- Methodology
- Open Access
A structural equation modeling approach for examining position effects in large-scale assessments
- Okan Bulut^{1}Email authorView ORCID ID profile,
- Qi Quo^{1} and
- Mark J. Gierl^{1}
https://doi.org/10.1186/s40536-017-0042-x
© The Author(s) 2017
- Received: 27 July 2016
- Accepted: 5 February 2017
- Published: 16 February 2017
Abstract
Position effects may occur in both paper–pencil tests and computerized assessments when examinees respond to the same test items located in different positions on the test. To examine position effects in large-scale assessments, previous studies often used multilevel item response models within the generalized linear mixed modeling framework. Using the equivalence of the item response theory and binary factor analysis frameworks when modeling dichotomous item responses, this study introduces a structural equation modeling (SEM) approach that is capable of estimating various types of position effects. Using real data from a large-scale reading assessment, the SEM approach is demonstrated for investigating form, passage position, and item position effects for reading items. The results from a simulation study are also presented to evaluate the accuracy of the SEM approach in detecting item position effects. The implications of using the SEM approach are discussed in the context of large-scale assessments.
Keywords
- Position effect
- Large-scale assessment
- Structural equation modeling
- Item response theory
Background
Large-scale assessments in education are typically administered using multiple test forms or booklets in which the same items are presented in different positions or locations within the forms. The main purpose of this practice is to improve test security by reducing the possibility of cheating among test takers (Debeer and Janssen 2013). This practice also helps test developers administer a greater number of field-test items embedded within multiple test forms. Although this is an effective practice for ensuring the integrity of the assessment, it may result in context effects—such as an item position effect—that can unwittingly influence the estimation of item parameters and the latent trait (Bulut 2015; Hohensinn et al. 2011). For example, test takers may experience either increasing item difficulty at the end of the test due to fatigue or decreasing item difficulty due to test-wiseness as they become more familiar with the content (Hohensinn et al. 2008).
It is often assumed that position effects are the same for all test takers or for all items and thus do not have a substantial impact on item difficulty or test scores (Hahne 2008). However, this assumption may not be accurate in operational testing applications, such as statewide testing programs. For example, in a reading assessment where items are often connected to a reading passage, it is challenging to maintain the original positions of the items from field test to final form to eliminate the possibility of any position effects (Meyers et al. 2009). Similarly, the positions of items cannot be controlled in computerized adaptive tests in which item positions typically differ significantly from one examinee to another (Davey and Lee 2011; Kolen and Brennan 2014; Meyers et al. 2009). Therefore, non-negligible item position effects may become a source of error in the estimation of item parameters and the latent trait (Bulut et al. 2016; Hahne 2008).
Several methodological studies have focused on item position effects in national and international large-scale assessments, such as the Trends in International Mathematics and Science Study (Martin et al. 2004), a mathematics assessment of the Germany Educational Standards (Robitzsch 2009), a mathematical competence test of the Austrian Educational Standards (Hohensinn et al. 2011), the Graduate Record Examination (Albano 2013), the Program for International Student Assessment (Debeer and Janssen 2013; Hartig and Buchholz 2012), and a German nationwide large-scale assessment in mathematics and science (Weirich et al. 2016). In these studies, item position effects were estimated as either fixed or random effects using multilevel item response theory (IRT) models within the generalized linear mixed modeling framework. This approach is also known as explanatory item response modeling (De Boeck and Wilson 2004), which is equivalent to Rasch modeling (Rasch 1960) with explanatory variables.
An alternative way of estimating IRT models is with a binary factor analysis (FA) model in which the item parameters and latent trait can be estimated using tetrachoric correlations among dichotomous item responses (Kamata and Bauer 2008; McDonald 1999; Takane and de Leeuw 1987). In addition to estimating the item parameters and latent trait, the binary FA model can be expanded to a structural equation model (SEM) in which item difficulty parameters can be predicted by other manifest (i.e., observed) variables (e.g., item positions, passage or testlet positions, and indicators of test forms). The purpose of this study is to (1) introduce the SEM approach for detecting position effects in large-scale assessments; (2) demonstrate the methodological adequacy of the SEM approach to model different types of position effects using an empirical study; and (3) examine the accuracy of the SEM approach in detecting position effects using a simulation study.
Theoretical framework
IRT and factor analysis
Although factor loadings and intercepts in the one-factor FA model are analogous to item discrimination and item difficulty in IRT, these factor analytic terms can be formally transformed into item parameters in the traditional IRT scale (Asparouhov and Muthén 2016; Muthén and Asparouhov 2002). Assuming that the latent trait is normally distributed as \(\eta \sim N\left( {\alpha ,\psi } \right)\) and \(\eta = \alpha + \sqrt \psi \theta\) where \(\theta\) is the IRT-based latent trait with mean 0 and standard deviation 1, the item discrimination parameter can be computed as \(a_{i} = \lambda_{i} /\sqrt \psi\), and the item difficulty parameter can be computed as \(b_{i} = (\tau_{i} - \lambda_{i} \alpha ) /\left( {\lambda_{i} \sqrt \psi } \right)\) [see Brown (2006) and Takane and de Leeuw (1987) for a review of similar transformation procedures].
Modeling position effects
As Brown (2006) noted, the use of the FA model provides greater analytic flexibility than the IRT framework because traditional IRT models can be embedded within a larger model that includes additional variables to explain the item parameters as well as the latent trait (e.g., Ferrando et al. 2013; Glöckner-Rist and Hoijtink 2003; Lu et al. 2005). Using the structural equation modeling (SEM) framework, an IRT model can be defined as a measurement model in which there is a latent trait (e.g., reading ability) underlying a set of manifest variables (e.g., dichotomous items in a reading assessment). In the structural part of the SEM model, the causal and correlational relations among the latent trait, the manifest variables, and other latent or manifest variables (e.g., gender and attitudes toward reading) can therefore be tested.
A well-known example of this modeling framework is the Multiple Indicators Multiple Cause (MIMIC) model for testing uniform and nonuniform differential item functioning in dichotomous and polytomous items (e.g., Finch 2005; Lee et al. 2016; Woods and Grimm 2011). In the MIMIC model, a categorical grouping variable (e.g., gender) is used as an explanatory variable to explain the relationship between the probability of responding to an item correctly and the grouping variable, after controlling for the latent trait. Based on the results of this analysis, one can conclude that the items become significantly less or more difficult depending on which group the examinee belongs to.
Model constraints and assumptions
The proposed SEM approach requires the use of constraints to ensure model identification and accurate estimation of model parameters. Using the marginal parameterization with a standardized factor (Asparouhov and Muthén 2016; Millsap and Yun-Tein 2004; Muthén and Asparouhov 2002), the variance of \(y_{i}^{*}\) is constrained to be 1 for all items; the mean and the variance of the latent trait (\(\eta\)) are constrained to be 0 and 1, respectively [see Kamata and Bauer (2008) for other parameterizations in the binary FA model]. Furthermore, additional constraints might be necessary depending on which the IRT model is used. For example, if the Rasch model is the underlying IRT model for the data, all factor loadings in the model must be constrained to be 1. The general assumptions of IRT must also hold in order to estimate the IRT model with item position effects within the SEM framework. These assumptions include a monotonic relationship between the probability of responding to an item correctly and the latent trait, the unidimensionality of the latent trait, local independence of items, and invariance in the item parameters and the latent trait across different subgroups in a population.
Model estimation
The proposed SEM models for examining item position effects can be estimated using commercial software programs for the SEM analysis, such as Mplus (Muthén and Muthén 1998–2015), LISREL (Jöreskog and Sörbom 2015), AMOS (Arbuckle 2011), and EQS (Bentler and Wu 2002), or non-commercial software programs, such as the sem (Fox et al. 2016), lavaan (Rosseel 2012), OpenMx (Pritikin et al. 2015), and nlsem (Umbach et al. 2017) packages in R (R Core Team 2016). It should be noted that these software programs differ with regard to their algorithms for estimating SEM models with binary variables, model estimators (e.g., ULS, MLR, and WLSMV), the capability to estimate interaction effects, and methods for handling missing data. Therefore, when choosing the most suitable program, researchers should consider the research questions that they aim to address, the statistical requirements of their hypothesized SEM model(s), and data characteristics (e.g., the number of items, amount of missing data).
As noted earlier, item position effects can be examined one item at a time using Eqs. 3 and 4. However, it is more convenient to estimate the position effects for all items within the same SEM model and then create a simplified model by removing non-significant effects from the model. Since the simplified model would be nested within the original model that includes the position effects for all items, the two models can be compared using a Chi square (\(\chi^{2}\)) difference test. The procedure for the \(\chi^{2}\) difference test varies depending on which model estimator (e.g., the robust maximum likelihood estimator ‘MLR’ or the weighted least square with mean- and variance-adjusted Chi square ‘WLSMV’ in Mplus) is used for estimating the SEM model. For example, the \(\chi^{2}\) difference test using the corrected loglikelihood values or the Satorra–Bentler \(\chi^{2}\) statistic (Satorra and Bentler 2001) are widely used when the model estimator is MLR. The reader is referred to Brown (2006, p. 385), Asparouhov and Muthén (2006), and the Mplus website (www.statmodel.com/chidiff.shtml) for detailed descriptions of the \(\chi^{2}\) difference testing in SEM. When the SEM models are not nested, the model selection or comparison can be done on the basis of information-based criteria that assess relative model fit, such as Akaike information criterion (AIC; Akaike 1974) and the Bayesian information criterion (BIC; Schwarz 1978).
Comparison with other approaches
To date, three different methodological approaches for investigating item position effects have been described: (1) logistic regression models (e.g., Davey and Lee 2011; Pomplun and Ritchie 2004; Qian 2014); (2) multilevel models based on the generalized linear mixed modeling (GLMM) framework (e.g., Albano 2013; Alexandrowicz and Matschinger 2008; Debeer and Janssen 2013; Hartig and Buchholz 2012; Li et al. 2012; Weirich et al. 2014); and (3) test equating methods (e.g., Kingston and Dorans 1984; Kolen and Harris 1990; Moses et al. 2007; Pommerich and Harris 2003; Meyers et al. 2009; Store 2013). Although there are some empirical studies that used the factor analytic methods for modeling position effects (e.g., Bulut et al. 2016; Schweizer 2012; Schweizer et al. 2009), the current study represents the first study that utilized the SEM framework as a methodological approach for examining item position effects.
The proposed SEM approach has four noteworthy advantages over the other methods mentioned above when it comes to modeling item position effects. First, the proposed approach overcomes the limitation of examining position effects only for dichotomous items, which is the case with the approaches based on the GLMM framework (e.g., Hartig and Buchholz 2012). Using the SEM framework, assessments that consist of polytomously scored items can also be examined for item position effects. Second, the proposed approach is applicable to assessments in which item parameters are obtained using the two-parameter IRT model. Because the one-factor FA model is analogous to the two-parameter IRT model, it is possible to estimate item position effects when both item difficulty and item discrimination parameters are present in the model. Third, the proposed approach can be used with multidimensional test structures in which there are multiple latent traits underlying the data. Fourth, once significant item position effects are detected, other manifest and/or latent variables (e.g., gender, test motivation, and test anxiety) can be incorporated into the SEM model to explain the underlying reasons of the found effects. For example, Weirich et al. (2016) recently found in an empirical study that item position effects in a large-scale assessment were affected by the examinees’ test-taking efforts. Response time effort (Wise and Kong 2005) and disability status (Abedi et al. 2007; Bulut et al. 2016) are other important factors highlighted in the literature.
Next, the results from an empirical study first are presented to demonstrate the use of the proposed SEM approach for investigating three types of position effects that are likely to occur in large-scale assessments: test form (or booklet) effect, passage (or testlet) position effect, and item position effect. Real data from a large-scale reading assessment are used for the empirical study. The interpretation of the estimated position effects and model comparisons are explained. Then, the results from a Monte Carlo simulation study are presented to investigate the extent to which the proposed SEM approach can detect item position effects accurately. For both the empirical and Monte Carlo studies, Mplus (Muthén and Muthén 1998–2015) is used because of its flexibility to formulate and evaluate IRT models within a broader SEM framework and its extensive Monte Carlo simulation capabilities (e.g., Glöckner-Rist and Hoijtink 2003; Lu et al. 2005).
Empirical study
Data
Position effects were evaluated using data from a large-scale statewide reading assessment administered annually to all students in elementary, middle, and high schools. The assessment was delivered as either a computer-based test or a paper-and-pencil test, depending on the availability of computers in the schools. The paper-and-pencil version was administered to the students using a single test form that consisted of the same items in the same positions. Unlike the paper–pencil version, the computer-based version was administered to the students by randomizing the positions of the items across the students. The sample used in this study consisted of 11,734 third-grade students who completed the reading test of the statewide assessment on a computer.
Instrument
Demographic summary of the students across test forms
Variable | Form 1 | Form 2 | Form 3 | Form 4 | ||||
---|---|---|---|---|---|---|---|---|
N | % | N | % | N | % | N | % | |
Gender | ||||||||
Female | 1460 | 49.1 | 1471 | 49.2 | 1477 | 50 | 1419 | 49 |
Male | 1515 | 50.9 | 1517 | 50.8 | 1479 | 50 | 1478 | 51 |
Ethnicity | ||||||||
American Indian | 50 | 1.7 | 63 | 2.1 | 34 | 1.2 | 57 | 2 |
Asian | 65 | 2.2 | 61 | 2 | 62 | 2.1 | 65 | 2.2 |
Black | 272 | 9.1 | 259 | 8.7 | 236 | 8 | 249 | 8.6 |
Hispanic | 373 | 12.5 | 465 | 15.6 | 428 | 14.5 | 398 | 13.7 |
White | 2215 | 74.5 | 2140 | 71.6 | 2196 | 74.3 | 2128 | 73.5 |
Model formulations
Rasch model (M_{1})
The first model was the Rasch model. It did not include any predictors for examining positions effects. Under the SEM framework, M_{1} is equivalent to a one-factor model with all factor loadings fixed to 1 (see Fig. 1a). The latent variable defines the reading ability and the intercepts of the items are equivalent to item difficulties.
Form effects model (M_{2})
Passage position effects model (M_{3})
Item position effects model (M_{4})
Model estimation
The layout of the data structure for the SEM analysis
Examinees | Item responses | Forms | Passage positions | Item positions | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
i1 | … | i45 | f_{1} | f_{2} | f_{3} | f_{4} | pp_{1} | … | pp_{7} | ip_{1} | … | ip_{45} | |
1 | 1 | 0 | 0 | 0 | 1 | … | 7 | 46 | … | 4 | |||
2 | 0 | 1 | 0 | 0 | 2 | … | 4 | 45 | … | 3 | |||
3 | 0 | 0 | 1 | 0 | 1 | … | 6 | 52 | … | 5 | |||
4 | 0 | 0 | 0 | 1 | 3 | … | 4 | 52 | … | 6 |
Results
Rasch model
Descriptive statistics of latent trait estimates from the Rasch model across four test forms
Form | N | M | SD | Min | Max |
---|---|---|---|---|---|
1 | 2975 | −.01 | 1.02 | −3.17 | 2.06 |
2 | 2901 | .01 | 1.04 | −2.75 | 2.06 |
3 | 2897 | .00 | 1.01 | −2.75 | 2.06 |
4 | 2961 | −.01 | 1.04 | −3.02 | 2.06 |
Form effects
M_{2} included the indicators for the test forms in the SEM model to examine the overall differences in the item difficulty levels across the four forms. Using one form as the reference form, the estimated regression coefficients indicated the overall difficulty differences between the reference form and the other three forms. The estimated regression coefficients for the form effects ranged from −0.032 to 0.032. None of the form effects was statistically significant at the alpha level of \(\alpha = .05\), suggesting that the forms did not differ in terms of their overall difficulty.
Passage position effects
Summary of estimated passage position effects
Passage | Number of items | Position effect |
---|---|---|
1 | 6 | −.029 (.014)* |
2 | 6 | .000 (.021) |
3 | 8 | .023 (.013) |
4 | 6 | −.044 (.015)** |
5 | 6 | −.080 (.014)*** |
6 | 6 | .004 (.014) |
7 | 7 | −.008 (.008) |
Item position effects
Summary of estimated item position effects
Item | Position effect | Item | Position effect | Item | Position effect |
---|---|---|---|---|---|
1 | −.008 (.005) | 16 | −.009 (.003)** | 31 | .006 (.004) |
2 | −.015 (.005)** | 17 | −.012 (.003)*** | 32 | .006 (.004) |
3 | −.025 (.005)*** | 18 | −.003 (.003) | 33 | −.007 (.005) |
4 | .000 (.004) | 19 | −.011 (.003)** | 34 | .001 (.004) |
5 | −.014 (.005)** | 20 | −.015 (.003)*** | 35 | −.007 (.004) |
6 | .009 (.005) | 21 | −.005 (.005) | 36 | −.005 (.004) |
7 | −.004 (.005) | 22 | .007 (.005) | 37 | −.010 (.004)* |
8 | −.023 (.005)*** | 23 | −.014 (.005)** | 38 | −.008 (.004) |
9 | .003 (.006) | 24 | −.015 (.005)** | 39 | −.011 (.004)** |
10 | −.017 (.006)** | 25 | .002 (.006) | 40 | −.014 (.006)* |
11 | −.023 (.006)*** | 26 | −.037 (.007)*** | 41 | −.015 (.004)*** |
12 | −.030 (.007)*** | 27 | −.020 (.005)*** | 42 | −.005 (.004) |
13 | −.014 (.006)* | 28 | −.004 (.005) | 43 | −.023 (.005)*** |
14 | −.013 (.006)* | 29 | −.002 (.004) | 44 | −.006 (.003) |
15 | −.008 (.003)* | 30 | −.005 (.004) | 45 | −.004 (.004) |
Model comparison
Summary of the model fit information from the SEM models
Model | Number of parameters | Loglikelihood value | Scaling factor | AIC | BIC |
---|---|---|---|---|---|
M_{1}: Rasch model | 45 | −257,591 | 0.992 | 515,272 | 515,604 |
M_{2}: Form effect | 48 | −257,590 | 1.008 | 515,277 | 515,631 |
M_{3}: Passage position effect | 52 | −257,571** | 1.007 | 515,246 | 515,629 |
M_{4}: Item position effect | 90 | −257,420** | 0.991 | 515,019 | 515,683 |
M_{4}: Item position effect* | 68 | −257,437** | 0.992 | 515,010 | 515,511 |
Simulation study
The empirical study demonstrated that the SEM approach is capable of detecting different types of position effects in large-scale assessments. In the second part of this study, the Monte Carlo simulation capabilities of Mplus (Muthén and Muthén 1998–2015) were used to investigate the extent to which the proposed SEM approach can detect item position effects accurately. More specifically, the recovery of the SEM model in the presence of a linear position effect on item difficulty was evaluated. Hit rates in detecting items with the linear position effect and Type I error rates in flagging items with no position effects were examined via simulated data sets.
Simulation design
Summary of the items with linear position effects in the simulation study
Position in form 1 | Position in form 2 | Change in position | Position effect per one position | Total position effect | Item difficulty in form 1 | Item difficulty in form 2 |
---|---|---|---|---|---|---|
1 | 41 | 40 | −.01 | −.4 | −0.99 | −0.59 |
2 | 27 | 25 | −.01 | −.25 | −0.98 | −0.73 |
3 | 13 | 10 | −.01 | −.1 | −0.97 | −0.87 |
4 | 44 | 40 | −.02 | −.8 | −0.92 | −0.12 |
5 | 30 | 25 | −.02 | −.5 | −0.90 | −0.40 |
6 | 26 | 10 | −.02 | −.2 | −0.88 | −0.68 |
The simulation study consisted of three factors: (a) the magnitude of the linear position effect on item difficulty (.01 and .02 per one position change); (b) sample size (1000, 5000, and 10,000 examinees); and (c) the size of position change for the six manipulated items across two forms (+10, +25, and +40 positions). The chosen values for the linear position effect were similar to those found in the empirical study as well as the position effects reported in earlier studies (e.g., Debeer and Janssen 2013). Similarly, sample size values resemble the number of examinees from previous empirical studies on item position effects (e.g., Bulut et al. 2016; Debeer and Janssen 2013; Qian 2014; Weirich et al. 2016). For each crossed condition, 1000 data sets were generated.
Model estimation
Results
Hit rates and Type I error rates in the simulation study
Simulation factors | Estimated position effect | Estimated item difficulty | |||||||
---|---|---|---|---|---|---|---|---|---|
Sample size | Position effect | Change in position | Total position effect (β) | \(\hat{\beta }\) | 95% coverage | Hit rate | Type I error rate | RMSE | ME |
1000 | −.01 | 40 | −.4 | −.405 | .958 | .723 | .051 | .0058 | .0033 |
−.01 | 25 | −.25 | −.248 | .951 | .351 | ||||
−.01 | 10 | −.1 | −.097 | .951 | .086 | ||||
−.02 | 40 | −.8 | −.805 | .947 | .999 | ||||
−.02 | 25 | −.5 | −.504 | .957 | .892 | ||||
−.02 | 10 | −.2 | −.204 | .948 | .252 | ||||
5000 | −.01 | 40 | −.4 | −.402 | .951 | 1 | .049 | .0017 | .0007 |
−.01 | 25 | −.25 | −.249 | .953 | .945 | ||||
−.01 | 10 | −.1 | −.099 | .946 | .279 | ||||
−.02 | 40 | −.8 | −.8 | .94 | 1 | ||||
−.02 | 25 | −.5 | −.499 | .96 | 1 | ||||
−.02 | 10 | −.2 | −.203 | .96 | .821 | ||||
10,000 | −.01 | 40 | −.4 | −.402 | .947 | 1 | .049 | .0009 | <.0001 |
−.01 | 25 | −.25 | −.248 | .95 | .999 | ||||
−.01 | 10 | −.1 | −.099 | .951 | .48 | ||||
−.02 | 40 | −.8 | −.8 | .942 | 1 | ||||
−.02 | 25 | −.5 | −.498 | .961 | 1 | ||||
−.02 | 10 | −.2 | −.202 | .954 | .976 |
Hit rates appeared to vary depending upon sample size, the magnitude of the position effect, and the size of position change between two forms. When the magnitude of the position effect was larger (\(\beta = - .02\) per one position change), hit rates were very high, except for the condition where sample size was 1000 and the size of position change between two forms was 10. Hit rates improved as sample size, the magnitude of the magnitude of the position effect, and the size of position change between two forms increased. Hit rates for the condition in which the magnitude of the position effect was −.01 per one position change and the size of position change was 10 remained low, despite increasing sample size from 1000 to 10,000. The average Type I error rates for the items with no position effects were near the nominal rate (\(\alpha = .05\)), which indicates that the SEM model did not falsely flag items for exhibiting position effects. The RMSE and ME values for the estimates of item difficulty were quite small, suggesting that the recovery of the item difficulty parameters was good. The size of the RMSE and ME values decreased even further as sample size increased.
Discussion and conclusions
Item position effect, which often is viewed as a context effect in assessments (Brennan 1992; Weirich et al. 2016), occurs when the difficulty or discrimination level of a test item varies depending on the location of the item on the test form. For example, the difficulty of an item can increase in later positions due to a fatigue effect or decreasing test-taking effort (Hohensinn et al. 2011; Weirich et al. 2016). To investigate item position effects, researchers have proposed different approaches using logistic regression (e.g., Davey and Lee 2011; Pomplun and Ritchie 2004), multilevel IRT models based on the GLMM framework (e.g., Albano 2013; Li et al. 2012; Weirich et al. 2014), and test equating (e.g., Pommerich and Harris 2003; Meyers et al. 2009; Store 2013). The purpose of the current study was to introduce a factor analytic approach for modeling item position effects using the SEM framework. In the first part of the study, the methodological capabilities of the proposed SEM approach were illustrated in an empirical study using data from an operational testing program in reading. Test form, passage position, and item position effects were investigated. In the second part of the study, a Monte Carlo simulation study was conducted to evaluate the accuracy of the SEM approach in detecting item position effects. The simulation study showed that the SEM approach is quite accurate in detecting linear item position effects, except for the conditions in which both the number of examinees and the magnitude of the item position effect are small.
The proposed SEM approach contributes to the literature of item position effects in large-scale assessments in three ways. First, the SEM approach allows researchers and practitioners to examine both linear position effects and interaction effects in the same model. It is typically assumed that item difficulty linearly increases or decreases as the items are administered in later positions. However, changing item positions can also result in changes in item difficulty as a result of the interaction of item positions and the latent trait (e.g., Debeer and Janssen 2013; Weirich et al. 2014). Hence, it is important to evaluate both linear position effects and interaction effects when designing a large-scale assessment containing multiple forms with different item orders or with randomized item ordering. Second, the SEM approach presented in this study is a flexible method for studying position effects with various IRT models for dichotomously and polytomously scored items—such as the two-parameter model, Partial Credit Model, and Graded Response Model. For example, the position analyses in the empirical part of this study could be easily extended to the two-parameter IRT model by freely estimating factor loadings of the items (see Fig. 2). Third, the SEM approach is applicable to large-scale assessments with more complex designs, such as multiple test forms (or booklets) consisting of the same set of items in different positions, test forms with completely randomized item ordering for each examinee, and multiple matrix booklet designs (Gonzalez and Rutkowski 2010).
Significance and future research
The current study has important implications in terms of educational testing practices. First, this study evaluated position effects in a large-scale assessment. The proposed SEM approach can help practitioners identify problematic test items with significant position effects and thereby leading to large-scale assessments with improved test fairness. Second, this study presents a straightforward and efficient approach to investigate different types of position effects (e.g., item position effect, passage position effect, and form effect). Hence, the proposed approach can be easily applied to assessments with a large number of items and examinees. Third, the results of this study can provide guidance for further research on position effects in computer-based and computerized adaptive tests. For example, future research can focus identifying which types of items are more likely to exhibit position effects in computer-based assessments and computerized adaptive tests. This can help practitioners select the most appropriate items when designing computer-based assessments and computerized adaptive tests.
This study introduced the SEM model that incorporates interaction effects, but did not investigate the statistical properties of the proposed model. Thus, further research is needed to evaluate the adequacy and accuracy of the proposed SEM model in detecting interaction effects. Given the increasing popularity of multidimensional IRT models, it would also be worthwhile to evaluate position effects in large-scale assessments that measure multiple latent traits. Finally, as Debeer and Janssen (2013) pointed out, there is a lack of research on the underlying reasons of item position effects in large-scale assessments. Future research with the SEM approach can include item-related predictors (e.g., cognitive demand, linguistic complexity) and examinee-related predictors (e.g., gender, test motivation, anxiety) to explain why item position effects occur in large-scale assessments.
The mean and variance are fixed to 0 and 1, respectively, to identify the scale of the latent variable.
When the WLSMV estimator was used, the SEM models in the empirical study did not converge due to high correlations among passage and item position variables.
Declarations
Authors’ contributions
OB and MJG developed the theoretical framework for the analysis of position effects using structural equation modeling. Furthermore, OB and QG carried out simulation and real data analyses for the study. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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