• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.59-70
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• 2013

The purpose of this study was to develop a zero-inflated Rasch (ZI-Rasch) model, a combination of the Rasch model and the ZIP model. The ZI-Rasch model was considered in this study as an appropriate alternative to the Rasch model for zero-inflated data. To investigate the relative appropriateness of the ZI-Rasch model, several analyses were conducted using PROC NLMIXED procedures in SAS under various simulation conditions. Sets of criteria for model evaluations (-2LL, AIC, AICC, and BIC) and parameter estimations (RMSE, and $r$) from the ZI-Rasch model were compared with those from the Rasch model. In the data-model fit indices, regardless of the simulation conditions, the ZI-Rasch model produced better fit statistics than did the Rasch model, even when the response data were generated from the Rasch model. In terms of item parameter ${\lambda}$ estimations, the ZI-Rasch model produced estimates similar to those of the Rasch model.

• Physical Therapy Korea
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• v.21 no.2
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• pp.74-81
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• 2014

The versions of the Oswestry disability questionnaire (ODQ) is regarded as one of the most extensively used condition-specific instruments measuring disability resulting from low back pain. It has been shown to have adequate psychometrics, reliability, validity, and responsiveness as a whole, yet the summated total score of the instrument often provide little information to rehabilitation clinicians. A keyform analysis based on Rasch measurement model is an innovative way of illustrating the specific test items that an individual may or may not perform. By applying the keyform of the Rasch measurement model to the ODQ, rehabilitation clinicians may able to select more challenging ODQ items matching an individual's ability and document them as attainable treatment goals. The results demonstrated how a keyform analysis assist to setting possible goals for the treatment of individuals with low back pain. Forty-two individuals with low back pain were recruited from rehabilitation clinics in Gainesville, Florida. A series of Rasch analyses on the 10 items of the ODQ were performed using Winsteps software. The performance of two individuals on those 10 items was illustrated on the keyform. The keyform analysis of the Rasch measurement model may be translated into a useful tool for making clinical judgements.

• Physical Therapy Korea
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• v.20 no.3
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• pp.89-99
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• 2013

The purposes of this study were: 1) to show the item difficulty hierarchy of walking/moving construct of the International Classification of Functioning, Disability and Health-Activity Measure (ICF-AM), 2) to evaluate the item-level psychometrics for model fit, 3) to describe the relevant physical activity defined by level of activity intensity expressed as Metabolic Equivalent of Tasks (MET), and 4) to explore what extent the empirical activity hierarchy of the ICF-AM is linked to the conceptual model based on the level of energy expenditure described as MET. One hundred and eight participants with lower extremity impairments were examined for the present study. A newly created activity measure, the ICF-AM using an item response theory (IRT) model and computer adaptive testing (CAT) method, has a construct on walking/moving construct. Based on the ICF category of walking and moving, the instrument comprised items corresponding to: walking short distances, walking long distances, walking on different surfaces, walking around objects, climbing, and running. The item difficulty hierarchy was created using Winstep software for 20 items. The Rasch analyses (1-parameter IRT model) were performed on participants with lower extremity injuries who completed the paper and pencil version of walking/moving construct of the ICF-AM. The classification of physical activity can also be performed by the use of METs that is often preferred to determine the level of physical activity. The empirical item hierarchy of walking, climbing, running activities of the ICF-AM instrument was similar to the conceptual activity hierarchy based on the METs. The empirically derived item difficulty hierarchy of the ICF-AM may be useful in developing MET-based activity measure questionnaires. In addition to convenience of applying items to questionnaires, implications of the finding could lead to the use of CAT method without sacrificing the objectivity of physiologic measures.

• Physical Therapy Korea
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• v.21 no.4
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• pp.40-48
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• 2014

Differential item functioning (DIF) based on Rasch model can be used to examine whether the items function similarly across different groups and identify items that appear to be too easy or difficult after controlling for the ability levels of the compared groups. The Oswestry low back pain disability (Oswestry) has traditionally been proved as an effective instrument measuring disability resulting from low back pain (LBP). In this study, DIF method was used to explore whether items on the Oswestry perform similarly across two different groups (participants with LBP and no LBP). A series of Rasch analyses on the 10 items of the Oswestry were performed using Winsteps$^{(R)}$ software. Forty-two participants with back pain were recruited from 3 rehabilitation hospitals in Gainesville, Florida. Another 42 participants with no LBP were recruited from several public places in the rehabilitation hospitals. Based on the DIF analysis across the two groups, several items were found to have an uniform DIF. Participants with no LBP had more difficulty on lifting and personal care items and participants with LBP had more difficulty on sleeping and social life items. For non-LBP group, a high ceiling effects (83% of participants with non-LBP) was detected, which was not be able to be effectively measured with the Oswestry items. Although 4 items of the Oswestry function differently across the two groups, all items of the Oswestry were well targeted the LBP group.

• Research in Vestibular Science
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• v.17 no.4
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• pp.152-159
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• 2018

Objectives: The Korean Dizziness Handicap Inventory (KDHI), which includes 25 patient-reported items, has been used to assess self-reported dizziness in Korean patients with Parkinson disease (PD). Nevertheless, few studies have examined the KDHI based on item-response theory within this population. The aim of our study was to address the feasibility and clinimetric properties of the KDHI instrument using polytomous Rasch measurement analysis. Methods: The unidimensionality, scale targeting, separation reliability, item difficulty (severity), and response category utility of the KDHI were statistically assessed based on the Andrich rating scale model. The utilities of the orderedresponse categories of the 3-point Likert scale were analyzed with reference to the probability curves of the response categories. The separation reliability of the KDHI was assessed based on person separation reliability (PSR), which is used to measure the capacity to discriminate among groups of patients with different levels of balance deficits. Results: Principal component analyses of residuals revealed that the KDHI had unidimensionality. The KHDI had satisfactory PSR and there were no disordered thresholds in the 3-point rating scale. However, the KDHI showed several issues for inappropriate scale targeting and misfit items (items 1 and 2) for Rasch model. Conclusions: The KDHI provide unidimensional measures of imbalance symptoms in patients with PD with adequate separation reliability. There was no statistical evidence of disorder in polytomous rating scales. The Rasch analysis results suggest that the KDHI is a reliable scale for measuring the imbalance symptoms in PD patients, and identified parts for possible amendments in order to further improve the linear metric scale.

• Physical Therapy Korea
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• v.20 no.4
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• pp.22-31
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• 2013

The aim of the present study was to compare measurement precisions of the Oswestry Back Pain Disability Questionnaire (ODQ) and a computer adaptive testing (CAT) method. The ODQ has been regarded as one of the most reliable condition-specific measure for back pain for decades. Cross-sectional study was carried out with two independent convenient samples from two out-patient rehabilitation clinics for back pain ($n_1=42$) and non-back pain group ($n_2=42$). Participants were asked to fill out the ODQ and CAT of International Classification of Functioning, Disability and Health-Activity Measure (ICF-AM). A series of Rasch analyses were performed to calculate person ability measures. The CAT measures had greater relative precision in discriminating the groups than did the ODQ measure in comparisons of the relative precision. The CAT measure appears to be more effective than did the ODQ measure in terms of measurement precision. By administering test items calibrated in a way, CAT measures using item response theory may promise a means with measurement precision as well as efficiency.

• Journal of Gifted/Talented Education
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• v.17 no.1
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• pp.1-26
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• 2007

The purpose of this study was to develop a math test for identification of the mathematically gifted on the basis of their math creative problem solving ability and to evaluate the goodness of the test. Especially, testing reliability and validity of scoring method on the basis of fluency only for evaluation of math creative problem solving ability was one of the main purposes. Ten closed math problems and 5 open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 closed math test items of Type I and the 5 open math test items of Type II were administered to 1,032 Grade 7 students who were recommended by their teachers as candidates for gifted education programs. Students' responses were scored by math teachers. Their responses were analyzed by BIGSTEPS and 1 parameter model of item analyses technique. The item analyses revealed that the problems were good in reliability, validity, item difficulty and item discriminating power even when creativity was scored based on the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creative problem solving ability of the candidates for math gifted education programs. In addition, it was found that the math creative problem solving tests discriminated applicants for the two different gifted educational institutions.

• Research in Mathematical Education
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• v.10 no.1 s.25
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• pp.55-70
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• 2006

The purpose of this study was to develop math creative problem solving test in order to identify the mathematically gifted on the basis of their math creative problem solving ability and evaluate the goodness of the test in terms of its reliability and validity of measuring creativity in math problem solving on the basis of fluency in producing valid solutions. Ten open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 open math test items were administered to 2,029 Grade 5 students who were recommended by their teachers as candidates for gifted education programs. Fluency, the number of valid solutions, in each problem was scored by math teachers. Their responses were analyzed by BIGSTEPTS based on Rasch's 1-parameter item-response model. The item analyses revealed that the problems were good in reliability, validity, difficulty, and discrimination power even when creativity was scored with the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creativity of the candidates for math gifted education programs. In addition, it discriminated applicants for two different gifted educational institutions and between male and female students as well.

• Journal of the Korean School Mathematics Society
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• v.9 no.3
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• pp.405-424
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• 2006

The purpose of this study was to develop the instruments which can measure behavior characteristics as a component of Mathematically Giftedness with in middle school period. This study prescribed the variable factors of measurement after classify the characteristics of Mathematically Giftedness through literature studies. And it produced instruments those are finally composed of 51 items through the preliminary test. The participants for the study were 424 Korean middle school students. Statistical analyses were carried out to verify the validities and reliability. Reliability(Cronbach $\alpha$) was in behavior characteristics, .95. Content validity was found to be satisfactory by internal validity evaluation on the test items. Internal validity were analyzed by BIGSTEPTS based on Rasch's 1-parameter item-response model. Construct validity was also found to be satisfactory through factor analysis which showed the four factors which the identification instruments were intended to measure such as, General mathematical mental ability, Mathematical Ability, Processing and Obtaining mathematical information Anility and Mathematical Disposition Ability. In conclusion, the instruments about behavior characteristics of Mathematically Giftedness during middle school period developed by this study are highly reliable on its reliability and validity.