Published on in Vol 16, No 2 (2014): February

Applying Computerized Adaptive Testing to the Negative Acts Questionnaire-Revised: Rasch Analysis of Workplace Bullying

Applying Computerized Adaptive Testing to the Negative Acts Questionnaire-Revised: Rasch Analysis of Workplace Bullying

Applying Computerized Adaptive Testing to the Negative Acts Questionnaire-Revised: Rasch Analysis of Workplace Bullying

Original Paper

1College of Nursing, Kaohsiung Medical University, Kaohsiung, Taiwan

2Nursing Department, Chi-Mei Medical Center, Tainan, Taiwan

3Department of Hospital and Health Care Administration, Chia-Nan University of Pharmacy and Science, Tainan, Taiwan

4Planning Department, Chi-Mei Medical Center, Tainan, Taiwan

5Orthopedics Department, Chi-Mei Medical Center, Tainan, Taiwan

Corresponding Author:

Hsiu-Hung Wang, RN, PhD, FAAN

College of Nursing

Kaohsiung Medical University

No. 100, Shih-Chuan 1st Road

Kaohsiung, 80708


Phone: 886 7 3121101 ext 2624

Fax:886 7 3218364


Background: Workplace bullying is a prevalent problem in contemporary work places that has adverse effects on both the victims of bullying and organizations. With the rapid development of computer technology in recent years, there is an urgent need to prove whether item response theory–based computerized adaptive testing (CAT) can be applied to measure exposure to workplace bullying.

Objective: The purpose of this study was to evaluate the relative efficiency and measurement precision of a CAT-based test for hospital nurses compared to traditional nonadaptive testing (NAT). Under the preliminary conditions of a single domain derived from the scale, a CAT module bullying scale model with polytomously scored items is provided as an example for evaluation purposes.

Methods: A total of 300 nurses were recruited and responded to the 22-item Negative Acts Questionnaire-Revised (NAQ-R). All NAT (or CAT-selected) items were calibrated with the Rasch rating scale model and all respondents were randomly selected for a comparison of the advantages of CAT and NAT in efficiency and precision by paired t tests and the area under the receiver operating characteristic curve (AUROC).

Results: The NAQ-R is a unidimensional construct that can be applied to measure exposure to workplace bullying through CAT-based administration. Nursing measures derived from both tests (CAT and NAT) were highly correlated (r=.97) and their measurement precisions were not statistically different (P=.49) as expected. CAT required fewer items than NAT (an efficiency gain of 32%), suggesting a reduced burden for respondents. There were significant differences in work tenure between the 2 groups (bullied and nonbullied) at a cutoff point of 6 years at 1 worksite. An AUROC of 0.75 (95% CI 0.68-0.79) with logits greater than –4.2 (or >30 in summation) was defined as being highly likely bullied in a workplace.

Conclusions: With CAT-based administration of the NAQ-R for nurses, their burden was substantially reduced without compromising measurement precision.

J Med Internet Res 2014;16(2):e50




Workplace bullying is defined as persistent exposure to interpersonal aggression and mistreatment from colleagues, superiors, or subordinates [1,2]. It is a prevalent problem in the workplace with adverse effects on both victims and organizations [3,4]. Many studies have investigated this problem by determining its frequency, identifying groups at risk in different occupational groups and sectors [5], and addressing prevalence of bullying in different countries and among different occupational groups [6]. However, none of these bullied victim evaluations have applied item response theory (IRT) [7] to assess item functioning of the workplace bullying-related questionnaire [8].

Similarly, no studies have reported results on workplace bullying using IRT-based computerized adaptive testing (CAT) to measure respondents’ bullying exposure, especially in the era of computer technology and when questionnaires have become more integrated in recent years. As of April 24, 2013, 127 articles were found on PubMed by searching the keywords “computer adaptive test” (CAT), 309 with “workplace bullying,” and 106 with “workplace bullying nurse”. It is necessary to investigate whether CAT can be applied to yield the same results as traditional nonadaptive testing (NAT) on a workplace bullying scale for nurses and, thereby, reduce their respondent burden.

Computer Assessment and Computer Adaptive Testing

From the literature, traditional paper-and-pencil or computer-based surveys (NAT) have a large respondent burden and require respondents to answer all the questions [9]. In contrast, CAT-based testing using IRT can achieve similar measurement precision levels as NAT and is approximately half the length of the test [10-13]. However, most CAT articles, except some [9,14,15], compared CAT to NAT with dichotomous items. Whether polytomously scored items on bullying can also be measured as precisely as dichotomous CAT should be further investigated.

Rasch Analysis

In classical test theory (CTT), raw scores are usually used as linear interval scale measures for additive latency to assess respondents’ underlying ability. Unfortunately, this is not correct [16,17]; therefore, subsequent statistical analyses can be problematic and incorrect in computing mean, variance, correlation coefficients, or Cronbach alpha [18,19]. In particular, CTT encounters problems when dealing with missing data.

To overcome this obstacle, the IRT-based Rasch model [20] was developed to represent the probabilistic relationship between a person measure and an item difficulty in log-odds units, or logits. A useful scale using the Rasch model should be evaluated by 3 steps (prior tests, Rasch fit statistics, and post hoc tests) suggested by Smith [21] and Tennant and Pallant [22] (details shown in Methods) to verify a single domain. In many articles, authors used Rasch modeling to develop CAT on clinical samples, but none adopted the model testing steps recommended by Smith to verify scales before implementing CAT [9,10,23-26].


First, we used a polytomous Rasch rating scale model to examine the workplace bullying scale for CAT use. Second, we developed an Excel Visual Basic for Applications (VBA) CAT module for comparison with NAT on efficiency, precision, and inference from the data of 300 hospital nurses. Third, similar inferences made by CAT and NAT were conducted in addition to investigating significant differences in work tenure between 2 groups. Fourth, a cutoff point of the studied bullying scale was determined for discriminating persons who were bullied victims with a predicted (individual) probability.

We report the CAT advantages if the precision and inference of results made by CAT and NAT are similar. Several limitations of CAT application will be raised for consideration in future studies.

Study Participants

The study sample was randomly selected and recruited using the last 3 digits of the identification card number from nurses of a 1333-bed medical center in southern Taiwan in the summer of 2010. No incentive for participation was offered. A total of 300 nurses completed 2 effective eligibility scales (shown in the following section) using NAT. This study was approved and monitored by the Research Ethics Review Board of the Chi-Mei Medical Center.

Demographic data collected included gender, work tenure in hospitals of all types, age, marital status, and education level.

Scales Used

Exposure to Bullying

The Negative Acts Questionnaire-Revised (NAQ-R) [27] used in this study has 22 items with 5 response alternatives (1=never, 2=occasionally, 3=monthly, 4=weekly, 5=daily) to measure exposure to workplace bullying within the past 6 months. Victimization from bullying during the past 6 months was additionally measured by a single self-labeling victimization question that was used for determining the cutoff point of the studied bullying scale after bullying measures were obtained. The NAQ-R was professionally translated into Chinese by authors in Taiwan using a back-translation technique (English-Chinese-English). With permission from the author [28], we conducted Rasch analysis to test scale unidimensionality (shown in the dimensionality section), the appropriateness level of the 5-category NAQ-R [29], as well as reporting reliability (Cronbach alpha) and dimension coefficient (DC) [30] using the CTT method.

Negative Actions Caused by Bullying

Participants were asked questions about their own personal negative experience of bullying and its impact on 5 areas (physical aspects, psychological aspects, interpersonal relations at work, willingness to work, and quality of work) and they were asked to respond to personal symptoms or emotions (eg, gastrointestinal symptoms, fatigue, loss of appetite, crying, fear, anxiety, no sense of belonging, absenteeism, intent to leave the job, hating work, not being able to concentrate on work, loss of patience when caring for patients, frequent occurrence of abnormalities, low self-esteem, sleep disorders, anxiety, concentration disorders, chronic fatigue, anger, depression, several somatic disorders) [31], all of which were subjective self-judgments (yes=1; no=0) and were evolved into a global scale to verify discriminant validity of the NAQ-R.


Tennant and Pallant [22] reported that 3 steps should be applied to assess scale unidimensionality: (1) conduct prior testing using Horn’s parallel analysis [32] to make sure that a single dimension is suitable; (2) use Rasch fit statistics ranging from 0.5 to 1.5 [33,34] to determine the usefulness of the 1-dimensional scaling; and (3) run post hoc tests using the first principal components analysis (PCA) component of Rasch standardized residuals [35] close to zero to inspect the convergent validity, and then performing Smith [36] independent t tests to compare estimates of the percentages (<5%, within ±1.96) and verify invariance of Rasch model (details presented in following section).

Differential Item Functioning

The Rasch rating scale model (used in this study) requires the item estimation to be independent of the subgroups of individuals completing the questions. In other words, item parameters should be invariant across populations [37]. Items not demonstrating invariance are commonly referred to as exhibiting differential item functioning or item bias.

The chi-square test used for detecting the item-trait interaction was computed from a comparison of the observed overall performance of each trait group on the item with its expected performance [38]. Its probability (eg, <.05) reports the statistical probability of observing the chi-square value (or worse) when the data fit the Rasch model. Thus, WINSTEPS table 3.4 was referred to detect differential item functioning items for a significantly different group of person measures [39].

Computer Adaptive Test Procedures and Features

We ran a VBA module in Microsoft Excel in compliance with rules and regulations of CAT (Figures 1 and 2). Cronbach alpha and Rasch person separation reliability calculated from the NAQ-R of the study were used to determine the CAT termination criterion using the standard error of measurement (SEM=SD × √reliability), whereas Rasch reliability refers to reliability in the previously mentioned SEM formula.

We also set another rule that the minimum number of questions required for completion was 10 (10/22 items on NAQ-R item length=45%) because CAT could achieve similar precision in measurement as NAT with approximately half the length [9-12]. The first question was selected randomly from the 22 items when performing the CAT. The provisional measures were estimated by a maximum log likelihood function using an iterative Newton-Raphson procedure [9,12] after 3 questions were answered without responding similarly and sequentially to either 1 or 5. The next question selected was the one with the most information obtained from the remaining unanswered questions, interacting with the provisional person measures. All responses and their respective consumption time for each nurse were recorded after CAT termination.

Figure 1. Computer adaptive test applied to Negative Acts Questionnaire-Revised (NAQ-R) in workplace.
View this figure
Figure 2. Bullying report produced by Negative Acts Questionnaire-Revised (NAQ-R) computer adaptive test with a maximum likelihood estimation plot.
View this figure

Comparison of Efficiency and Precision

Four indexes between CAT and NAT were compared, including test length (efficiency), estimated measures (precision), time saved (in seconds) per item (efficiency), and the area under the receiver operating characteristic (AUROC) curve (precision).

Accordingly, all person measures based on NAT should be estimated in advance, assuming all 22 items were answered. The following steps were adopted: (1) using the WINSTEPS software [39] to calibrate item and threshold difficulties, and (2) performing the studied dataset of 300 people × 22 items to re-estimate both NAT (through all 22 items) and CAT (by less than 22 items) measures using the CAT Excel-VBA module.

Comparison of Groups by Making Inferences

We compared the prediction effects of CAT and NAT on the 4 indexes by regressing person measures, respectively, on (1) the global symptom score, and (2) differences in demographic characteristics (eg, age, work tenure, and marital status) and in self-judgments (victimization from bullying during the past 6 months).

Statistical Analysis

For all statistical analyses, SPSS software for Windows version 12 (SPSS, Chicago, IL, USA) was used. The CAT and NAT person measures were compared using the Pearson correlation coefficient. Test length (efficiency) and estimated measures (precision) were compared by paired t tests. Time saved per item (efficiency) in favor of CAT was computed by a margin of 25.07 seconds (SD 16.04; range 12-43). The total time saving from NAT to CAT was computed by the formula: time saved per item (25.07) multiplies both item lengths shortened by CAT (eg, 2109 items in total), and the sample size (N=300).

The AUROC (precision) was calculated by both Rasch-transformed logit scores and the single self-labeled victimization question from bullying (bullied=1; not bullied=0) to determine a cutoff point with 95% confidence intervals (CIs), sensitivity, and specificity. The criterion of alpha=.05 was considered statistically significant. Horn’s parallel analysis was performed using an online calculator [40] that is based on the literature [32,41].


Two age groups (separated by a cutoff point of 30 years) were contrasted on demographic characteristics (eg, self-labeled victimization from bullying, gender, work tenure within the study hospital, work tenure in health care, marital status, and education level). As seen in Table 1, the prevalence of bullying within the study hospital was 24.0% (72/300). CAT and NAT measures were highly correlated (r=.97)

Table 1. Demographic characteristics of participants (N=300).
CharacteristicsAge (years), n (%)Total, n

Age109 (36.3)191 (63.7)300
Bullied or not

No84 (36.8)144 (63.2)228

Yes25 (34.7)47 (65.3)72

Male1 (25.0)3 (75.0)4

Female108 (36.5)188 (63.5)296
Work tenure in the hospital (years)

≤350 (92.6)4 (7.4)54

3-647 (69.1)21 (30.9)68

6-911 (16.2)57 (83.8)68

>91 (0.9)109 (99.1)110
Work tenure in health care (years)

≤346 (95.8)2 (4.2)48

3-647 (83.9)9 (16.1)56

6-915 (21.7)54 (78.3)69

>91 (0.8)126 (99.2)127
Marital status

Married22 (16.7)110 (83.3)132

Unmarried87 (51.8)81 (48.2)168
Education diploma

Undergraduate109 (37.7)180 (62.3)189

Postgraduate11 (100)11


The NAQ-R can be considered unidimensional given that (1) one factor was extracted by parallel analysis; (2) all infit and outfit mean squares for the 22 items were in a range of 0.5 to 1.5 (shown in Table 2); (3) item loadings from the Rasch PCA of residuals on the first contrast were closely clustered within 0.6 or near 0.6; PTME (ie, point measure regarding the Pearson correlation between the observations of an item and the item difficulties that is similar to factor loading) between 0.48 and 0.78; Rasch person separation reliability=0.90, Cronbach alpha=.98 (>.70), DC=0.89 (>0.70), and Smith’s t test of proportions [36] reach zero outside the range ±1.96 (ie, all persons’ paired t values were within ±1.96). In addition, category structure for the NAQ-R should display the monotonically increasing threshold (-3.39, -0.55, 1.11, and 2.83 logits; Figure 3) with the Linacre’s guidelines [29] to improve the utility of the resulting measures. The absence of differential item functioning suggests good support for measurement invariance. The range of threshold difficulties for those least difficult items 1 and 8 are shown as examples in 2 columns on the right-hand side in Figure 4, indicating that item difficulties cannot sufficiently cover all the person measures with mild or nonbullied symptoms shown on the left bottom in Figure 4 using the NAQ-R scale.

Table 2. One factor extracted from the Negative Acts Questionnaire-Revised (NAQ-R) scale with mean square between 0.50 and 1.50.
During the last 6 months, how often have you been subjected to the following negative acts in the work place?ItemMean squareRasch

Work-related bullying

19. Pressure not to claim something to which by right you are entitled0.370.681.220.88–0.26

21. Being exposed to an unmanageable workload0.180.671.221.12–0.27

16. Being given tasks with unreasonable deadlines0.040.710.940.95–0.21

3. Being ordered to do work below your level of competence–0.240.681.111.100.59

18. Excessive monitoring of your work–0.410.770.930.84–0.43

14. Having your opinions ignored–0.610.750.870.92–0.45

1. Someone withholding information which affects your performance–2.210.731.211.280.47
Person-related bullying

10. Hints or signals from others that you should quit your job1.650.600.960.760.03

20. Being the subject of excessive teasing and sarcasm1.090.690.750.63–0.30

6. Being ignored or excluded0.610.680.930.900.17

15. Practical jokes carried out by people you don’t get along with0.460.720.810.65–0.32

17. Having allegations made against you0.200.730.810.67–0.32

4. Having key areas of responsibility removed or replaced with more trivial or unpleasant tasks–0.090.691.121.080.31

7. Having insulting or offensive remarks made about your person, attitudes or your private life–0.190.720.990.900.14

13. Persistent criticism of your errors or mistakes–0.330.780.770.65–0.49

12. Being ignored or facing a hostile reaction when you approach–0.570.721.171.04–0.34

11. Repeated reminders of your errors or mistakes–0.680.760.950.90–0.26

2. Being humiliated or ridiculed in connection with your work–0.790.721.070.980.59

5. Spreading of gossip and rumors about you–0.900.750.970.960.31
Physically intimidating bullying

22. Threats of violence or physical abuse or actual abuse2.560.481.490.56–0.12

9. Intimidating behaviors such as finger-pointing, invasion of personal space, shoving, blocking your way1.350.611.060.970.11

8. Being shouted at or being the target of spontaneous anger–1.500.711.371.360.25
Figure 3. Threshold step difficulties monotonically increasing for the Negative Acts Questionnaire-Revised (NAQ-R).
View this figure
Figure 4. Variable map for person and item dispersion on Rasch logit scores.
View this figure

Comparison of Efficiency and Precision

The CAT required substantially fewer items than NAT (P<.001). NAT required all 300 participants to respond to all 22 items, yielding 6600 responses. In CAT, only 4491 responses were required, meaning that each nurse answered 14.97 questions on average. As compared to NAT, CAT provided an efficient gain in test length of 0.32, calculated as 1–(ratio of total responses by CAT and NAT), or 1–(4491/6600).

For precision of measurement, person measures from CAT did not statistically differ from those from NAT (P=.14). The total time saving from NAT to CAT was 52,848 seconds (25.07×7.03×300) or 14.68 hours.

Cutoff point values were >–4.2 logits (approximately >30 in traditional summation); AUROC (95% CI), sensitivity, and specificity were found to be similar between CAT and NAT.

Similar Results in Making Inferences

Rasch logit measures (x) of CAT and NAT can yield similar response slope parameters to predict the global scores (y) for negative actions. A 2-way ANOVA revealed that person measures only differed in groups of the bullied and the nonbullied as well as groups with job tenure of less than and more than 30 years (in the study hospital) (Table 3).

Table 3. Similar inferences made by computer adaptive testing (CAT) and nonadaptive testing (NAT).
Demographic characteristicsNATCAT

Mean squareF1,1PMean squareF1,1P



Age × victim10.531.85.1821.873.69.06



Bullied in logit


Work tenure 1 (in this hospital)



Tenure × victim6.531.16.2814.992.55.11



Tenure (years) in logit


Work tenure 2 (in health care)



Tenure × victim2.750.49.499.951.68.19



Marital status



Marry × victim0.570.10.750.440.07.79



Key Findings

The results from this study indicate that the 22-item NAQ-R is considered unidimensional. The CAT is up to 32% more efficient for answering questions and achieved similar precision and inferences in measurements as did NAT. A cut point of >–4.2 logits (or >30 in summation) with AUROC 0.75 (95% CI 0.68-0.79) was determined for future use in workplace bullying surveys. The prevalence of bullying for the study sample was 0.24.

What This Adds to What Was Known

Consistent with the literature [9-12], the efficiency of CAT over NAT was supported. We confirm the CAT-based NAQ-R requires significantly fewer questions to measure victimization from workplace bullying than NAT without compromising its measurement precision.

What It Implies and What Should Be Changed?

Easy to Detect Unexpected Responses

The CAT module can help us efficiently and precisely gather responses from nurses and it was technically applicable. Outfit mean square values of 2.0 or greater can be used to examine whether responses are distorted or abnormal. That is, much more unexpected responses deemed to occur because of possibly careless, mistaken, or awkward endorsement were found in the measurement [9,10,29] (eg, nurse A gained outfit 1.41 and gave unexpected responses on items 4 and 9 as shown in Figure 2). It is easier to detect problematic responses by using CAT than CTT. Multimedia Appendix 1 is a CAT module that can be downloaded and practiced by interested readers.

Steps to Detect Scale Dimensionality Used for Computer Adaptive Testing

Some studies [2,3,5,8] reported that there were 2 or 3 factors extracted from the NAQ-R because it used the eigenvalue greater than 1 (K1) rule to extract a number of factors. A number of studies have shown that the K1 rule is inaccurate and tends to overfactor [32,42,43]. In contrast, Zwick and Velicer’s [44] comparison concluded that parallel analysis was the most accurate evaluation method and it was correct 92% of the time (greater than 22% using K1). That explained why the factor determined using the parallel analysis method in the present study was different from others.

We also uniquely examined it using Smith’s [21] recommended other 2 steps (Rasch analyses shown in Methods) to detect scale dimensionality. Compared to the traditional way of using either parallel analysis or Kayser’s rule to detect the number of factors, Rasch-based analysis is superior in studying the dimensionality of a given instrument (eg, infit and outfit criteria and PCA residuals). Accordingly, the CAT module can be implemented after the scale unidimensionality and item difficulties have been determined using the Smith’s 3 steps and Rasch analysis.

Cutoff Point Recommended for Determining Bully Victims

The AUROCs (0.74 and 0.75 for NAT and CAT, respectively) were not as high as expected (>0.80). It might be acceptable in social science when it is greater than 0.70 because the single self-labeled victimization question (bullied=1; not bullied=0) might be subjectively answered with some bias by examinees’ personal perception of bullying.

Regarding another issue that the cutoff point of –4.2 logits is too low to be confident in the lower 24% prevalence of bullying for the study sample, we can see the visualized person and item map in Figure 4. The person sample is not dispersed as normal (with mean 0 and SD 1) as we expected, so that most nurses earn low Rasch-transformed scores. It is because items on the top right-hand side are presented as difficult for nurses to respond to.

In addition, we can use individual Rasch-transformed logit scores to predict their probability of the bullied victimization using the formula: probability=exp(theta–delta)/(1+exp(theta–delta)), where theta=person measure and delta=item difficulty at cutoff point. For instance, a person with –1.5 logits in bully measurement will present his/her probability at 0.94, calculated as exp(–1.5–(–4.2))/(1+exp(–1.5–(–4.2))), where the item difficulty at cutoff point=–4.2 and the specified person measure=–1.5). The 95% confidence intervals are determined by the dispersion of the person’s measured error (ie, the value of 1.96×SE transformed to the previously mentioned probability formula).

Strengths of This Study

Using Computer Adaptive Testing to Endorse the NAQ-R

There are 2 major types of standardized assessments in clinical settings [45]: (1) a lengthy questionnaire that requires significant amounts of time and training for administration to achieve a precise assessment, and (2) a rapid, short-form one that briefly screens for the most common symptoms using cutoff points to determine degrees of impairment [46,47]. CAT has the advantages of both types: precision and efficiency. This paper used the Rasch rating scale model (instead of dichotomy or Rasch partial credit model) to design CAT and then applied it to endorse the NAQ-R. We conducted an actual CAT survey procedure (see the module in Multimedia Appendix 1) instead of CAT simulation as other published studies.

Detecting the Appropriateness of Level of Scaling

If the item threshold difficulties (calibrated by Rasch rating scale model) collapsed, categories should be combined to be more efficient for respondents to answer [29]. Unlike NAQ-R on which the responses “about weekly” and “about daily” were subjectively thrown together into one category [48], this study used the Rasch model for detecting the appropriateness of level of scaling [49].

Unique Features

Although the efficiency of a CAT has been well validated in the literature, the findings of this study do not appear to contribute any important information on the CAT approach. In this study, 2 unique features were reported to readers: (1) the 22-item polytomous NAQ-R is suited for CAT administration in practice, and (2) the module of animation CAT presented in Multimedia Appendix 1 is available for interested readers to practice, which is rare in any previously published articles.

Limitations of the Study

Issues for Further Consideration in Future Research

Several issues should be considered more thoroughly in further studies. First, few male nurses were included in the sample so that the differential item functioning for gender could not be identified by Rasch analysis. Second, there is potential sampling bias in this study. More studies are needed to assess the generalizability of the study with different samples and in different institutes using the Chinese version of NAQ-R. Third, the prevalence of bullying in this study hospital was 24%, higher than seen in studies of Japanese nurses (19%) [8], Italian employees (15.2%) [50], and general service workers in general services (from 2% to 17%) [51]. Fourth, more objective estimates of the prevalence for bullying based on the Leymann criterion [52] is worthy of carrying out in future because the self-labeling approach in this study might produce some biases [50].

Computer Adaptive Testing Stopping Rules Used in This Study

The CAT stopping rules are usually determined by SEM and/or no more than a specific number of items needed for achieving both precision and fast assessment. We applied the former and set minimal items for an acceptable level of person conditional reliability in CAT results.

In Figure 2, we demonstrated a CAT example terminated at SE <0.44, calculated as √(1–0.80), where reliability is set at 0.80, instead of 0.32, calculated as √(1–0.90), where reliability is set at 0.90. If using the latter criterion of 0.32, the item length in CAT will approach the total of 22 items. One way to improve the CAT efficiency and precision is to add more easy bullying questions to the scale (see Figure 4), especially for item difficulties located around the cutoff of –4.2 logits to increase the power of diagnostic discrimination for the bullied victims. Another way is to temporarily lower the acceptable level of precision to 0.80 reliability as was done in this study.

Lenient Criterion to Support a Good Model-Data-Fit

According to the literature [34], the range of 0.6 and 1.4 is recommended for rating scales (Likert/survey). Item 22 has a slightly high value of infit mean square error (mean square error=1.49) which is <1.5, but a lower outfit mean square error of 0.56. The high value of infit mean square error suggests that those nurses with highly negative actions caused by bullying have a sensitive misfit to item 22, but will not be influenced by the too-low cutoff score at -4.2 logits. In contrast, the low outfit mean square error shown in Table 2 indicates that item 22 has a good model-data-fit for most general nurses. WINSTEPS’ guidelines [33] supports that a mean square error >1.5 suggests a deviation from unidimensionality in the data. The other 2 model testing steps Smith recommended also verified that the NAQ-R 22-item scale is unidimensional and suggests that it suits CAT administration.


Developing an Online Computer Adaptive Testing System

Many issues should be further explored in the future, including studies addressing the limitations noted previously and subsequently. For example, the CAT module should be extended to the Internet for easy use so that the NAQ-R can be administered in more workplaces.

Applying the Animation Computer Adaptive Testing Module

One of the important advantages of CAT scoring is that the item pool for the 22-item NAQ-R can be expanded to match a wide range of participants covering different kinds of bullied workers without changing the module and measurement accuracy. The CAT users may also expand the NAQ-R item pools or replace them with other kinds of workplace bullying scales. It must be noted that (1) overall (ie, on average) and step (threshold) difficulties of the questionnaire must be calibrated in advance using Rasch analysis, (2) pictures and audio files for each question shown in the CAT Excel-module should be well-prepared and put in an appropriate folder that can be shown simultaneously to correspond to questions for the animation CAT module, and (3) pictures and audio files included in the CAT need to match original meaning of the items as much as possible to avoid distorting the validity of the scale.

If readers would like to conduct Rasch partial credit model for the NAQ-R, the distinct threshold step difficulties across items should be reset in specific Excel cells in Multimedia Appendix 1.

More Items Added to Decrease Standard Error

We described the category structure in Figure 3 displaying the NAQ-R monotonically increasing threshold (–3.39, –0.55, 1.11, and 2.83 logits). The Rasch rating scale model indicates each item has a common threshold difficulty. Therefore, the overall difficulties (ie, delta in Table 2) for each item plus the threshold step difficulties (eg, items 1 and 8 in Figure 4) form its own range of item difficulties, and only items 5, 8, and 1 with difficulty ranges include the cutoff point at –4.2 logits. To decrease the person’s measured error (ie, SE), we suggest the NAQ-R 22-item scale should add more easy items in the future to increase individual person conditional reliability.


The CAT-based NAQ-R forming a unidimensional construct reduces respondents’ burden without compromising measurement precision and increases endorsement efficiency. The computer module developed by the authors is recommended for assessing workers with scores beyond a cut point of >–4.2 logits (or >30 in summed score), who should be treated with more concern as soon as possible at an earlier stage.


We would like to thank the study participants for their contributions and the participating hospital’s support in facilitating this study.

Conflicts of Interest

None declared.

Multimedia Appendix 1

Excel VBA CAT module offered to interested readers for own practice (

ZIP File (Zip Archive), 2MB

  1. Einarsen S, Hoel H, Notelaers G. Measuring exposure to bullying and harassment at work: Validity, factor structure and psychometric properties of the Negative Acts Questionnaire-Revised. Work & Stress 2009 Jan;23(1):24-44. [CrossRef]
  2. Leymann H. The content and development of mobbing at work. European Journal of Work and Organizational Psychology 1996 Jun;5(2):165-184. [CrossRef]
  3. Einarsen S. Bullying and Emotional Abuse in the Workplace: International Perspectives in Research and Practice. New York: Taylor & Francis; 2003.
  4. Andersson LM, Aquino K, Barling J, Baron RJ, Bennett R, Bies RJ, et al. Bullying at work: a perspective from BritainNorth America. In: Fox S, Spector PE, editors. Counterproductive Work Behavior: Investigations Of Actors And Targets. Washington, DC: American Psychological Association (APA); 2005.
  5. Zapf D, Einarsen S, Hoel H, Vartia M. Empirical findings on bullying in the workplace. In: Einarsen S , Hoel H , Zapf D , Cooper CL , editors. Bullying and Emotional Abuse in the Workplace: International Perspectives in Research and Practice. New York: Taylor & Francis; 2003.
  6. Mikkelsen EG, Einarsen S. Bullying in Danish work-life: Prevalence and health correlates. European Journal of Work and Organizational Psychology 2001 Dec;10(4):393-413. [CrossRef]
  7. Lord FM. Applications of Item Response Theory to Practical Testing Problems. Hillsdale, NJ: L Erlbaum Associates; 1980.
  8. Abe K, Henly SJ. Bullying (ijime) among Japanese hospital nurses: modeling responses to the revised Negative Acts Questionnaire. Nurs Res 2010;59(2):110-118. [CrossRef] [Medline]
  9. Chien TW, Wang WC, Huang SY, Lai WP, Chow JC. A web-based computerized adaptive testing (CAT) to assess patient perception in hospitalization. J Med Internet Res 2011 Aug;13(3):e61 [FREE Full text] [CrossRef] [Medline]
  10. Chien TW, Wu HM, Wang WC, Castillo RV, Chou W. Reduction in patient burdens with graphical computerized adaptive testing on the ADL scale: tool development and simulation. Health Qual Life Outcomes 2009;7:39 [FREE Full text] [CrossRef] [Medline]
  11. Wainer HW, Dorans NJ. Computerized Adaptive Testing: A Primer. Hillsdale, NJ: L Erlbaum Associates; 1990.
  12. Embretson S, Reise S, Reise SP. Item Response Theory for Psychologists. Mahwah, NJ: L Erlbaum Associates; 2000.
  13. Weiss DJ. Improving measurement quality and efficiency with adaptive testing. Applied Psychological Measurement 1982 Sep 01;6(4):473-492. [CrossRef]
  14. Hsueh IP, Chen JH, Wang CH, Hou WH, Hsieh CL. Development of a computerized adaptive test for assessing activities of daily living in outpatients with stroke. Phys Ther 2013 May;93(5):681-693. [CrossRef] [Medline]
  15. Hsueh IP, Chen JH, Wang CH, Chen CT, Sheu CF, Wang WC, et al. Development of a computerized adaptive test for assessing balance function in patients with stroke. Phys Ther 2010 Sep;90(9):1336-1344 [FREE Full text] [CrossRef] [Medline]
  16. Wright BD, Linacre JM. Observations are always ordinal; measurements, however, must be interval. Arch Phys Med Rehabil 1989 Nov;70(12):857-860. [Medline]
  17. Wang WC. Recent Developments in Rasch Measurement. Hong Kong: The Hong Kong Institute of Education Press; 2010.
  18. Crocker L, Algina J. Introduction to Classical and Modern Test Theory. New York: Holt, Rinehart, and Winston; 1986.
  19. Nunnally JC, Bernstein IH. Psychometric Theory. New York: McGraw-Hill; 1994.
  20. Rasch G. Rasch Measurement Transactions, Part 1. Chicago: Univ of Chicago Social Research; 1993.
  21. Smith RM. A comparison of methods for determining dimensionality in Rasch measurement. Structural Equation Modeling: A Multidisciplinary Journal 1996 Jan;3(1):25-40. [CrossRef]
  22. Tennant A, Pallant JF. Unidimensionality matters! (A tale of two Smiths?). Rasch Meas Trans 2006;20(1):1048-1051 [FREE Full text]
  23. Velozo CA, Wang Y, Lehman L, Wang JH. Utilizing Rasch measurement models to develop a computer adaptive self-report of walking, climbing, and running. Disabli Rehabil 2008;30(6):458-467. [CrossRef]
  24. Lehman LA, Woodbury M, Shechtman O, Wang YC, Pomeranz J, Gray DB, et al. Development of an item bank for a computerised adaptive test of upper-extremity function. Disabil Rehabil 2011 Oct;33(21-22):2092-2104. [CrossRef] [Medline]
  25. Öztuna D, Elhan AH, Küçükdeveci AA, Kutlay S, Tennant A. An application of computerised adaptive testing for measuring health status in patients with knee osteoarthritis. Disabil Rehabil 2010 Jan;32(23):1928-1938. [CrossRef] [Medline]
  26. Elhan AH, Oztuna D, Kutlay S, Küçükdeveci AA, Tennant A. An initial application of computerized adaptive testing (CAT) for measuring disability in patients with low back pain. BMC Musculoskelet Disord 2008;9:166 [FREE Full text] [CrossRef] [Medline]
  27. Nielsen MB, Skogstad A, Matthiesen SB, Glasø L, Aasland MS, Notelaers G, et al. Prevalence of workplace bullying in Norway: Comparisons across time and estimation methods. European Journal of Work and Organizational Psychology 2009 Mar;18(1):81-101. [CrossRef]
  28. Einarsen S, Skogstad A. Bullying at work: Epidemiological findings in public and private organizations. European Journal of Work and Organizational Psychology 1996 Jun;5(2):185-201. [CrossRef]
  29. Linacre JM. Optimizing rating scale category effectiveness. J Appl Meas 2002;3(1):85-106. [Medline]
  30. Chien TW. Cronbach's alpha with the dimension coefficient to jointly assess a scale's quality. Rasch Meas Trans 2012;26(3):1379 [FREE Full text]
  31. Einarsen S, Raknes BI, Matthiesen SB. Bullying and harassment at work and their relationships to work environment quality: An exploratory study. European Work and Organizational Psychologist 1994 Oct;4(4):381-401. [CrossRef]
  32. Horn JL. A rationale and test for the number of factors in factor analysis. Psychometrika 1965 Jun;30(2):179-185. [CrossRef]
  33. Linacre JM. User's Guide to Winsteps. Chicago: Mesa Press; 2010.
  34. Bond TG, Fox CM. Applying the Rasch Model: Fundamental Measurement in Human Sciences (2nd ed). Mahwah, NJ: Lawrence Erlbaum; 2007:179-179.
  35. Linacre JM. Structure in Rasch residuals: why principal components analysis (PCA). Rasch Meas Trans 1998;12(2):636 [FREE Full text]
  36. Smith EV. Detecting and evaluating the impact of multidimensionality using item fit statistics and principal component analysis of residuals. J Appl Meas 2002;3(2):205-231. [Medline]
  37. Smith RM, Suh KK. Rasch fit statistics as a test of the invariance of item parameter estimates. J Appl Meas 2003;4(2):153-163. [Medline]
  38. Linacre JM. RUMM2020 Item-Trait Chi-Square and Winsteps DIF Size. Rasch Mea Trans 2007;21(1):1096 [FREE Full text]
  39. Linacre JM. WINSTEPS.   URL: [accessed 2013-06-27] [WebCite Cache]
  40. Patil VH, Surendra NS, Sanjay M, Donavan T. Parallel Analysis Engine to Aid Determining Number of Factors to Retain. 2007.   URL: [accessed 2013-12-17] [WebCite Cache]
  41. Patil VH, Singh SN, Mishra S, Todd Donavan D. Efficient theory development and factor retention criteria: Abandon the ‘eigenvalue greater than one’ criterion. Journal of Business Research 2008 Feb;61(2):162-170. [CrossRef]
  42. Linn RL. A Monte Carlo approach to the number of factors problem. Psychometrika 1968 Mar;33(1):37-71. [CrossRef]
  43. Silverstein AB. Comparison of two criteria for determining the number of factors. Psychological Reports 1977 Oct;41(2):387-390. [CrossRef]
  44. Zwick WR, Velicer WF. Comparison of five rules for determining the number of components to retain. Psychological Bulletin 1986;99(3):432-442. [CrossRef]
  45. Eack SM, Singer JB, Greeno CG. Screening for anxiety and depression in community mental health: the beck anxiety and depression inventories. Community Ment Health J 2008 Dec;44(6):465-474. [CrossRef] [Medline]
  46. Ramirez Basco M, Bostic JQ, Davies D, Rush AJ, Witte B, Hendrickse W, et al. Methods to improve diagnostic accuracy in a community mental health setting. Am J Psychiatry 2000 Oct;157(10):1599-1605. [Medline]
  47. Shear MK, Greeno C, Kang J, Ludewig D, Frank E, Swartz HA, et al. Diagnosis of nonpsychotic patients in community clinics. Am J Psychiatry 2000 Apr;157(4):581-587. [Medline]
  48. Tsuno K, Kawakami N, Inoue A, Abe K. Measuring workplace bullying: reliability and validity of the Japanese version of the negative acts questionnaire. J Occup Health 2010;52(4):216-226 [FREE Full text] [Medline]
  49. Hsueh IP. Rasch analysis of combining two indices to assess comprehensive ADL function in stroke patients. Stroke 2004 Feb 12;35(3):721-726. [CrossRef]
  50. Giorgi G, Arenas A, Leon-Perez JM. An operative measure of workplace bullying: the negative acts questionnaire across Italian companies. Ind Health 2011;49(6):686-695 [FREE Full text] [Medline]
  51. Nielsen MB, Notelaers G, Einarsen S. Measuring exposure to workplace bullying. In: Einarsen S , Hoel H , Zapf D , Cooper CL , editors. Bullying and Harassment in the Workplace: Developments in Theory, Research, and Practice. Boca Raton: Boca Raton CRC Press; 2011:149-176.
  52. Leymann H. Mobbing and psychological terror at workplaces. Violence Vict 1990;5(2):119-126. [Medline]

AUROC: area under the ROC
CAT: computerized adaptive testing
CTT: classical test theory
DC: dimension coefficient
IRT: item response theory
MNSQ: mean square residual
SEM: standard error of the mean
NAQ-R: Negative Acts Questionnaire-Revised
NAT: nonadaptive testing
ROC: receiver operating characteristic
VBA: Visual Basic for Applications

Edited by G Eysenbach; submitted 09.07.13; peer-reviewed by CL Hsieh, C Lalanne; comments to author 29.08.13; revised version received 17.09.13; accepted 28.11.13; published 17.02.14


©Shu-Ching Ma, Tsair-Wei Chien, Hsiu-Hung Wang, Yu-Chi Li, Mei-Shu Yui. Originally published in the Journal of Medical Internet Research (, 17.02.2014.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in the Journal of Medical Internet Research, is properly cited. The complete bibliographic information, a link to the original publication on, as well as this copyright and license information must be included.