Faculty Profile

Njål Foldnes

Professor - Campus Stavanger, Department of Economics

Department of Economics


I hold a Ph.D. in combinatorial optimization from the University of Oslo, Centre of Mathematics for Applications. Currently I am working with problems in covariance structure analysis; structural equation modeling, and simulation of non-normal multivariate data.

I am also interested in education, and do research on the flipped classroom in higher education, as well as statistical analysis for the Norwegian Reading Centre.

Area of Expertise


Foldnes, Njål & Grønneberg, Steffen (2019)

Pernicious Polychorics: The Impact and Detection of Underlying Non-normality

Structural Equation Modeling Doi: 10.1080/10705511.2019.1673168 - Full text in research archive

Ordinal data in social science statistics are often modeled as discretizations of a multivariate normal vector. In contrast to the continuous case, where SEM estimation is also consistent under non-normality, violation of underlying normality in ordinal SEM may lead to inconsistent estimation. In this article, we illustrate how underlying non-normality induces bias in polychoric estimates and their standard errors. This bias is strongly affected by how we discretize. It is therefore important to consider tests of underlying multivariate normality. In this study we propose a parametric bootstrap test for this purpose. Its performance relative to the test of Maydeu-Olivares is evaluated in a Monte Carlo study. At realistic sample sizes, the bootstrap exhibited substantively better Type I error control and power than the Maydeu-Olivares test in ordinal data with ten dimensions or higher. R code for the bootstrap test is provided.

Foldnes, Njål & Grønneberg, Steffen (2019)

On Identification and Non-normal Simulation in Ordinal Covariance and Item Response Models

Psychometrika, 84(4), s. 1000- 1017. Doi: 10.1007/s11336-019-09688-z

A standard approach for handling ordinal data in covariance analysis such as structural equation modeling is to assume that the data were produced by discretizing a multivariate normal vector. Recently, concern has been raised that this approach may be less robust to violation of the normality assumption than previously reported. We propose a new perspective for studying the robustness toward distributional misspecification in ordinal models using a class of non-normal ordinal covariance models. We show how to simulate data from such models, and our simulation results indicate that standard methodology is sensitive to violation of normality. This emphasizes the importance of testing distributional assumptions in empirical studies. We include simulation results on the performance of such tests.

Marcoulides, Katerina; Foldnes, Njål & Grønneberg, Steffen (2019)

Assessing Model Fit in Structural Equation Modeling Using Appropriate Test Statistics

Structural Equation Modeling, s. 1- 11. Doi: 10.1080/10705511.2019.1647785

The assessment of model fit has received widespread interest by researchers in the structural equation modeling literature for many years. Various model fit test statistics have been suggested for conducting this assessment. Selecting an appropriate test statistic in order to evaluate model fit, however, can be difficult as the selection depends on the distributional characteristics of the sampled data, the magnitude of the sample size, and/or the proposed model features. The purpose of this paper is to present a selection procedure that can be used to algorithmically identify the best test statistic and simplify the whole assessment process. The procedure is illustrated using empirical data along with an easy to use computerized implementation.

McTigue, Erin; Solheim, Oddny Judith, Walgermo, Bente R., Frijters, Jan & Foldnes, Njål (2019)

How can we determine students' motivation for reading before formal instruction? Results from a self-beliefs and interest scale validation study

Early Childhood Research Quarterly, 48, s. 122- 133. Doi: 10.1016/j.ecresq.2018.12.013

Foldnes, Njål & Olsson, Ulf H. (2019)

The choice of normal-theory weight matrix when computing robust standard errors in confirmatory factor analysis

Structural Equation Modeling, s. 1- 15. Doi: 10.1080/10705511.2019.1600408 - Full text in research archive

Robust standard errors are of central importance in confirmatory factor models. In calculating these statistics a central ingredient is the inverse of the asymptotic covariance matrix of second-order moments calculated under the assumption of normality. Currently, two ways of estimating this matrix are employed in software packages. One approach uses the sample covariance matrix, the other the model-implied covariance matrix. Previous research based on a small confirmatory factor model demonstrated that the latter approach yielded a slight improvement in standard error performance. The present study argues theoretically that the discrepancy between the two approaches increases in models where there are few model parameters relative to p(p+1)/2, where p is the number of observed variables. We present simulation results that support this claim, in both small and large correctly specified models, across a large variety of non-normal conditions. We recommend the model-implied covariance matrix for robust standard error computation.

Grønneberg, Steffen & Foldnes, Njål (2019)

A problem with discretizing Vale-Maurelli in simulation studies

Psychometrika, 84(2), s. 554- 561. Doi: 10.1007/s11336-019-09663-8 - Full text in research archive

Previous influential simulation studies investigate the effect of underlying non-normality in ordinal data using the Vale–Maurelli (VM) simulation method. We show that discretized data stemming from the VM method with a prescribed target covariance matrix are usually numerically equal to data stemming from discretizing a multivariate normal vector. This normal vector has, however, a different covariance matrix than the target. It follows that these simulation studies have in fact studied data stemming from normal data with a possibly misspecified covariance structure. This observation affects the interpretation of previous simulation studies.

Foldnes, Njål; Marcoulides, George A. & Olsson, Ulf H. (2019)

Examining the Performance of the Modified ADF Goodness-of-fit Test Statistic in Structural Equation Models

Structural Equation Modeling Doi: 10.1080/10705511.2019.1586545

The asymptotically distribution-free (ADF) test statistic depends on very mild distributional assumptions and is theoretically superior to many other so-called robust tests available in structural equation modeling. The ADF test, however, often leads to model overrejection even at modest sample sizes. To overcome its poor small-sample performance, a family of robust test statistics obtained by modifying the ADF statistics was recently proposed. This study investigates by simulation the performance of the new modified test statistics. The results revealed that although a few of the test statistics adequately controlled Type I error rates in each of the examined conditions, most performed quite poorly. This result underscores the importance of choosing a modified test statistic that performs well for specific examined conditions. A parametric bootstrap method is proposed for identifying such a best-performing modified test statistic. Through further simulation it is shown that the proposed bootstrap approach performs well

Grønneberg, Steffen & Foldnes, Njål (2018)

Testing Model Fit by Bootstrap Selection

Structural Equation Modeling Doi: 10.1080/10705511.2018.1503543 - Full text in research archive

Walgermo, Bente R.; Foldnes, Njål, Uppstad, Per Henning & Solheim, Oddny Judith (2018)

Developmental Dynamics of Early Reading Skill, Literacy Interest and Reader's Self-Concept Within the First Year of Formal Schooling

Reading and writing, 31(6), s. 1379- 1399. Doi: 10.1007/s11145-018-9843-8 - Full text in research archive

Previous studies have documented robust relationships between emergent literacy and later reading performance. A growing body of research has also reported associations between motivational factors and reading in early phases of reading development. However, there is less research about cross-lagged relationships between motivational factors and reading skills in beginning readers. To examine relationships between early reading skills, literacy interest and reader self-concept, we tested 1141 children twice during their first year of formal reading instruction in school. Cross-lagged analysis showed strong stability in reading skills and medium stability in literacy interest and reader self-concept over the first school year. We also found bidirectional relationships between reading skills and self-concept and between the motivational components of literacy interest and reader self-concept. In the final part of the article, we address the potential theoretical progress attainable through the use of cross-lagged designs in this field.

Steen-Utheim, Anna Therese & Foldnes, Njål (2018)

A qualitative investigation of student engagement in a flipped classroom

Teaching in Higher Education, 23(3), s. 307- 324. Doi: 10.1080/13562517.2017.1379481 - Full text in research archive

The flipped classroom is gaining acceptance in higher education as an alternative to more traditional methods of teaching. In the current study, twelve students in a Norwegian higher education institution were in-depth interviewed about their learning experiences in a two-semester long mathematics course. The first semester was taught using flipped classroom and the second semester using lectures, where both teaching modes contained a substantial amount of active learning. Overall, students report a more positive learning experience and higher engagement in the flipped classroom. The analysis revealed seven categories that the students highlight as especially conducive to their learning; commitment to peers, being recognized, feeling safe, instructor relationship, physical learning environment, learning with peers and using videos to learn new content. The results indicate that the affective dimension of student engagement is particularly prominent when students reflect upon learning in the flipped classroom.

Foldnes, Njål & Grønneberg, Steffen (2018)

Approximating Test Statistics Using Eigenvalue Block Averaging

Structural Equation Modeling, 25(1), s. 101- 114. Doi: 10.1080/10705511.2017.1373021 - Full text in research archive

We introduce and evaluate a new class of approximations to common test statistics in structural equation modeling. Such test statistics asymptotically follow the distribution of a weighted sum of i.i.d. chi-square variates, where the weights are eigenvalues of a certain matrix. The proposed eigenvalue block averaging (EBA) method involves creating blocks of these eigenvalues and replacing them within each block with the block average. The Satorra–Bentler scaling procedure is a special case of this framework, using one single block. The proposed procedure applies also to difference testing among nested models. We investigate the EBA procedure both theoretically in the asymptotic case, and with simulation studies for the finite-sample case, under both maximum likelihood and diagonally weighted least squares estimation. Comparison is made with 3 established approximations: Satorra–Bentler, the scaled and shifted, and the scaled F tests.

Strand, Olaug; Wagner, Åse Kari H. & Foldnes, Njål (2017)

Flerspråklige elevers leseresultater

Gabrielsen, Egil (red.). Klar framgang! Leseferdighet på 4. og 5. trinn i et femtenårsperspektiv

Foldnes, Njål & Grønneberg, Steffen (2017)

The asymptotic covariance matrix and its use in simulation studies

Structural Equation Modeling, 24(6), s. 881- 896. Doi: 10.1080/10705511.2017.1341320 - Full text in research archive

Foldnes, Njål (2017)

The impact of class attendance on student learning in a flipped classroom

Nordic Journal of Digital Literacy, 12(1-2), s. 8- 18. Doi: 10.18261/issn.1891-943x-2017-01-02-02

We investigate the relationship between class attendance and academic achievement in a flipped classroom that was designed to foster social learning in fixed groups. Controlling for initial mathematical skill and attitudes, we found a substantial effect of class attendance on student achievement. Increasing class attendance by one standard deviation was associated with an increase in mathematics performance of 0.28 standard deviations. Neither attitudes nor initial mathematical skill predicted class attendance. We conclude that availability of online videos does not eliminate the need for carefully designed in-class sessions in order to maximise student learning. Communicating this finding may help reduce absenteeism in the flipped classroom.

Grønneberg, Steffen & Foldnes, Njål (2017)

Covariance Model Simulation Using Regular Vines

Psychometrika, 82(4), s. 1035- 1051. Doi: 10.1007/s11336-017-9569-6 - Full text in research archive

We propose a new and flexible simulation method for non-normal data with user-specified marginal distributions, covariance matrix and certain bivariate dependencies. The VITA (VIne To Anything) method is based on regular vines and generalizes the NORTA (NORmal To Anything) method. Fundamental theoretical properties of the VITA method are deduced. Two illustrations demonstrate the flexibility and usefulness of VITA in the context of structural equation models. R code for the implementation is provided.

Foldnes, Njål & Olsson, Ulf H. (2016)

A simple simulation technique for non-normal data with pre-specified skewness, kurtosis and covariance matrix

Multivariate Behavioral Research, 51(2-3), s. 207- 219. Doi: 10.1080/00273171.2015.1133274

Foldnes, Njål (2016)

The flipped classroom and cooperative learning: Evidence from a randomised experiment

Active Learning in Higher Education, 17(1), s. 39- 49. Doi: 10.1177/1469787415616726 - Full text in research archive

This article describes a study which compares the effectiveness of the flipped classroom relative to the traditional lecturebased classroom.We investigated two implementations of the flipped classroom. The first implementation did not actively encourage cooperative learning, with students progressing through the course at their own pace. With this implementation student examination scores did not differ between the lecture classes and the flipped classroom. The second implementation was organised with cooperative learning activities. In a randomised control-group pretest-posttest experiment student scores on a post-test and on the final examination were significantly higher for the flipped classroom group than for the control group receiving traditional lectures. This demonstrates that the classroom flip, if properly implemented with cooperative learning, can lead to increased academic performance.

Foldnes, Njål & Olsson, Ulf (2015)

Correcting too much or too little? The performance of three chi-square corrections

Multivariate Behavioral Research, 50(5), s. 533- 543. Doi: 10.1080/00273171.2015.1036964

Foldnes, Njål & Grønneberg, Steffen (2015)

How general is the Vale-Maurelli simulation approach?

Psychometrika, 80(4), s. 1066- 1083. Doi: 10.1007/s11336-014-9414-0

Foldnes, Njål & Hagtvet, Knut Arne (2014)

The Choice of Product Indicators in Latent Variable Interaction Models: Post Hoc Analyses

Psychological methods, 19(3), s. 444- 457. Doi: 10.1037/a0035728

Foldnes, Njål; Foss, Tron & Olsson, Ulf H. (2012)

Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models

Journal of educational and behavioral statistics, 37(3), s. 367- 386. Doi: 10.3102/1076998611411920

Foldnes, Njål; Olsson, Ulf H. & Foss, Tron (2012)

The effect of kurtosis on the power of two test statistics in covariance structure analysis

British Journal of Mathematical & Statistical Psychology, 65(1), s. 1- 18. Doi: 10.1111/j.2044-8317.2010.02010.x

Dahl, Geir & Foldnes, Njål (2006)

LP based heuristics for the multiple knapsack problem with assignment restrictions

Annals of Operations Research, 146(1), s. 91- 104. - Full text in research archive

Dahl, Geir; Foldnes, Njål & Gouveia, Luis (2004)

A note on hop-constrained walk polytopes

Operations Research Letters, 32, s. 345- 349.

Dahl, Geir & Foldnes, Njål (2003)

Complete description of a class of knapsack polytopes

Operations Research Letters, 31, s. 335- 340.

Thomson, Jenny; Foldnes, Njål, Lundetræ, Kjersti, Solheim, Oddny Judith, Njå, Morten Bergsten & Uppstad, Per Henning (2019)

Can childrens instructional gameplay Activity be used as a diagnostic indicator of Reading difficulties?

[Academic lecture]. Skriv!Les! Nordisk forskerkonferanse om lesing og skriving.

Walgermo, Bente R.; Foldnes, Njål, Uppstad, Per Henning & Solheim, Oddny Judith (2018)

First Grade Reading Skill and Motivation Dynamics

[Academic lecture]. Sig EARLI 2018 – Learning and development in early childhood.

Foldnes, Njål; Grønneberg, Steffen & Hermansen, Gudmund Horn (2018)

Statistikk og Dataanalyse

[Textbook]. Cappelen Damm Akademisk.

Strand, Olaug; Wagner, Åse Kari H. & Foldnes, Njål (2017)

Flerspråklige elevers leseresultater i PIRLS 2016

[Academic lecture]. PIRLS konferanse.

Wagner, Åse Kari H.; Foldnes, Njål, Lundetræ, Kjersti, Solheim, Oddny Judith & Uppstad, Per Henning (2017)

På sporet - effekt av tidlig innsats for andrespråkselever med risiko for å utvikle lese- og skrivevansker

[Academic lecture]. SkrivLes! 2017 Nordisk forskerkonferanse om lesing og skriving.

McTigue, Erin; Solheim, Oddny Judith, Walgermo, Bente R., Foldnes, Njål & Frijters, Jan c (2017)

Measuring multiple dimensions of early literacy motivation through self-report at school entry

[Academic lecture]. 17th Biennial EARLI Conference for research on learning and instruction.

Uppstad, Per Henning; Foldnes, Njål, Lundetræ, Kjersti, Solheim, Oddny Judith & Wagner, Åse Kari H. (2016)

Effect of early intervention for minority children at-risk for reading difficulties

[Academic lecture]. National Network series on Perspectives on Developmental Deficits.

Foldnes, Njål & Hagtvet, Knut Arne (2014)

The Choice of Product indicators in latent variable interaction models

[Academic lecture]. Two-Day Research SEminar.

Foldnes, Njål (2010)

The effect of kurtosis on the power of two test statistics

[Academic lecture]. SEM working group annual meeting.

Foldnes, Njål (2008)

Testing Structural Equation Models: The effect of Kurtosis

[Academic lecture]. 7th International Conference on Social Science Methodology.

Dahl, Geir; Flatberg, Truls, Foldnes, Njål & Gouveia, Luis (2006)

The Jump Formulation for the Hop-Constrained Minimum Spanning Tree Problem

[Academic lecture]. The 8th INFORMS Telecommunications Conference.

Foldnes, Njål; Mørken, Knut Martin & Vistnes, Arnt Inge (2005)

En ny verden: Datamaskinen, beregninger og realfagsundervisning

[Popular scientific article]. UNIPED (Tromsø), 28(3), s. 36- 43.

Dahl, Geir & Foldnes, Njål (2003)

On hop-constrained walk polytopes

[Academic lecture]. 18th International Symposium on Mathematical Programming.

Dahl, Geir & Foldnes, Njål (2003)

A randomized algorithm for the multiple knapsack problem with assignment restrictions

[Academic lecture]. Int. network optimization conf..

Dahl, Geir & Foldnes, Njål (2002)

Complexity of certain multiple knapsack problems

[Academic lecture]. Nordic Mathematical Prog. Society Conference.

Dahl, Geir & Foldnes, Njål (2002)

Polyhedral Properties of certain 0/1 Knapsack Polytopes

[Academic lecture]. IFORS 2002.

Academic Degrees
Year Academic Department Degree
2004 University of Oslo Ph.D Dr. Scient.
Work Experience
Year Employer Job Title
2006 - Present BI Norwegian Business School Associate professor