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Rasch Model Analysis of the Indonesian Version of World Health Organization Disability Assessment Schedule (WHODAS 2.0)

Background & Aims: This study evaluated the construct validity of the Indonesian version of WHODAS 2.0 among persons with physical impairment. Methods: WHODAS 2.0 was self-administered to 212 participants with physical impairment in Bandung, Indonesia. The Rasch model was used to analyse the instrument ’ s construct validity. Results: Data of 212 participants were analysed. The average outﬁt mean-square ( MnSq ) of the 36-item and 32-item versions of WHODAS 2.0 satisﬁed the Rasch model expectations (0.99 ± 0.28 vs 0.99 ± 0.24). Item D2.5 ‘ walking a long distance such as a kilometre ’ and item D4.5 ‘ sexual activity ’ were identiﬁed as misﬁtting items in both versions ( inﬁt or outﬁt MnSq ＞ 1.4 ) . The variance explained by measures of the 32 - item version was 56.7 ％ , and the 36 - item version was 49.0 ％ . Both versions ’ reliability and separation index were excellent, with Cronbach ’ s alpha ＞ 0.90 and a separation index ＞ 2 . The response category function and targeting did not fully satisfy the Rasch model expectations. A strong correlation between both versions of WHODAS 2.0 and WHOQOL BREF (r ＞ 0.60) established the convergent validity. Conclusions: The Indonesian version of the 32-item version of WHODAS 2.0 has acceptable construct validity in a physical impairment sample in Bandung, Indonesia.


Introduction
Physical impairments are problems such as a significant deviation or loss of body function or structure. 1 Disability is the umbrella term for impairments, activity limitations and participation restrictions, and refers to the negative aspects of the interaction between an individual (with a health condition) and that individual' s contextual factors (environmental and personal factors). 2 A person with disabilities frequently experiences physical, social and environmental barriers limiting their activity and participation in the community. 3,4 The United Nations Sustainable Development Goals (SDGs) 2015-2030 5 and the Convention on the Rights of Persons with Disabilities (CRPD) urge countries to collect accurate data on disability to understand the impact of barriers on persons with disabilities. 6,7 To address the data accuracy on disability, the International Classification of Functioning, Disability and Health (ICF) framework on disability is broadly used. 2 This framework redefines disability as a limitation on activity and a restriction on participation. 8 Reflecting the ICF framework, the World Health Organization Disability Assessment Schedule (WHODAS 2.0) has been developed to assess the activity limitations and participation restrictions of persons with disabilities. 4 WHODAS 2.0 was translated into many languages and developed specifically to measure activities and participation. 4 The Indonesian version of the WHODAS 2.0 has been used in several censuses to assess the preva-lence rate of disability. However, a lack of evidence on the accuracy of WHODAS 2.0 has become an issue in Indonesia. 9 To provide an accurate measurement, critical psychometric properties of a measurement instrument, such as reliability and validity, must be exhibited. [10][11][12][13][14] The psychometric theory offers two approaches to analyse an instrument to determine the validity and reliability: the factor analysis based on a classical test theory (CTT) approach and the Rasch model analysis based on an item response theory (IRT) approach. 15, 16 The CTT analysis focuses mainly on the observed total score of analysing validity and reliability. 17 Using this approach, the WHODAS 2.0 was found valid in internal diseases, musculoskeletal conditions, stroke 18,19 and back pain. 20 A study conducted by Yuliana et al. (2020) also concluded that the WHODAS 2.0 was valid and reliable to assess the level of disability of stroke survivors in Indonesia. 21 However, the CTT has some conceptual limitations. The CTT often uses the ordinal response scale as an interval scale 22 and assumes that a sum of the score observed can define a person' s actual ability or trait. 15 However, it is not appropriate for measuring empirical reality 23,24 and can lead to erroneous conclusions because the test score achieved by a person often differs from a person' s actual score. 22 Moreover, this approach does not consider the ordered continuum of items and lacks the response category data additivity. 23,24 Rasch model analysis provides supplementary evidence for the construct validity of the instrument 25 and focuses on the probabilistic unidimensional analysis that models the interaction between the item and person. 26 This approach can distribute the persons' ability and the items' difficulty levels along the same logit scale. Rasch model analysis gives statistical information on the ordinal response categories' appropriateness 27 and converts ordinal scores into equal-interval level data to increase measurement precision. 25,28 To date, WHODAS 2.0 has been evaluated using Rasch model analysis. 29 In previous studies, 4,[30][31][32][33] Rasch model analysis proved that WHODAS 2.0 has acceptable validity and reliability to assess several health conditions and cultural environments. In contrast, a study by Kutlay et al. (2009), conducted in Turkey, found that the construct validity of WHODAS 2.0 in patients with osteoarthritis, for some domains, was less than satisfactory. 34 The Indonesian version of WHODAS 2.0 has never been psychometrically calibrated and validated using Rasch model analysis. Therefore, this study was conducted to provide evidence of construct validity of the WHODAS 2.0 among persons with physical impairment using the Rasch model analysis approach. The results of this study are essential to assess the value of WHODAS 2.0 and its utility in Indonesia.

Materials and Methods
This study was conducted in April-May 2019 using self-administered WHODAS 2.0. Ethics approval for the study has been granted from the Research Ethical Com-mittee of Universitas Padjadjaran (No. 140╱UN6.KEP╱ EC╱2019) and Gunma University (No. HS2019-318). The Social Office of Bandung City has approved this study permission (No. 460╱1966-Dinsosnangkis). Prior to data collection, trained surveyors explained the study and received the participants' informed consent. The participants filled in the questionnaire by themselves but could ask questions to the surveyor if they did not understand. The participants could withdraw from the study at any stage.

Study Setting
This study was carried out in Bandung, Indonesia. Bandung is a large city with an area of 168 km 2 and serves as the capital of the West Java Province. Bandung is the third most populous city in Indonesia after Jakarta (the country' s capital) and Surabaya and is one of the most important National Activity Centres for political, economic, and social activities. The industry sector is critical since it contributes significantly to Bandung' s gross domestic product (GDP), utilises local labour, and stimulates local economic activity. 35 Bandung' s population is estimated to be over 2.5 million people, expanding at a rate of 3.5％ per year, and is expected to reach 4.1 million people by 2031, much beyond the city' s current capacity. In 2019, the Bandung Social and Welfare Office registered 5358 people as having impairments, with 2344 of them suffering from physical impairments or a combination of physical and other impairments. A total of 1380 (59％) had only a physical impairment.

Participants
We recruited participants with a physical impairment. We used two steps for the sampling technique: purposive sampling and stratified random sampling. Purposive sampling was performed to collect data from potential participants aged 18 and 60 years who had only a physical impairment, had no cognitive decline and lived in Bandung. Persons with other impairments, such as vision impairment, hearing impairment or cognitive impairment, were not eligible for this study. A list of 1380 persons with a physical impairment was obtained from the social and welfare office of Bandung. We then used stratified random sampling to achieve the targeted sample size within 121 to 303. We calculated a maximum sample size of 303 based on an estimated 22％ of persons with disabilities in Indonesia. 36 The minimum sample size of 121 was estimated using EZR version 1.51 (the standard deviation of 14, a confidence interval of 5, and a confidence level of 95％). We had 271 participants with physical impairments who responded to the questionnaire.

Instruments
(1) Demography Data Using a questionnaire, we gathered socio-demographic information such as age, gender, married status, education status, occupation status, type of impairment, and assistive device usage status.
(2) WHODAS 2.0 The World Health Organization Disability Assessment Schedule (WHODAS 2.0) is a standardised method for measuring health and disability across cultures developed by the WHO. 4 WHODAS 2.0 captures the level of functioning during the 30 days preceding the interview in six domains of life. We used the Indonesian version of the self-administered WHODAS 2.0, which was officially obtained from the WHODAS group. It has been pilottested, back-translated into English, and used in previous studies. 21,[37][38][39] The WHODAS 2.0' items are designed on 5 Likert scales from 0 to 4, where 0 is no difficulty; 1 is mild difficulty; 2 is moderate difficulty; 3 is severe difficulty, and 4 is extreme difficulty╱cannot do. WHODAS 2.0 generates scores for the six domains of functioning (cognitive, getting around, self-care, getting along with people, daily activities, and participation in society) and calculates an overall functioning score. The score ranges from 0 to 100, in which higher scores indicate more significant disability (0＝ no disability; 100＝ very high degree of disability). The WHODAS 2.0 total score for the worker or student is the sum of 36 items. For those who were not working or in school, the score is the sum of 32 items. The 36-item version of WHODAS 2.0 was used in this study to measure the level of disability of the participants. Following the WHODAS 2.0 manual, 4 participants with more than 30％ missing values were excluded from the analysis.  30 This instrument has 26 items comprising 2 items measuring overall QOL and general health, and 24 items measuring four domains: physical, psychological, social relationships, and environmental. 40 The Indonesian version of the WHOQOL-BREF is available and has been proven to be a valid questionnaire in Indonesia. 41,42 In this study, Rasch model analysis showed that this instrument was unidimensional. Thus, the interval logit scale of WHOQOL-BREF was used in the analysis of WHODAS 2.0 convergent validity.

Statistical Analysis
We used Rasch model analysis to evaluate the construct validity of WHODAS 2.0. Rasch model analysis is a mathematical model which assumes that each scale item has a different value or difficulty level. It can provide item and person distributions based on the item' s difficulty and the person' s level of disability using a unit of measurement called a logit (log-odds unit). Rasch model analysis can convert raw ordinal scores into interval logit measures 28 to satisfy the data assumption of normality. According to Messick (1989), construct validity is the integration of any evidence that bears on the interpre-tation or meaning of test scores. Construct validity emphasizes the development of models explaining processes underlying performance on various tests and their relationships to other phenomena. 43 In this study, we separately evaluated the construct validity of the 36-item version, 32-item version, and six domains of WHODAS 2.0 based on the following seven indicators. 14,44 (1) Fit Statistics Fit statistics were used to evaluate the fit of items to the model. 45 WHODAS 2.0 fit statistics were evaluated using the average outfit mean-square (MnSq) and the item and person' s fit statistics. 25,46 MnSq is the mean of the squared residuals for an item, has a chi-square distribution and an expected value. 45 Item fit statistics evaluate the performance of a given item in a test. 47 If fit statistics are greater than the expected value, they suggest more distortion of the measurement system. 48 A misfitting item suggests that the item measures a different and irrelevant construct. Person fit statistics indicate the degree to which persons' response patterns follow what would be expected by the model. 49 There were three steps for fit statistical analysis 25 used in this study.
1 . The average outfit MnSq was evaluated to determine if the set of WHODAS 2.0 fit the Rasch model expectation. The MnSq 1.4 logit is the cutoff point of the acceptable fit statistics, 25 indicating 40％ more variation than predicted by the Rasch model. 45 Item infit or outfit MnSq ＞1.4 logit 46 was used to determine the misfitting item. Infit (inlier-sensitive or information-weighted fit) is relatively affected by unexpected responses closer to item and person measures. Outfit (outlier-sensitive fit) is relatively affected by unexpected responses distance from the item or person measures. 48 2 . If items were misfit, participants with more than 30％ missing values 30 and infit or outfit MnSq ＞ 1.4 logit 46 (misfitting person) were excluded. 3 . The remaining data were used to re-evaluate the average outfit MnSq of a set of items and the infit or outfit MnSq of each item to identify the misfitting item. We might not exclude the misfitting item if the other construct validity indicators satisfied the Rasch model expectations.
(2) Unidimensionality Unidimensionality is a fundamental requirement of construct validity and is necessary to validate a single score of an instrument 50 such as WHODAS 2.0. The unidimensionality assumes that the measurement instrument must measure only one trait at a time. 45 A principal component analysis (PCA) of residuals evaluates the unidimensional exploration of additional explanatory dimensions in the data. The criterion for unidimensionality used in this study is that the first latent dimension should explain at least 50％ of the total variance. 48 If the measurement is unidimensional, a single score for the whole test can be used. In contrast, separate scores for each dimension should be considered if the instrument is not unidimensional. 51

(3) Response Category Function
The response category function assumes that the transition from one ordered response category to the next do not vary across the items. The response category function was evaluated according to the following four indicators. 48,52 1 . The average measures and the Andrich thresholds for each step category should advance monotonically. 2 . The Andrich threshold difference should be between 1.4-5 logit. 3 . The outfit MnSq for each step category should be less than 2.0. 4 . Each category should have the same peak as the most probable response at some point along the continuum. If the response category scale is disordered, we could adjust response options by collapsing the adjacent categories. However, as long as the instrument' s construct validity fits the Rasch model expectations, adjusting the response category is unnecessary. 48 (4) Reliability and Separation Reliability or internal consistency refers to how all the items or questions assess the same characteristic. Cronbach' s alpha, the average of all the correlations between each item and the total score, is often calculated to determine the internal consistency. 53 The Cronbach' s alpha values range from 0 to 1.0. The closer the value is to 1.0, the less the variability can be attributed to measurement error. 54 Any Cronbach' s alpha value between 0.80 and 0.90 is considered good, and a value of more than 0.90 is considered excellent. 45 The separation index was also calculated to determine whether the instrument could differentiate items and persons with different difficulty levels. For differentiating at least two distinct groups, a separation index of 2 is required. 25 When the instrument fails to meet the item and person separation criteria, it is likely because the items are not sufficiently different in terms of difficulty levels and do not match all the disability levels represented among the participants. 55 (5) Appropriateness of the item difficulty level for the sample The appropriateness of the item difficulty level for the sample was examined using targeting and can be seen on the Wright map (person-item map) in Fig. 2. On the left side of the map, the participants were ranked based on their latent traits (or in our study, their level of disability), and on the right side of the map, the items were ranked based on their difficulty (or in our study, the level of disability implied by the item). According to the Rasch model principle, 56 we assumed that participants with lower disability levels had a higher probability of easily doing more difficult activities (more negative logits). Participants with higher disability levels were highly likely to find it difficult to do even the easier activities (more positive logits). Rasch model analysis examines the targeting by evaluating the person-item mean difference and sample target coverage. 57 A difference of zero and below one logit indicate a perfect targeting and a well-targeting of the scale, respectively, whereas a difference of more than one logit indicates mistargeting. 58 The other targeting evaluation is to measure the sample target coverage. The more the scale covers the sample targets (targeting area), the better the targeting. 59 (6) Differential Item Functioning of Misfitting Item Differential item functioning (DIF) occurs when participants who are similar in certain latent traits but differ in another characteristic (DIF group) are more likely to score higher (or lower) on particular items than members of another group. 45,49 A DIF is considered present if the average item calibration for the DIF group differs by ＞0.5 logit (p ≤ 0.05). In this study, DIF was explicitly evaluated to investigate the possible bias of the socio-demographic variables as the causes of the misfitting items. We evaluated the DIF group concerning socio-demographic variables, including age, sex, marital status, occupational status, and assistive device usage status. (7) Convergent Validity Convergent validity investigates how scores obtained from one test correlate with scores from another test. 53 In this study, the WHOQOL-BREF was chosen for the convergent validity assessment because of the similarity of the questionnaire structure with the WHODAS 2.0. The WHODAS 2.0 measures functioning, while the WHOQOL measures subjective well-being. 60,61 In addition, since the WHOQOL-BREF was unidimensional, its raw scores were converted to interval logit measures to evaluate Pearson' s correlation coefficient with that of the WHODAS 2.0 and, therefore, the convergent validity of the instruments was determined. A correlation coefficient (r) of around 0.60 was expected. 62

Ordinal to Interval Scale Conversion
The conversion was used to interpret the size of the disability scores. The interval scale is used to analyse and compare outcomes across groups. 50 If the instrument' s construct validity is confirmed, conversion of raw ordinal scores to interval logit measures can be applied. 63 This will be helpful for WHODAS 2.0 users such as clinicians or rehabilitation staff 64 who are not familiar with Rasch model analysis to use the interval logit measures directly. In this study, the IBM SPSS statistics 27 (IBM Corp., Armonk, New York) was used for data entry, descriptive statistics, and correlation statistics, and the WINSTEPS 3.75 (Winsteps ® , Beaverton, Oregon) 48 was used to conduct the Rasch model analysis. 14

Results
(1) Fit Statistics A total of 271 participants with physical impairments was first used to evaluate the 36-item version, 32-item version and six domains of WHODAS 2.0. These were the steps to evaluate the fit statistics. 'severe difficulty' to category 4 'extreme╱cannot do' in the 36-item version, and all categories in the 32-item version were less than 1.4 logit, indicating that the category did not fit the model. 3 . The outfits MnSq of the 5-category were less than 2.0, and therefore fit the model. 4 . The probability peak of the 5-category of both versions did not satisfy the model expectation. The probability of mild, moderate, and severe difficulty was much lower than none, and extreme╱cannot do. The category probability curves are shown in Fig.1. The x-axis represents what is being measured (level of disability). The y-axis represents the probability of responding to any category, ranging from 0 to 1.

(4) Reliability and Separation
The reliability and separation of WHODAS 2.0 and participants were satisfied and supported the internal consistencies ( Table 1) Table 5 shows the targeting statistics for the 36-item and 32-item versions of WHODAS 2.0. For the 36-item version, the average logit for persons (M＝-1.84, SD＝ 1.54) was lower than that for items (M＝0.00, SD＝0.78) with a difference of 1.84 logit, indicating mistargeting. The targeting area between item difficulty and a person' s level of disability for this sample was 41 participants (64.1％). Twenty-five participants (35.9％) scored below the range of item difficulty (the actual level of disability was lower than that measured by WHODAS 2.0), and no participants scored above the range. For the 32-item version, the average logit for persons (M＝-0.96, SD＝1.43) was lower than that for the items (M＝0.00, SD＝0.68) with a difference of 0.96 logit, indicating well-targeted. The targeting between item difficulty and person' s level of disability for this sample was 149 participants (70.3％). Fifty-six participants (26.4％) scored below the range of item difficulty (the actual level of disability was lower than that mea-sured by WHODAS 2.0), and only 7 participants (3.3％) scored above the range (the actual level of disability was higher than that measured by WHODAS 2.0). Fig. 2 shows the Wright maps to illustrate the targeting of WHODAS 2.0. (

6) DIF of The Misfitting Item
The DIF contrast ＞0.5 of misfitting items D2.5, D3.4, and D4.5 was evaluated based on age, sex, marital status, occupational status, and assistive device usage status. In the 36-item version, DIF was found among the assistive device usage status groups for the misfitting item D2.5 (DIF contrast＝-0.66, p＝0.002), and in the 32-item version, DIF was found among the marital status groups for the misfitting item D4.5 'sexual activity' (DIF contrast: 0.99, p＝0.011). We did not find the DIF of D3.4 based on those characteristics' groups. (7) Convergent Validity WHODAS 2.0 and its domains had a significantly negative correlation with WHOQOL BREF. The 36-item and 32-item version scores were strongly correlated with WHOQOL BREF scores at r＝-0.65 and r＝-0.64, respectively. These correlations supported the convergent validity of WHODAS 2.0.

Ordinal to Interval Scale Conversion
The 32-item version of WHODAS 2.0 satisfied the Rasch model expectations, supported the construct validity, and, therefore, a converted interval logit measure can be used. Table 6 presents the conversion of the raw score (0 to 128) to the Rasch measure (-6.82 to 6.53 logit).

Discussion
This is the first study to evaluate the construct validity of the self-administered Indonesian version of WHODAS 2.0 among persons with physical impairments using a Rasch model analysis. WHODAS 2.0 has been used by the Indonesian health and social ministry since 2011 to evaluate a person' s level of disability to prioritise health and welfare-oriented programs. However, the disability-related data in Indonesia are inconsistent, which challenges the validity of the WHODAS 2.0. According to 2019 impairment data from the Social and Welfare Office, Bandung has the greatest percentage of persons with physical impairments (and combination with other impairment types) at approximately 44％. More than half of them suffered from only physical impairment (59％). Thus, we recruited persons with physical impairments to participate in this study. We used 271 participants to evaluate the instrument. It was identified that both versions of WHODAS 2.0 were reliable, and the 32-item version was unidimensional. There were misfitting items: four items in the 36-item version (D2.1, D2.2, D2.5 and D6.7) and four items in the 32-item version (D4.5, D5.4, D6.1 and D6.7) that might reduce their overall performance. According to guidance, 25,30 participants with missing values ＞30％ and participants with infit or outfit MnSq ＞1.4 (misfitting person) were necessarily excluded to prevent bias in data analysis. Misfitting persons are those who have unexpected responses to the questions. It could be due to special knowledge, lucky guessing, carelessness, mistakes, misunderstanding or exceptional ignorance. 46 The results provided evidence for several aspects of validity. After the 59 data were excluded, the principal components analysis (PCA) analysis using the 212 remaining participants (66 working participants) showed that the instrument was unidimensional. The    Each "#" represents 2 subjects, each "． " or "x" represents 1 subject (M＝mean; S = 1 standard deviation from the mean; T＝2 standard deviations from the mean) over, 57％ of them did not have any assistive devices supporting them in daily activities. They might have no experience of undertaking such activities as walking a long distance. Therefore, it is not surprising that responses to this item diverged from the expected difficulty pattern based on the overall performance of WHODAS 2.0. According to the assistive device status group, the DIF evaluation of item D2.5 also showed bias and might function differently. The finding of D3.4 'Staying by yourself for a few days' as a misfitting item is consistent with the result obtained by De Wolf et al. The participants need assistance for doing daily activities such as eating, bathing, dressing, and bowel and bladder care. This finding explains why they could not stay home alone for more than one day, despite experiencing low levels of disability in everyday life. 31 The misfitting item D4.5 'sexual activities' is also similar to the result obtained by De Wolf et al. 31 . It could be related to the missing response to the item as a result of the person' s discouragement in response to the item. 21.2％ of participants did not answer question D4.5. Unmarried (30％) and widows or widowers (30％) participants were among those who did not respond to the question (47.4％). On the other hand, only 6％ of married participants did not respond to this question. The DIF evaluation on item D4.5 showed bias on marital status. The single participants had difficulty answering item D4.5 compared to those who were married. These conditions might be related to Indonesian social norms.
In Indonesia, premarital sex is socially inappropriate and taboo. Thus, choosing not to answer the sexual-related questions might be the best way for them, especially for singles (unmarried and widow╱widower). WHODAS 2.0 revealed good to excellent internal consistency for our sample, with a Cronbach' s alpha ranging from 0.85 to 0.97. This finding is similar to the previous studies conducted in Indonesia, 21 Taiwan, 33 and the United States. 49 The separation index of both versions of WHODAS 2.0 satisfied the requirement for discriminating the persons and items based on their disability level. The  We acknowledge that this study has the following limitations. The participant' s level of disability was not equally distributed to enough participants with a higher level of disability. The sample size of workers in this study was insufficient to evaluate the 36-item version and domain 5 (work and school). WHODAS 2.0 is used for assessing disability levels in persons with various impairments, such as physical, vision, cognitive, and hearing impairments. However, because this study focused on persons with physical impairments, the scope of invariant measurement analysis may be limited. We could not analyse the equality of the relationship between the level of disability (latent trait) and the observed scores across the persons with various impairments. Therefore, whether they were different at certain disability levels could not be determined. We recruited participants with physical impairments from one Indonesian region (Bandung). This could limit the generalizability of the findings to other regions of Indonesia. However, we believe that these findings will contribute to expanding impairment and disability-related evidence in Indonesia. We conclude that even though the Indonesian version of WHODAS 2.0 has misfitting items, an unsatisfying response category function, and is not fully well-targeted to the sample, Rasch model analysis reveals that the instrument is unidimensional and has satisfactory internal consistency. These results indicate that the Indonesian version of WHODAS 2.0, mainly the 32-item version, has acceptable construct validity to assess the level of disability in a physical impairment sample in Bandung, Indonesia. Further analysis would be necessary to guarantee the construct validity assessment results of the 36 Logit: log-odds unit Table 6 Interval score conversion of the 32-item version of WHODAS 2.0