Øyvind Langsrud

Oyvind.Langsrud krøllalfa

ssb.no

50-50 MANOVA

Rotation Tests

Software

Fisher's Exact Test

Publications

I am employed at
Statistics Norway, Division for Statistical Methods and Standards.

Links : Tilfeldig Gang , Functional Genomics , Statistics Resources , Chemometrics , The European Network for Business and Industrial Statistics .

PUBLICATIONS

Selected Journal Papers

Langsrud, Ø., Jørgensen, K., Ragni Ofstad, R. and Næs, T. (2007), Analyzing Designed Experiments with Multiple Responses, Journal of Applied Statistics, 34, 1275-1296. [Abstract] [pdf]

Langsrud, Ø. (2006), Explaining Correlations by Plotting Orthogonal Contrasts, The American Statistician, 60, 335-339. [Abstract] [pdf]

Langsrud, Ø. (2005), Rotation Tests, Statistics and Computing, 15, 53-60. [Abstract]

Langsrud, Ø. (2004), The Geometrical Interpretation of Statistical Tests in Multivariate Linear Regression, Statistical Papers, 45, 111-122. [Abstract]

Langsrud, Ø. and Næs, T. (2003), Optimised Score Plot by Principal Components of Predictions, Chemometrics and Intelligent Laboratory Systems, 68, 61-74. [Abstract]

Langsrud, Ø. (2003), ANOVA for Unbalanced Data: Use Type II Instead of Type III Sums of Squares, Statistics and Computing, 13, 163-167. [Abstract]

Langsrud, Ø. (2002), 50-50 Multivariate Analysis of Variance for Collinear Responses, The Statistician, 51, 305-317. [Abstract]

Langsrud, Ø. (2001), Identifying Significant Effects in Fractional Factorial Multiresponse Experiments, Technometrics, 43, 415-424. [Abstract]

Other Journal Papers

Moen B., Janbu A.O., Langsrud S., Langsrud Ø., Hobman J., Constantinidou C., Kohler A., and Rudi K. (IN PRESS), Global responses of Escherichia coli to adverse conditions determined by microarrays and FT-IR spectroscopy, Canadian Journal of Microbiology.

Bahuaud D., Mørkøre T., Langsrud Ø., Sinnes K., Veiseth E., Ofstad R., Thomassen M.S. (2008), Effects of -1.5 °C Super-chilling on Quality of Atlantic Salmon (Salmo salar) Pre-Rigor Fillets: Cathepsin activity, Muscle Histology, Texture and Liquid Leakage, Food Chemistry. 111, 329-339.

Bjerke, F., Langsrud, Ø., Aastveit, A.H. (2008), Restricted randomisation and multiple responses in industrial experiments, Quality and Reliability Engineering International. 24, 167-181.

Hollung, K., Veiseth, E., Frøystein, T., Aass, L., Langsrud, Ø., Hildrum, K.I. (2007), Variation in the response to manipulation of post mortem glycolysis in beef muscles by low-voltage electrical stimulation and conditioning temperature, Meat Science. 77, 372-383.

Nordvi, B, Langsrud, Ø., Egelandsdal, B., Slinde, E., Vogt, G., Gutierrez, M., Olsen, E. (2007), Characterization of Volatile Compounds in a Fermented and Dried Fish Product during Cold Storage, Journal of Food Science. 72, S373-S380.

Bore, E., Langsrud, S., Langsrud, Ø., Rode, T.M., Holck, A. (2007), Acid shock responses in staphylococcus aureus investigated by global gene expression analysis, Microbiology, 153, 2289-2303.

Nordvi, B, Egelandsdal, B., Langsrud, Ø., Ofstad, R., Slinde, E. (2007), Development of a novel, fermented and dried saithe and salmon product, Innovative Food Science & Emerging Technologies, 8, 163-171.

Bore, E., Hebraud, M., Chafsey, I., Chambon, C., Skjæret, C., Moen, B., Møretrø, T., Langsrud, Ø., Rudi, K., Langsrud, S. (2007), Adapted tolerance to benzalkonium chloride in Escherichia coli K-12 studied by transcriptome and proteome analyses, Microbiology, 153, 935-946.

Sørheim, O., Langsrud, Ø., Cornforth, D.P., Johannessen, T.C., Slinde, E., Berg, P., Nesbakken, T. (2006), Carbon monoxide as a colorant in cooked or fermented sausages, Journal of Food Science, 71, C549-C555.

Egelandsdal, B., Dingstad, G.I., Tøgersen, G., Lundby, F., Langsrud, Ø. (2005), Autofluorescence quantifies collagen in sausage batters with a large variation in myoglobin content, Meat Science, 69, 35-46.

Ofstad, R., Langsrud, Ø., Nyvold, T.E., Enersen, G., Høst, V., Willers, E.P., Nordvi, B., Egelandsdal, B. (2005), Heat processed whey-protein food emulsions and growth of shear-induced cracks during cooling, LWT - Food Science and Technology, 38, 29-39.

Kihlberg, I., Johansson, L., Langsrud, Ø., Risvik, E. (2005), Effects of information on liking of bread, Food Quality and Preference, 16, 25-35.

Egelandsdal, B., Langsrud, Ø., Nyvold, T.E., Sontum, P.K., Sørensen, C., Enersen, G., Hølland, S. and Ofstad, R. (2001), Estimating significant causes of variation in emulsions’ droplet size distributions obtained by the electrical sensing zone and laser low angle light scattering techniques, Food Hydrocolloids, 15, 521-532.

Langsrud, Ø. and Næs, T. (1998), A Unified Framework for Significance Testing in Fractional Factorials, Computational Statistics and Data Analysis, 28, 413-431.

Næs, T. and Langsrud, Ø. (1998), Fixed or random assessors in sensory profiling?, Food Quality and Preference, 9, 145-152.

Langsrud, Ø. and Næs, T. (1995), On the Structure of PLS in Orthogonal Designs, Journal of Chemometrics, 9, 483-487.

Langsrud, Ø., Næs, T. and Ellekjær, M. R. (1994), Identifying Significant Effects in Fractional Factorial Designs, Journal of Chemometrics, 8, 205-219.

Some Conference Proceedings

Langsrud, Ø. (2005): Adjusted p-values by rotation testing, MCP 2005, The 4th international conference on Multiple Comparison Procedures, (SLIDES ONLY), The slides can be found at the conference website.
Langsrud, Ø., Jørgensen, K. and Haugdal, J. (2003): Tools for analysing designed multiresponse experiments, Proceedings of the Third Annual meeting of ENBIS and ISIS3, (SLIDES ONLY), The proceedings were published on a CD-Rom. See the ENBIS website. [ pdf ]
Langsrud, Ø. and Næs, T. (2001): Optimised score plot by principal components of predictions, Proceedings of the 2nd International Symposium of PLS and Related Methods , (Eds. Vinzi, Lauro, Morineau, Tenenhaus) Cisia-Ceresta Montreuil, France, ISBN 2-906711-48-9. [ pdf ]
Langsrud, Ø., Egelandsdal, B., and Ofstad, R. (2001): Analysing Designed Experiments with Multiple Responses, Proceedings of the First Annual ENBIS Conference, (SLIDES ONLY), The proceedings were published on a CD-Rom. See the ENBIS website. [ pdf ]
Langsrud Ø. (2000): Fifty-Fifty MANOVA: Multivariate Analysis of Variance for Collinear Responses, Proceedings of The Industrial Statistics in Action 2000, vol. 2, p. 250-264, University of Newcastle upon Tyne.

Other

Langsrud, Ø. (1997): Identifying Significant Effects in Fractional Factorial Single- and Multi-response Experiments
Doctor Scientarium Thesis, Agricultural University of Norway.
Langsrud, Ø. and Næs, T. (2002) [in Norwegian]: PCP: Nytt og Optimalisert Plott av Skårer og Ladninger.
Poster presentert på Det 14. Norske Kjemometrisymposium, Gol.
pdf
Also see:: Publications at Norwegian Computing Center ( NR )

Abstracts of Selected Journal Papers

Langsrud, Ø., Jørgensen, K., Ragni Ofstad, R. and Næs, T. (2007), Analyzing Designed Experiments with Multiple Responses, Journal of Applied Statistics, 34, 1275-1296. [pdf]

ABSTRACT: This paper is an overview of a unified framework for analyzing designed experiments with univariate or multivariate responses. Both categorical and continuous design variables are considered. To handle unbalanced data, we introduce the so-called Type II* sums of squares. This means that the results are independent of the scale chosen for continuous design variables. Furthermore, it does not matter whether two-level variables are coded as categorical or continuous. Overall testing of all responses is done by 50-50 MANOVA, which handles several highly correlated responses. Univariate p-values for each response are adjusted by using rotation testing. To illustrate multivariate effects, mean values and mean predictions are illustrated in a principal component score plot or directly as curves. For the unbalanced cases, we introduce a new variant of adjusted means, which are independent to the coding of two-level variables. The methodology is exemplified by case studies from cheese and fish pudding production.

KEY WORDS: 50-50 MANOVA, General linear model, Least-squares means, Multiple testing, Principal component, Rotation test, Unbalanced factorial design.

Langsrud, Ø. (2006), Explaining Correlations by Plotting Orthogonal Contrasts, The American Statistician, 60, 335-339. [pdf]

ABSTRACT ( Copyright © 2006 American Statistical Association ) : This article describes a new plot that aids understanding the relationship between two response variables in a designed experiment. In addition to plotting the observed values directly, we make a scatter plot of orthogonal contrasts from the general linear model. This plot contains the same correlation information as the ordinary scatter plot. Therefore, one can interpret how the effects of the various design variables contribute to the correlation coefficient. This idea is also useful in more general cases. Any graphic presentation of the original observations can be accompanied by a corresponding plot of orthogonal contrasts that often will clarify the interpretation.

KEY WORDS: Design of experiments, Fractional factorial design, Scatterplot, General linear model, Partial least squares, Principal component analysis.

Langsrud, Ø. (2005), Rotation Tests, Statistics and Computing, 15, 53-60.

ABSTRACT

This paper describes a generalised framework for doing Monte Carlo tests in multivariate linear regression. The rotation methodology assumes multivariate normality and is a true generalisation of the classical multivariate tests - any imaginable test statistic is allowed. The generalised test statistics are dependent on the unknown covariance matrix. Rotation testing handles this problem by conditioning on sufficient statistics.

Compared to permutation tests, we replace permutations by proper random rotations. Permutation tests avoid the multinormal assumption, but they are limited to relatively simple models. On the other hand, a rotation test can, in particular, be applied to any multivariate generalisation of the univariate F-test.

As an important application, a detailed description of how each single response p-value can be non-conservatively adjusted for multiplicity is given. This method is exact and non-conservative (unlike Bonferroni), and it is a generalisation of the ordinary F-test (except for the computation by simulations). Hence, this paper offers an exact Monte Carlo solution to a classical problem of multiple testing.

KEY WORDS: Conditional inference, Multiple testing, Random orthogonal matrix, Adjusted p-value, Multiple endpoints, Spherical distribution, Microarray data analysis.

Moen, B., Oust, A., Langsrud, Ø., Dorrell, N., Gemma, L., Marsden, G.L., Hinds, J., Kohler, A., Wren, B.W. and Rudi, K. (2005), An explorative multifactor approach for investigating global survival mechanisms of Campylobacter jejuni under environmental conditions, Applied and Environmental Microbiology, 71, 2086-2094. [ pdf ]

ABSTRACT ( Copyright © American Society for Microbiology ) : Explorative approaches such as DNA microarray experiments are becoming increasingly important in microbial research. Despite these major technical advancements, approaches to study multifactor experiments are still lacking. We have addressed this problem using rotation testing and a novel MANOVA approach (50-50 MANOVA) to investigate interacting experimental factors in a complex experimental design. Furthermore, a new rotation testing based method was introduced to calculate false discovery rates for each response. This novel analytical concept was used to investigate global survival mechanisms in the environment of the major food borne pathogen C. jejuni. We simulated non-growth environmental conditions by investigating combinations of the factors temperature (5 and 25° C) and oxygen tension (anaerobic, microaerobic and aerobic). Data were generated using DNA microarrays for information about gene expression patterns coupled with FT-IR spectroscopy to study global macromolecular changes in the cell. Microarray analyses showed that most genes are either unchanged or down regulated compared to the reference (day 0) for the conditions tested, and that the 25° C anaerobic condition gave the most distinct expression pattern with the fewest genes expressed. The few up regulated genes are generally stress related and/or related to the cell envelope. We found, using FT-IR spectroscopy, that the amount of polysaccharides/oligosaccharides increases under the non-growth survival conditions. Potential mechanisms for survival could be to down regulate most functions to save energy, and produce polysaccharides/oligocaccharides for protection against harsh environments. Basic knowledge about the survival mechanisms is of fundamental importance in preventing transmission of this bacterium through the food chain.

KEY WORDS: Campylobacter jejuni, survival in the environment, microarray, FT-IR spectroscopy, 50-50 MANOVA, False Discovery Rate.

Langsrud, Ø. (2004), The Geometrical Interpretation of Statistical Tests in Multivariate Linear Regression, Statistical Papers, 45, 111-122.

ABSTRACT: A geometrical interpretation of the classical tests of the relation between two sets of variables is presented. One of the variable sets may be considered as fixed and then we have a multivariate regression model. When the Wilks' lambda distribution is viewed geometrically it is obvious that the two special cases, the F distribution and the Hotelling T ² distribution are equivalent. From the geometrical perspective it is also obvious that the test statistic and the p-value are unchanged if the responses and the predictors are interchanged.

KEY WORDS: Multivariate analysis, Wilks' lambda distribution, MANOVA, Canonical correlation, Random rotation, Invariance.

Langsrud, Ø. and Næs, T. (2003), Optimised Score Plot by Principal Components of Predictions, Chemometrics and Intelligent Laboratory Systems, 68, 61-74.

ABSTRACT: A common problem in statistics/chemometrics is to relate two data matrices (X and Y) to each other, with the purpose of either prediction or interpretation. Usually one is interested in understanding which directions in Y-space that can be predicted by which directions in X-space. Several methods exist for this, for instance PLS regression and canonical correlation. The present paper presents a new plot for visualising the relationship between X and Y. The plot is based on a decomposition of the X-space that is optimal with respect to Y-variance. The new procedure can accompany any regression method.

KEY WORDS: PLS, PCR, principal components, scores plot, loading plot, reduced-rank regression.

Langsrud, Ø. (2003), ANOVA for Unbalanced Data: Use Type II Instead of Type III Sums of Squares, Statistics and Computing, 13, 163-167.

ABSTRACT: Methods for analyzing unbalanced factorial designs can be traced back to Yates in 1934 ¹⁾. Today, most major statistical programs perform, by default, unbalanced ANOVA based on Type III sums of squares (Yates's weighted squares of means). As criticized by Nelder and Lane ²⁾, this analysis is founded on unrealistic models - models with interactions, but without all corresponding main effects. The Type II analysis (Yates's method of fitting constants) is usually not preferred because of the underlying assumption of no interactions. This argument is, however, also founded on unrealistic models. Furthermore, by considering the power of the two methods, it is clear that Type II is preferable.

1) F. Yates (1934) The Analysis of Multiple Classifications With Unequal Numbers in the Different Classes, Journal of the American Statistical Association , 29, 51-66 .
2) J. A. Nelder and P. W. Lane (1995) The Computer Analysis of Factorial Experiments: In Memoriam - Frank Yates, The American Statistician 49, 382-385.

KEY WORDS: Unbalanced factorial design, Linear model, Fixed effect, Nonorthogonal, Fitting constants, Constraint.

Langsrud, Ø. (2002), 50-50 Multivariate Analysis of Variance for Collinear Responses, The Statistician, 51, 305-317.

ABSTRACT: Classical multivariate analysis-of-variance tests perform poorly in cases with several highly correlated responses and the tests collapse when the number of responses exceeds the number of observations. This paper presents a new method which handles this problem. The dimensionality of the data is reduced by using principal component decompositions and the final tests are still based on the classical test statistics and their distributions. The methodology is illustrated with an example from the production of sausages with responses from near infrared reflectance spectroscopy. A closely related method for testing relationships in uniresponse regression with collinear explanatory variables is also presented. The new test, which is called the 50-50 F-test, uses the first k components to calculate SS_MODEL. The next d components are not involved in SS_ERROR and they are called buffer components.

KEY WORDS: Multiresponse, Significance testing, Principal component, Hotelling's T ², Experimental design, Stabilized multivariate tests.

Langsrud, Ø. (2001), Identifying Significant Effects in Fractional Factorial Multiresponse Experiments, Technometrics , 43, 415-424.

ABSTRACT: A forward selection procedure for identifying active contrasts in unreplicated factorial multiresponse experiments is presented. To test the multivariate effects, p-values are calculated by Monte Carlo sampling; the ordinary Hotelling's T ² test is a special case. Collinear responses are effectively handled by successive principal component decompositions, as when, for instance, the number of response variables exceeds the number of observations. In the univariate case, the test statistic pools the smallest effects as error. Independent sources for error degrees of freedom can be incorporated. The method is illustrated with examples from baguette and mayonnaise production.

KEY WORDS: Active factors, Experimental design, Monte Carlo testing, Multiple response, Subset selection, Unreplicated fractional factorials.