reveal that, at higher values of between-dimension correlation, AIC indicated the correct two-dimension generating structure slightly more often than the BIC or CAIC. The results also demonstrated that violations of the Rasch model assumptions are magnified at higher between-dimension correlations. We recommend that practitioners working with highly correlated multidimensional data use moderate length (roughly 40 items) instruments and minimize data-to-model misfit in the choice of model used for confirmatory factor analysis (multidimensional random coefficient multinomial logit or other multidimensional item response theory models).

Using a multidimensional Rasch model approach to measure the police's perceived ability to detect, detain and intercept DWI vehicles when conducting sobriety checkpoints

This study developed a scale to measure 502 Taiwan traffic police officers’ perceived ability to detect, detain, and intercept those vehicles whose drivers are driving while intoxicated (DWI) when conducting sobriety checkpoints. Through factor analysis, the officers’ enforcement ability was found to consist of two component latent traits: detecting ability (DA) and detaining and intercepting ability (DIA). A multidimensional approach of Rasch models was then applied to measure the police officers’ perceived abilities and particular difficulties in conducting sobriety checkpoints. The study results indicated that the majority of police officers performed well in detecting DWI vehicles, but half of the study participants lacked confidence in detaining DWI vehicles and intercepting escaping DWI vehicles. DWI with weaving was found to be the most aggressive and threatening behavior to traffic police when conducting sobriety checkpoints. Police officers over age 46 were found to have significantly lower DA and DIA, while branch captains were found to have significantly higher DA than their colleagues. Several strategies and programs are suggested based on the study findings to improve the enforcement ability of police officers.

Summarizing Item Difficulty Variation with Parcel Scores

A new method for analyzing differential item functioning is proposed to investigate the relative strengths and weaknesses of multiple groups of examinees. Accordingly, the notion of a conditional measure of difference between two groups (Reference and Focal) is generalized to a conditional variance. The objective of this article is to present and illustrate a strategy for aggregating results across sets of similar items that exhibit item difficulty variation. Logically, this aggregation strategy is related to the idea of DIF amplification, but estimation is ultimately carried out in the framework of a confirmatory multidimensional Rasch model. Grade 4 data from the 2000 National Assessment of Educational Progress are used to illustrate the technique.

Measurement Precision and Efficiency of Multidimensional Computer Adaptive Testing of Physical Functioning Using the Pediatric Evaluation of Disability Inventory

Haley SM, Ni P, Ludlow LH, Fragala-Pinkham MA. Measurement precision and efficiency of multidimensional computer adaptive testing of physical functioning using the Pediatric Evaluation of Disability Inventory. Objective To compare the measurement efficiency and precision of a multidimensional computer adaptive testing (M-CAT) application to a unidimensional CAT (U-CAT) comparison using item bank data from 2 of the functional skills scales of the Pediatric Evaluation of Disability Inventory (PEDI). Design Using existing PEDI mobility and self-care item banks, we compared the stability of item calibrations and model fit between unidimensional and multidimensional Rasch models and compared the efficiency and precision of the U-CAT– and M-CAT–simulated assessments to a random draw of items. Setting Pediatric rehabilitation hospital and clinics. Participants Clinical and normative samples. Interventions Not applicable. Main Outcome Measures Not applicable. Results The M-CAT had greater levels of precision and efficiency than the separate mobility and self-care U-CAT versions when using a similar number of items for each PEDI subdomain. Equivalent estimation of mobility and self-care scores can be achieved with a 25% to 40% item reduction with the M-CAT compared with the U-CAT. Conclusions M-CAT applications appear to have both precision and efficiency advantages compared with separate U-CAT assessments when content subdomains have a high correlation. Practitioners may also realize interpretive advantages of reporting test score information for each subdomain when separate clinical inferences are desired.

A Simplified Stroke Rehabilitation Assessment of Movement Instrument

An efficient, reliable, and valid instrument for assessing motor function in patients with stroke is needed by both clinicians and researchers. To improve administration efficiency, we applied the multidimensional Rasch model to the 30-item, 3-subscale Stroke Rehabilitation Assessment of Movement (STREAM) instrument to produce a concise, reliable, and valid instrument (simplified STREAM [S-STREAM]) for measuring motor function in patients with stroke. The STREAM (consisting of 3 subscales: upper-limb movements, lower-limb movements, and mobility) was administered to 351 subjects with first stroke occurrence and a median time after stroke of 12.5 months. The unidimensionality of each subscale of the STREAM first was verified with unidimensional Rasch analysis. Each subscale of the STREAM then was simplified by deleting redundant items on the basis of expert opinion and the results of the Rasch analysis. The Rasch reliability of the S-STREAM and the concurrent validity of the S-STREAM with the STREAM were examined with multidimensional Rasch analysis and the intraclass correlation coefficient (ICC), respectively. After deleting the items that did not fit the Rasch model, we found that the 8-item upper-limb movement subscale, the 9-item lower-limb movement subscale, and the 10-item mobility subscale assessed single, unidimensional upper-limb movements, lower-limb movements, and mobility, respectively. We selected 5 items from each subscale to construct the S-STREAM and found that the reliability of each subscale of the resulting simplified instrument was high (Rasch reliability coefficients of > or =.91). The agreement between the subscale scores (Rasch estimates) of the S-STREAM and those of the STREAM was excellent (ICC of > or =.99, with a lower limit for the 95% confidence interval of > or =.985), indicating good concurrent validity of the S-STREAM with the STREAM. The S-STREAM demonstrates high Rasch reliability, unidimensionality, and concurrent validity with the STREAM in patients with stroke. Furthermore, the S-STREAM is efficient to administer, as it consists of only half the number of items in the original STREAM. Additional studies to examine other psychometric properties (eg, predictive validity and responsiveness) of the S-STREAM or its psychometric properties in various recovery stages after stroke are needed to further establish its utility in both clinical and research settings.

Clustering Binary Variables in Subscales Using an Extended Rasch Model and Akaike Information Criterion

In this work, we handle the problem of selection of dichotomous items (questions with two possible answers) of a Quality of Life (QoL) questionnaire in sub-scales (subgroup of items producing unidimensional score). A procedure of clustering binary variables (items) in sub-scales with nice measurement properties is proposed. It is based on a new multidimensional Rasch model chosen in order to guarantee some specific measurement properties to the produced scores. The proposed process is presented, discussed and compared by simulations with the Mokken scale procedure (MSP). These simulations show that this new procedure is promising, specially when the structure of the set of binary variables is multidimensional, even if, several drawbacks persist, specially the time of computing of the procedure.

Gain Score in Item Response Theory as an Effect Size Measure

Because of the requirement of reporting effect sizes and in the interest of measurement of change within the item response theory framework, their combination becomes a new issue. In the present study, repeated measures are decomposed as an initial ability and one or more modifiabilities (gain score) using a multidimensional Rasch model. The modifiability can be directly interpreted in terms of logit scale. The standardized mean modifiability is recommended for meta-analysis when test equating is not possible across studies. A simulation study was conducted to assess parameter recovery. It appeared that the point estimates were accurate whereas the error variances were underestimated. The bootstrap method was used and found appropriate for estimating the error variances. Implications and applications are illustrated through an empirical example.

Contemporary Extensions of the Rasch Model

This paper will introduce, discuss and illustrate two contemporary extensions of theRasch model: the one parameter logistic model (Verhelst and Glas, 1995) and theMultidimensional Rasch model (Hoijtink et al., 1999). Using data with respect tothe measurement of schizotypy (Vollema and Hoijtink, 2000) the most importantfeatures of both models will be illustrated. For the one parameter logistic modelthese include: a (discrete) discrimination parameter for each item; a test for itembias; and, estimation of the location of a person on the (latent) trait that is beingmeasured. For the multidimensional Rasch model these include: specification ofthe model; and, model selection. All analyses presented in this paper can be executedusing either OPLM (Verhelst et al., 1995), TESTFACT (Wilson et al.,1984) or ConQuest (Wu et al., 1998). At the end of the paper some features ofmodels and software that have not been discussed will be summarized.

Multidimensional Rasch Measurement via Item Component Models and Faceted Designs

A multidimensional Rasch model is presented here, which is a multidimensional extension of item component models. Relations to existing multidimensional item response theory models are discussed. Apart from other applications, it is also suitable for analyzing tests and questionnaires, which are designed according to two or more facets. An application to a 77-item questionnaire on students’ interest in physics with a two-facet structure demonstrates that the model parameters can even be estimated when 17 latent dimensions are to be measured simultaneously (by means of joint maximum likelihood methods).

The multidimensionality of self-report schizotypy in a psychiatric population: an analysis using multidimensional Rasch models.

There is increasing empirical evidence from factor analytical studies that schizotypy is composed of three dimensions. All studies into the multidimensionality of schizotypy used common factor analysis of scales, either exploratory or confirmatory. We argue that for research into the multidimensionality of schizotypy with dichotomous item responses on questionnaires (as with the Schizotypal Personality Questionnaire [SPQ], Raine 1991) much can be learned using generalized multidimensional Rasch models (GMRMs). GMRMs require a priori postulated models of schizotypy, which can be tested in confirmatory analyses. We hypothesized four competing models of schizotypy, based on the literature and clinical impressions-two two-dimensional models and two three-dimensional models. We also hypothesized that items differ in the degree they are indicative of a particular dimension of schizotypy. The sample was 418 psychiatric inpatients and outpatients, with moderate levels of psychopathology, who filled in the SPQ. Both three-dimensional models yielded a much better fit to the data than both two-dimensional models. Our revised three-dimensional model, a revision of that by Raine et al. (1994) and Gruzelier (1996), yielded the best fit. It consisted of positive schizotypy, disorganization, and negative schizotypy. The results strongly suggest that schizotypy, as measured with the SPQ, is a three-dimensional construct.

The Multidimensional Random Coefficients Multinomial Logit Model

A multidimensional Rasch-type item response model, the multidimensional random coefficients multinomial logit model, is presented as an extension to the Adams & Wilson (1996) random coefficients multinomial logit model. The model is developed in a form that permits generalization to the multidimensional case of a wide class of Rasch models, including the simple logistic model, Masters' partial credit model, Wilson's ordered partition model, and Fischer's linear logistic model. Moreover, the model includes several existing multidimensional models as special cases, including Whitely's multicomponent latent trait model, Andersen's multidimensional Rasch model for repeated testing, and Embretson's multidimensional Rasch model for learning and change. Marginal maximum likelihood estimators for the model are derived and the estimation is examined using a simulation study. Implications and applications of the model are discussed and an example is given.

Loglinear Rasch models for the analysis of stability and change

Loglinear unidimensional and multidimensional Rasch models are considered for the analysis of repeated observations of polytomous indicators with ordered response categories. Reparameterizations and parameter restrictions are provided which facilitate specification of a variety of hypotheses about latent processes of change. Models of purely quantitative change in latent traits are proposed as well as models including structural change. A conditional likelihood ratio test is presented for the comparison of unidimensional and multiple scales Rasch models. In the context of longitudinal research, this renders possible the statistical test of homogeneity of change against subject-specific change in latent traits. Applications to two empirical data sets illustrate the use of the models.

Measurement Model for Linking Individual Learning to Processes and Knowledge: Application to Mathematical Reasoning

Contemporary instructional theories increasingly emphasize the importance of linking an individual's learning to changes in cognitive processes and knowledge structures. In this article, an extension of the multidimensional Rasch model for learning and change (MRMLC) is presented so as to permit theories of processes and knowledge structures to be incorporated into the item response model. Like the MRMLC, this extension (MRMLC+) resolves some basic problems in measuring individual change and permits adaptive testing so that precise estimates of learning may be obtained. Additionally, MRMLC+ permits individual learning to be linked to substantive changes in processing and knowledge. An application to a study on the impact of short‐term instruction on mathematical problem solving shows the potential of MRMLC + for interpretations. In this study, a theoretically plausible model of knowledge structures (Mayer, Larkin, & Kadane, 1984) provides the basis of individual learning interpretations.

A multidimensional latent trait model for measuring learning and change

A latent trait model is presented for the repeated measurement of ability based on a multidimensional conceptualization of the change process. A simplex structure is postulated to link item performance under a given measurement condition or occasion to initial ability and to one or more modifiabilities that represent individual differences in change. Since item discriminations are constrained to be equal within a measurement condition, the model belongs to the family of multidimensional Rasch models. Maximum likelihood estimators of the item parameters and abilities are derived, and an example provided that shows good recovery of both item and ability parameters. Properties of the model are explored, particularly for several classical issues in measuring change.