Björn Andersson

• Ofstad, Sverre Berg; Tan, Tony & Andersson, Björn (2026). Comparing the difficulty of elective subjects in high school using a population-based Norwegian registry. Scandinavian Journal of Educational Research. ISSN 0031-3831. doi: 10.1080/00313831.2026.2648976. Full text in Research Archive Show summary

  When grade point averages (GPAs) are used for admission into tertiary education, there is an implicit assumption that any two identical GPAs convey the same level of academic competency. However, this assumption does not hold when students are free to choose elective subjects and there are differences in their difficulty and dimensionality. In this study, we utilized item response theory to examine dimensionality and difficulty of 11 elective subjects in Norwegian high school, while accounting for self-selection bias, using data from 21,666 third year students. Our results show that the GPA is best represented as a multidimensional construct. Additionally, we demonstrate that the selection bias in observed subject grade averages for electives conceals considerable differences in difficulty levels. Hence, the GPA of Norwegian high school students does not only reflect academic competency but also the decisions made regarding which elective subjects to take.

• Zhang, Lu & Andersson, Björn (2026). Likelihood ratio tests with marginal maximum likelihood using Laplace approximations and adaptive quadrature. Journal of Statistical Computation and Simulation. ISSN 0094-9655. p. 1–26. doi: 10.1080/00949655.2026.2616410. Full text in Research Archive Show summary

  Estimation of generalized linear latent variable models is typically done with marginal maximum likelihood (MML) estimation which requires approximation methods to compute integrals without a closed form solution. In applied settings, likelihood ratio tests are often used to test hypotheses regarding parameter restrictions. This study examines the properties of likelihood ratio tests when using approximate MML estimation. We consider first- and second-order Laplace approximations, along with adaptive Gauss-Hermite quadrature with varying numbers of quadrature points. In two simulation studies we perform likelihood ratio tests, varying data types (binary, ordinal, and count data), sample sizes, and the number of observed variables. The first simulation examines slope parameter equivalence, while the second focuses on group restrictions in multiple group models. Results indicate adaptive quadrature and second-order Laplace approximations provide reliable inference across most settings. Meanwhile, the first-order Laplace approximation generally works well except in some binary data cases.

• Andersson, Björn (2025). Multidimensional item response theory. In Nesi, Hilary & Milin, Petar (Ed.), Reference Module in Social Sciences. Elsevier. ISSN 9780443157851. p. 1–7. doi: 10.1016/b978-0-443-26629-4.00225-2. Full text in Research Archive Show summary

  Item response theory is a class of statistical models for the analysis of item scores from educational tests and psychological scales, where a latent construct is assumed to underlie the observed item scores. When multiple latent variables are measured by a set of item scores, a multidimensional item response theory model is required to accurately model the dependence between the observed variables. In this introduction to multidimensional item response theory, we present key models for binary, ordinal, and nominal data, and present how the models can be estimated and used to draw inferences at the individual level. We give examples of how to use the models to assess the psychometric properties of scales and tests, study the validity of test score uses and interpretations, and improve measurement precision for individual-level inferences.

• Paredes, Yuriko Kirilovna Sosa & Andersson, Björn (2025). Linking the first, second and third IEA science studies. Studies in Educational Evaluation. ISSN 0191-491X. 87. doi: 10.1016/j.stueduc.2025.101529. Full text in Research Archive Show summary

  International comparative assessments are crucial for examining country-level educational changes over time, but requires a comparable achievement scale. This study develops a unified science achievement scale that links the First and Second International Science Studies with the Trends in International Mathematics and Science Study for upper primary school students. The science measures in each study are analyzed with respect to construct consistency, inferences, population differences, and test conditions. Analyses showed that, despite some evolution in frameworks and a transition from age-based to grade-based definitions, the core constructs remain consistent, enabling similar inferences. By identifying common items among the three studies, we rigorously assessed measurement invariance using item response modeling, with partial invariance models supporting reliable long-term comparisons. We applied latent regression models using contextual student data, creating imputed scale scores for each student. These results enable vast further research to investigate long-term inequalities in educational outcomes.

• Zhang, Maoxin; Andersson, Björn & Jin, Shaobo (2024). Fast estimation of generalized linear latent variable models for performance and process data with ordinal, continuous, and count observed variables. British Journal of Mathematical & Statistical Psychology. ISSN 0007-1102. doi: 10.1111/bmsp.12337. Full text in Research Archive Show summary

  Different data types often occur in psychological and educational measurement such as computer‐based assessments that record performance and process data (e.g., response times and the number of actions). Modelling such data requires specific models for each data type and accommodating complex dependencies between multiple variables. Generalized linear latent variable models are suitable for modelling mixed data simultaneously, but estimation can be computationally demanding. A fast solution is to use Laplace approximations, but existing implementations of joint modelling of mixed data types are limited to ordinal and continuous data. To address this limitation, we derive an efficient estimation method that uses first‐ or second‐order Laplace approximations to simultaneously model ordinal data, continuous data, and count data. We illustrate the approach with an example and conduct simulations to evaluate the performance of the method in terms of estimation efficiency, convergence, and parameter recovery. The results suggest that the second‐order Laplace approximation achieves a higher convergence rate and produces accurate yet fast parameter estimates compared to the first‐order Laplace approximation, while the time cost increases with higher model complexity. Additionally, models that consider the dependence of variables from the same stimulus fit the empirical data substantially better than models that disregarded the dependence.

• Helland-Riise, Fredrik; Norrøne, Tore Nøttestad & Andersson, Björn (2024). Large-Scale Item-Level Analysis of the Figural Matrices Test in the Norwegian Armed Forces: Examining Measurement Precision and Sex Bias. Journal of Intelligence. 12(9). doi: 10.3390/jintelligence12090082. Full text in Research Archive Show summary

  Figural matrices tests are common in intelligence research and have been used to draw conclusions regarding secular changes in intelligence. However, their measurement properties have seldom been evaluated with large samples that include both sexes. Using data from the Norwegian Armed Forces, we study the measurement properties of a test used for selection in military recruitment. Item-level data were available from 113,671 Norwegian adolescents (32% female) tested between the years 2011 and 2017. Utilizing item response theory (IRT), we characterize the measurement properties of the test in terms of difficulty, discrimination, precision, and measurement invariance between males and females. We estimate sex differences in the mean and variance of the latent variable and evaluate the impact of violations to measurement invariance on the estimated distribution parameters. The results show that unidimensional IRT models fit well in all groups and years. There is little difference in precision and test difficulty between males and females, with precision that is generally poor on the upper part of the scale. In the sample, male latent proficiency is estimated to be slightly higher on average, with higher variance. Adjusting for measurement invariance generally reduces the sex differences but does not eliminate them. We conclude that previous studies using the Norwegian GMA data must be interpreted with more caution but that the test should measure males and females equally fairly.

• Paredes, Yuriko Kirilovna Sosa & Andersson, Björn (2024). Validity of test score interpretations and cross-cultural comparisons in the First and Second International Science Studies. Educational Assessment, Evaluation and Accountability. ISSN 1874-8597. p. 1–24. doi: 10.1007/s11092-024-09444-7. Full text in Research Archive Show summary

  In international large-scale assessments, student performance comparisons across educational systems are frequently done to assess the state and development in different domains. These results often have a large impact on educational policy and on the perceptions of an educational system’s performance. Early assessments, such as the First and Second International Science Studies (FISS and SISS), have been used alongside recent studies to create unique scales for investigating changes in constructs. The implicit assumptions in system comparisons are that the measures are valid, reliable, and comparable. However, these assumptions have not always been investigated thoroughly. This study aims to investigate the validity and cross-system comparability of scores from the FISS and SISS, conducted by the International Association for the Evaluation of Educational Achievement in 1970–1971 and 1983–1984. Findings based on item response theory (IRT) modeling indicate that scores in most educational systems can be viewed as reliable measures of a single science construct, supporting the validity of test score interpretations in these educational systems individually. In a robust assessment of measurement invariance using standard IRT methods, an alignment-based method, and the root mean square difference (RMSD) fit statistic, we demonstrate that measurement invariance is violated across systems. The alignment-based method identified a well-fitting model with complex restrictions but no items exhibited invariance across all systems, a result supported by the RMSD statistics. These results question the appropriateness of score comparisons across systems in FISS and SISS. We discuss the implications of these results and outline consequences for score comparisons across time.

• Zhang, Maoxin; Andersson, Björn & Greiff, Samuel (2023). Investigating Planning and Non-Targeted Exploration in PIAAC 2012: Validating Their Measures Based on Process Data and Investigating Their Relationships with Problem-Solving Competency. Journal of Intelligence. 11(8). doi: 10.3390/jintelligence11080156. Full text in Research Archive Show summary

  Problem-solving is a critical aspect of intelligence that has become increasingly important in modern society. Mapping out the determinants of success in problem-solving helps understand the underlying cognitive processes involved. This article focuses on two key cognitive processes in problem-solving: non-targeted exploration and planning. We generalize previously defined indicators of planning and non-targeted exploration across tasks in the 2012 Programme for the International Assessment of Adult Competencies and examine the internal construct validity of the indicators using confirmatory factor analysis. We also investigate the relationships between problem-solving competency, planning, and non-targeted exploration, along with the specific dependence between indicators from the same task. The results suggest that (a) the planning indicator across tasks provides evidence of internal construct validity; (b) the non-targeted exploration indicator provides weaker evidence of internal construct validity; (c) overall, non-targeted exploration is strongly related to problem-solving competency, whereas planning and problem-solving competencies are weakly negatively related; and (d) such relationships vary substantially across tasks, emphasizing the importance of accounting for the dependency of measures from the same task. Our findings deepen our understanding of problem-solving processes and can support the use of digital tools in educational practice and validate task design by comparing the task-specific relationships with the desired design.

• Kristensen, Jarl Kleppe; Andersson, Björn; Bratlie, Siri Steffensen & Torkildsen, Janne von Koss (2023). Dimensionality of Morphological Knowledge—Evidence from Norwegian Third Graders. Reading Research Quarterly. ISSN 0034-0553. doi: 10.1002/rrq.497. Full text in Research Archive Show summary

  Abstract This study aimed to determine the dimensionality of morphological knowledge by examining different sources of variance. According to the Morphological Pathways Framework ( Levesque et al., Journal of Research in Reading, 44, 10–26, 2021 ), morphological awareness, morphological analysis and morphological decoding are related, but distinct dimensions of morphological knowledge. However, multidimensionality might also stem from construct‐irrelevant variance due to methodological artifacts. We assessed 612 Norwegian third graders on five measures of morphological knowledge and one measure of general vocabulary. Fitting a series of confirmatory factor analysis (CFA) models, we evaluated the dimensionality of morphological knowledge both within and across the five tests. Furthermore, we fitted three structural equation models (SEMs) to explore how different conceptualizations affect the relationship between morphological knowledge and general vocabulary: a five‐factor model, a bifactor model, and a higher‐order model representing morphological awareness, morphological analysis and morphological decoding. CFAs supported a multidimensional view of morphological knowledge and highlighted the need to account for construct‐irrelevant variance. SEM analyses further illustrated that construct‐irrelevant variance introduces a confounding element to the relations between morphological knowledge and vocabulary in the test‐specific five‐factor model, as only the bifactor and higher‐order models separate between construct‐relevant variance and variance due to methodological artifacts. The bifactor model is useful for separating sources of variance, especially during test development. For research purposes, however, we recommend conceptualizing morphological knowledge in line with Levesque et al., Journal of Research in Reading, 44, 10–26, 2021 , to increase knowledge of morphological dimensions and their relations to other areas of literacy.

• Zhang, Maoxin & Andersson, Björn (2023). Identifying Problem-Solving Solution Patterns Using Network Analysis of Operation Sequences and Response Times. Educational Assessment. ISSN 1062-7197. doi: 10.1080/10627197.2023.2222585. Full text in Research Archive Show summary

  Process data from educational assessments enhance the understanding of how students answer cognitive items. However, effectively making use of these data is challenging. We propose an approach to identify solution patterns from operation sequences and response times by generating networks from process data and defining network features that extract essential information from them. With these features, we group respondents to a problem-solving task from PISA 2012 using Gaussian mixture models. The results indicate the presence of two and four clusters for groups defined by failure and success on the task, respectively. We interpret the clusters as less-able, low-effort, adaptable, back-and-forth, deliberate, and trial-and-error clusters by considering the cluster-specific feature statistics. The proposed approach sheds light on students’ problem-solving mental processes, which can aid item development and facilitate individualized feedback to students. The method is applicable to many computer-based problems, but a limitation is that the feature definitions can be task-dependent.

• Kristensen, Jarl Kleppe; Torkildsen, Janne von Koss & Andersson, Björn (2023). Repeated mistakes in app-based language learning: Persistence and relation to learning gains. Computers & Education. ISSN 0360-1315. 210. doi: 10.1016/j.compedu.2023.104966. Full text in Research Archive Show summary

  Over the past decade, there has been an enormous upsurge in the use of educational apps in primary schools. However, few studies have examined how children interact with these apps and how their interaction patterns relate to learning outcomes. An interaction pattern that is potentially detrimental to learning is repeated mistakes, defined as making the same mistake more than once when answering a task. With interaction data from an eight-week digital vocabulary intervention, we examined 1) whether the propensity to make repeated mistakes changes across app sessions, and 2) how repeated mistakes relate to children's prior knowledge and their learning gains from the intervention. Our sample consisted of 363 Norwegian second graders who worked with the vocabulary app in a randomized controlled trial. Using growth curve modeling and confirmatory factor analyses, we found that the propensity to repeat mistakes remained stable over time. Furthermore, a structural equation model showed that repeated mistakes related negatively to both pre-test and post-test scores. A substantial proportion of the total effect of prior knowledge on learning gains was mediated by the propensity to repeat mistakes. Children who made more repeated mistakes had lower expected learning gains across all levels of prior knowledge. We suggest that the propensity to repeat mistakes may pose a double threat to learning by diminishing exposure to relevant content, and amplifying the exposure to incorrect input. Considering the stability of mistake repetition, it is crucial to identify students with a high propensity to repeat mistakes and help them break the pattern to support learning. App developers can help this process by implementing automatic detection and feedback.

• Andersson, Björn; Jin, Shaobo & Zhang, Maoxin (2023). Fast estimation of multiple group generalized linear latent variable models for categorical observed variables. Computational Statistics & Data Analysis. ISSN 0167-9473. 182. doi: 10.1016/j.csda.2023.107710. Full text in Research Archive Show summary

  A computationally efficient method for marginal maximum likelihood estimation of multiple group generalized linear latent variable models for categorical data is introduced. The approach utilizes second-order Laplace approximations of the integrals in the likelihood function. It is demonstrated how second-order Laplace approximations can be utilized highly efficiently for generalized linear latent variable models by considering symmetries that exist for many types of model structures. In a simulation with binary observed variables and four correlated latent variables in four groups, the method has similar bias and mean squared error compared to adaptive Gauss-Hermite quadrature with five quadrature points while substantially improving computational efficiency. An empirical example from a large-scale educational assessment illustrates the accuracy and computational efficiency of the method when compared against adaptive Gauss-Hermite quadrature with three, five, and 13 quadrature points.

• Hukkelberg, Silje Sommer & Andersson, Björn (2023). Assessing social competence and antisocial behaviors in children: item response theory analysis of the home and community social behavior scales. BMC Psychology. 11(1). doi: 10.1186/s40359-023-01045-1. Full text in Research Archive Show summary

  The Home and Community Social Behavior Scales (HCSBS) is a rating scale that assesses social competence and antisocial behavior among children and youths between ages 5–18. The present study aimed to investigate the psychometric properties of the HCSBS by applying item response theory (IRT).

• Marcq, Kseniia & Andersson, Björn (2022). Standard Errors of Kernel Equating: Accounting for Bandwidth Estimation. Applied Psychological Measurement. ISSN 0146-6216. 46(3). doi: 10.1177/01466216211066601. Full text in Research Archive Show summary

  In standardized testing, equating is used to ensure comparability of test scores across multiple test administrations. One equipercentile observed-score equating method is kernel equating, where an essential step is to obtain continuous approximations to the discrete score distributions by applying a kernel with a smoothing bandwidth parameter. When estimating the bandwidth, additional variability is introduced which is currently not accounted for when calculating the standard errors of equating. This poses a threat to the accuracy of the standard errors of equating. In this study, the asymptotic variance of the bandwidth parameter estimator is derived and a modified method for calculating the standard error of equating that accounts for the bandwidth estimation variability is introduced for the equivalent groups design. A simulation study is used to verify the derivations and confirm the accuracy of the modified method across several sample sizes and test lengths as compared to the existing method and the Monte Carlo standard error of equating estimates. The results show that the modified standard errors of equating are accurate under the considered conditions. Furthermore, the modified and the existing methods produce similar results which suggest that the bandwidth variability impact on the standard error of equating is minimal.

• Andersson, Björn & Luo, Hao (2022). Impact of Sampling Variability When Estimating the Explained Common Variance. Applied Psychological Measurement. ISSN 0146-6216. 46(4). doi: 10.1177/01466216221084215. Full text in Research Archive
• Ræder, Henrik Galligani; Andersson, Björn & Olsen, Rolf Vegar (2022). Numeracy across grades–vertically scaling the Norwegian national numeracy tests. Assessment in Education: Principles, Policy & Practice. ISSN 0969-594X. p. 1–21. doi: 10.1080/0969594X.2022.2147483. Full text in Research Archive Show summary

  Enabling comparable scores across grades is of interest for policymakers to evaluate educational systems, for researchers to investigate substantive questions, and for teachers to infer student growth. This study implemented a vertical scaling design to numeracy tests given in grades 5 and 8 as part of the Norwegian national testing system. Our design bridges the gap between grades 5 and 8 with a linking test tailored for grades 6 and 7, without the need for new item development. The design combines the existing administration for all grade 5 and 8 students with additional tests for samples of grade 6 and 7 students. The findings indicate that vertically scaling existing tests is possible through a cost-effective design and that numeracy, as measured by the Norwegian national tests, is comparable across four grades. We discuss the implications of our study for creating vertical scales in the context of national assessment systems.

• Luo, Hao; Andersson, Björn; Wong, Gloria & Lum, Terry (2022). Longitudinal measurement properties of the Montreal Cognitive Assessment. Journal of Clinical and Experimental Neuropsychology. ISSN 1380-3395. p. 1–13. doi: 10.1080/13803395.2022.2148634. Full text in Research Archive Show summary

  Introduction The Montreal Cognitive Assessment (MoCA) has started to be used in longitudinal investigations to measure cognition trends but its measurement properties over time are largely unknown. This study aimed to examine the longitudinal measurement invariance of individual MoCA items. Method We used four waves of data collected between 2014 and 2017 from a cohort study on health and well-being of older adults from twelve public housing estates in Hong Kong. We identified people aged 65 years or older at baseline who answered the MoCA items across all time points and had a valid indicator of educational level. A total of 1028 participants were included. We applied confirmatory factor analysis of ordinal variables to examine measurement invariance of the Chinese (Cantonese) MoCA (version 7.0) items across four time points, stratified by educational level, where invariant items were identified by sequential model comparisons. Results Four items exhibited a lack of measurement invariance across the four time points in both education groups (Clock Hand, abstraction, Delayed Recall, and Orientation). The items Cube and Sentence Repetition lacked longitudinal measurement invariance only in the “some education” group and the items Clock Shape and Clock Number only in the “no education” group. However, accounting for the lack of measurement invariance did not substantially affect classification properties for major neurocognitive disorder and mild cognitive impairment. Conclusions Our findings support using MoCA to assess changes in cognition over time in the study population while calling for future research in other populations.

• Chen, Chia-Wen; Andersson, Björn & Zhu, Jinxin (2022). A Factor Mixture Model for Item Responses and Certainty of Response Indices to Identify Student Knowledge Profiles. Journal of Educational Measurement. ISSN 0022-0655. doi: 10.1111/jedm.12344. Full text in Research Archive Show summary

  The certainty of response index (CRI) measures respondents' confidence level when answering an item. In conjunction with the answers to the items, previous studies have used descriptive statistics and arbitrary thresholds to identify student knowledge profiles with the CRIs. Whereas this approach overlooked the measurement error of the observed item responses and indices, we address this by proposing a factor mixture model that integrates a latent class model to detect student subgroups and a measurement model to control for student ability and confidence level. Applying the model to 773 seventh graders' responses to an algebra test, where some items were related to new material that had not been taught in class, we found two subgroups: (1) students who had high confidence in answering items involving the new material; and (2) students who had low confidence in answering items involving the new material but higher general self-confidence than the first group. We regressed the posterior probability of the group membership on gender, prior achievement, and preview behavior and found preview behavior a significant factor associated with the membership. Finally, we discussed the implications of the current study for teaching practices and future research.

• Andersson, Björn; Luo, Hao & Marcq, Kseniia (2022). Reliability coefficients for multiple group item response theory models. British Journal of Mathematical & Statistical Psychology. ISSN 0007-1102. doi: 10.1111/bmsp.12269. Full text in Research Archive Show summary

  Reliability of scores from psychological or educational assessments provides important information regarding the precision of measurement. The reliability of scores is however population dependent and may vary across groups. In item response theory, this population dependence can be attributed to differential item functioning or to differences in the latent distributions between groups and needs to be accounted for when estimating the reliability of scores for different groups. Here, we introduce group-specific and overall reliability coefficients for sum scores and maximum likelihood ability estimates defined by a multiple group item response theory model. We derive confidence intervals using asymptotic theory and evaluate the empirical properties of estimators and the confidence intervals in a simulation study. The results show that the estimators are largely unbiased and that the confidence intervals are accurate with moderately large sample sizes. We exemplify the approach with the Montreal Cognitive Assessment (MoCA) in two groups defined by education level and give recommendations for applied work.

• Costa, Denise Reis; Bolsinova, Maria; Tijmstra, Jesper & Andersson, Björn (2021). Improving the Precision of Ability Estimates Using Time-On-Task Variables: Insights From the PISA 2012 Computer-Based Assessment of Mathematics. Frontiers in Psychology. 12. doi: 10.3389/fpsyg.2021.579128. Full text in Research Archive Show summary

  Log-file data from computer-based assessments can provide useful collateral information for estimating student abilities. In turn, this can improve traditional approaches that only consider response accuracy. Based on the amounts of time students spent on 10 mathematics items from the PISA 2012, this study evaluated the overall changes in and measurement precision of ability estimates and explored country-level heterogeneity when combining item responses and time-on-task measurements using a joint framework. Our findings suggest a notable increase in precision with the incorporation of response times and indicate differences between countries in how respondents approached items as well as in their response processes. Results also showed that additional information could be captured through differences in the modeling structure when response times were included. However, such information may not reflect the testing objective.

• Andersson, Björn; Luo, Hao; Wong, Gloria & Lum, Terry (2021). Linking the Scores of the Montreal Cognitive Assessment 5-min and the interRAI Cognitive Performance Scale in Older Adults With Mild Physical or Cognitive Impairment. Frontiers in Psychiatry. 12. doi: 10.3389/fpsyt.2021.705188. Full text in Research Archive Show summary

  Background: Bridging scores generated from different cognitive assessment tools is necessary to efficiently track changes in cognition across the continuum of care. This study linked scores from the Montreal Cognitive Assessment-5 min (MoCA 5-min) to the interRAI cognitive Performance Scale (CPS), commonly adopted tools in clinical and long-term care settings, respectively. Methods: We included individual-level data from persons who participated in a home- and community-based care program for older people with mild impairment in Hong Kong. The program used the interRAI-Check Up instrument for needs assessment and service matching between 2017 and 2020. Each participant's cognitive performance was assessed using CPS, CPS Version 2 (CPS2), and MoCA 5-min. We performed equipercentile linking with bivariate log-linear smoothing to establish equivalent scores between the two scales. Results: 3,543 participants had valid data on both scales; 66% were female and their average age was 78.9 years (SD = 8.2). The mean scores for MoCA 5-min, CPS, and CPS2 were 18.5 (SD = 5.9), 0.7 (SD = 0.7), and 1.3 (SD = 1.1), respectively. A CPS or CPS2 score of 0 (intact cognition) corresponds to MoCA 5-min scores of 24 and 25, respectively. At the higher end, a CPS score of 3 (moderately impaired) and a CPS2 score of 5 (moderately impaired Level-2) corresponded to MoCA 5-min scores of 0 and 1, respectively. The linking functions revealed the floor and ceiling effects that exist for the different scales, with CPS and CPS2 measuring more-severe cognitive impairment while the MoCA 5-min was better suited to measure mild impairment. Conclusions: We provided score conversions between MoCA 5-min and CPS/CPS2 within a large cohort of Hong Kong older adults with mild physical or cognitive impairment. This enabled continuity in repeated assessment with different tools and improved comparability of cognitive scores generated from different tools from diverse populations and research cohorts.

• Sun, Xiaojian; Andersson, Björn & Xin, Tao (2021). A New Method to Balance Measurement Accuracy and Attribute Coverage in Cognitive Diagnostic Computerized Adaptive Testing. Applied Psychological Measurement. ISSN 0146-6216. doi: 10.1177/01466216211040489. Full text in Research Archive Show summary

  As one of the important research areas of cognitive diagnosis assessment, cognitive diagnostic computerized adaptive testing (CD-CAT) has received much attention in recent years. Measurement accuracy is the major theme in CD-CAT, and both the item selection method and the attribute coverage have a crucial effect on measurement accuracy. A new attribute coverage index, the ratio of test length to the number of attributes (RTA), is introduced in the current study. RTA is appropriate when the item pool comprises many items that measure multiple attributes where it can both produce acceptable measurement accuracy and balance the attribute coverage. With simulations, the new index is compared to the original item selection method (ORI) and the attribute balance index (ABI), which have been proposed in previous studies. The results show that (1) the RTA method produces comparable measurement accuracy to the ORI method under most item selection methods; (2) the RTA method produces higher measurement accuracy than the ABI method for most item selection methods, with the exception of the mutual information item selection method; (3) the RTA method prefers items that measure multiple attributes, compared to the ORI and ABI methods, while the ABI prefers items that measure a single attribute; and (4) the RTA method performs better than the ORI method with respect to attribute coverage, while it performs worse than the ABI with long tests.

• Zhang, Maoxin; Andersson, Björn & Fang, Wang (2021). Are competitive people less altruistic and more manipulative? Associations among subtypes of competitiveness, hypothetical altruism, and Machiavellianism. Personality and Individual Differences. ISSN 0191-8869. 181. doi: 10.1016/j.paid.2021.111037. Full text in Research Archive Show summary

  Competitiveness as a personality trait is commonly viewed as having three dimensions – competing to win (CW; to dominate and suppress others unscrupulously), competing to surpass (CS; to surpass or excel above others), and competing to develop (CD; to focus on personal development). Using a sample of 926 participants in mainland China, this study examined the structure of competitiveness and inferred relationships between competitiveness and hypothetical altruism in resource allocation games and Machiavellianism. We found that CW was associated with lower levels of hypothetical altruism. Additionally, CW and CS were positively related to Machiavellianism, while CD had a negative association with Machiavellianism. These findings indicated that different dimensions of competitiveness function differently concerning altruism and manipulation, advancing the understanding of competitiveness.

• Liu, Chen-Wei; Andersson, Björn & Skrondal, Anders (2020). A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models. Psychometrika. ISSN 0033-3123. 85, p. 322–357. doi: 10.1007/s11336-020-09707-4. Full text in Research Archive Show summary

  In diagnostic classification models (DCMs), the Q matrix encodes in which attributes are required for each item. The Q matrix is usually predetermined by the researcher but may in practice be misspecified which yields incorrect statistical inference. Instead of using a predetermined Q matrix, it is possible to estimate it simultaneously with the item and structural parameters of the DCM. Unfortunately, current methods are computationally intensive when there are many attributes and items. In addition, the identification constraints necessary for DCMs are not always enforced in the estimation algorithms which can lead to non-identified models being considered. We address these problems by simultaneously estimating the item, structural and Q matrix parameters of the Deterministic Input Noisy “And” gate model using a constrained Metropolis–Hastings Robbins–Monro algorithm. Simulations show that the new method is computationally efficient and can outperform previously proposed Bayesian Markov chain Monte-Carlo algorithms in terms of Q matrix recovery, and item and structural parameter estimation. We also illustrate our approach using Tatsuoka’s fraction–subtraction data and Certificate of Proficiency in English data.

• Jin, Shaobo & Andersson, Björn (2020). A note on the accuracy of adaptive Gauss–Hermite quadrature. Biometrika. ISSN 0006-3444. 107(3). doi: 10.1093/biomet/asz080. Full text in Research Archive
• Andersson, Björn & Xin, Tao (2020). Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation. Journal of educational and behavioral statistics. ISSN 1076-9986. doi: 10.3102/1076998620945199. Full text in Research Archive Show summary

  The estimation of high-dimensional latent regression item response theory (IRT) models is difficult because of the need to approximate integrals in the likelihood function. Proposed solutions in the literature include using stochastic approximations, adaptive quadrature, and Laplace approximations. We propose using a second-order Laplace approximation of the likelihood to estimate IRT latent regression models with categorical observed variables and fixed covariates where all parameters are estimated simultaneously. The method applies when the IRT model has a simple structure, meaning that each observed variable loads on only one latent variable. Through simulations using a latent regression model with binary and ordinal observed variables, we show that the proposed method is a substantial improvement over the first-order Laplace approximation with respect to the bias. In addition, the approach is equally or more precise to alternative methods for estimation of multidimensional IRT models when the number of items per dimension is moderately high. Simultaneously, the method is highly computationally efficient in the high-dimensional settings investigated. The results imply that estimation of simple-structure IRT models with very high dimensions is feasible in practice and that the direct estimation of high-dimensional latent regression IRT models is tractable even with large sample sizes and large numbers of items.

• Luo, Hao; Andersson, Björn Håkan; Tang, Jennifer & Wong, Gloria (2019). Applying Item Response Theory Analysis to the Montreal Cognitive Assessment in a Low-Education Older Population. Assessment (ASM). ISSN 1073-1911. p. 1–13. doi: 10.1177/1073191118821733. Full text in Research Archive
• Liu, Yanlou; Andersson, Björn Håkan; Tao, Xin; Zhang, Haiyan & Wang, Lingling (2018). Improved Wald Statistics for Item-Level Model Comparison in Diagnostic Classification Models. Applied Psychological Measurement. ISSN 0146-6216. doi: 10.1177/0146621618798664. Full text in Research Archive
• Liu, Yanlou; Xin, Tao; Andersson, Bjørn & Tian, Wei (2018). Information matrix estimation procedures for cognitive diagnostic models. British Journal of Mathematical & Statistical Psychology. ISSN 0007-1102. 72(1), p. 18–37. doi: 10.1111/bmsp.12134. Full text in Research Archive
• Gao, Yizhu; Zhai, Xiaoming; Andersson, Björn Håkan; Zeng, Pingfei & Xin, Tao (2018). Developing a Learning Progression of Buoyancy to Model Conceptual Change: A Latent Class and Rule Space Model Analysis. Research in Science Education. ISSN 0157-244X. p. 1–20. doi: 10.1007/s11165-018-9736-5. Full text in Research Archive Show summary

  We applied latent class analysis and the rule space model to verify the cumulative characteristic of conceptual change by developing a learning progression for buoyancy. For this study, we first abstracted seven attributes of buoyancy and then developed a hypothesized learning progression for buoyancy. A 14-item buoyancy instrument was administered to 1089 8th grade students to verify and refine the learning progression. The results suggest four levels of progression during conceptual change when 8th grade students understand buoyancy. Students at level 0 can only master Density. When students progress to level 1, they can grasp Direction, Identification, Submerged volume, and Relative density on the basis of the prior level. Then, students gradually master Archimedes’ theory as they reach level 2. The most advanced students can further grasp Relation with motion and arrive at level 3. In addition, this four-level learning progression can be accounted for by the Qualitative–Quantitative–Integrative explanatory model.

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• Ofstad, Sverre Berg; Tan, Tony & Andersson, Björn (2025). Comparing Elective Subject Difficulty Using a Joint Item Response Theory Model. Full text in Research Archive
• Andersson, Björn (2025). Trend estimation in the Norwegian National Tests. Full text in Research Archive Show summary

  In Norway, mandatory national tests are used to monitor performance over time and to identify student weaknesses and strengths. The testing program came under scrutiny in 2023, when it was uncovered that the results had been incorrectly reported for many years. We give an overview of the Norwegian National Tests in numeracy, reading, and English and discuss some particular features of the tests and linking design. We outline the source of the incorrect results and explain how the problem came to be. In a robust re-analysis of the original data, we present revised estimates of the performance trends across 2014-2021. The results show that performance in all domains varied during 2014-2021 and that the results differ markedly compared to the originally reported results, especially in the English domain. We assess the potential impact of model choice and measurement invariance on the trend estimation, demonstrating that these factors can not explain the differences to the original results. We present recommendations for best practices in trend estimation in large-scale assessments and discuss how to avoid similar problems occurring in the future.

• Andersson, Björn (2025). Higher-order extended variational approximation to estimate latent variable models. Full text in Research Archive Show summary

  Generalized linear latent variable models is a flexible class of models which supports joint modeling of continuous, count, ordinal, and binary variables with arbitrary structures among latent variables and observed variables. Estimation of GLLVMs is challenging when specifying complex models that include many types of observed variables and many latent variables. Recently, various methods based on the variational approximation have been proposed in the literature to estimate GLLVMs. To improve the estimation accuracy of variational approximation methods, we derive an extended variational approximation estimator for GLLVMs based on a higher-order expansion and evaluate its properties. In the implementation, we analytically compute the higher-order derivatives required and exploit the sparsity of the model structure to realize computational efficiencies. The approach is compared against alternative methods, such as the computationally efficient but less accurate Laplace approximation and the gold standard method of adaptive Gauss-Hermite quadrature. We discuss the trade off between accuracy and computational efficiency with respect to different estimation methods and different model structures.

• Liu, Chen-Wei; Andersson, Björn & Skrondal, Anders (2024). Erratum to: A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models (Psychometrika, (2020), 85, 2, (322-357), 10.1007/s11336-020-09707-4). Psychometrika. ISSN 0033-3123. doi: 10.1007/s11336-024-09974-5. Full text in Research Archive
• Ræder, Henrik Galligani; Olsen, Rolf Vegar & Andersson, Björn (2020). Comparing measures of numeracy across grades. Full text in Research Archive
• Ræder, Henrik Galligani; Andersson, Björn & Olsen, Rolf Vegar (2019). Exploring the unidimensionality of the Norwegian National Numeracy tests. Full text in Research Archive
• Ræder, Henrik Galligani; Andersson, Björn; Blömeke, Sigrid & Olsen, Rolf Vegar (2018). Development of Numeracy Proficiency in Primary and Lower Secondary School. Full text in Research Archive
• Ofstad, Sverre Berg & Andersson, Björn (2026). Karakterulempen ved å velge realfag: I hvilken grad veier realfagspoengene opp for den? Universitetet i Oslo. doi: https:/www.uv.uio.no/cemo/english/about/news-events-and-publications/news/2026/bonus-points-natural-science.html. Full text in Research Archive

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