Accepted Manuscript

Automated Mixed ANOVA Modelling of sensory and consumer data

Alexandra Kuznetsova, Rune H.B. Christensen, Cecile Bavay, Per Bruun

Brockhoff

PII: S0950-3293(14)00172-4

DOI: http://dx.doi.org/10.1016/j.foodqual.2014.08.004

Reference: FQAP 2830

To appear in: Food Quality and Preference

Received Date: 30 January 2014

Revised Date: 24 June 2014

Accepted Date: 15 August 2014

Please cite this article as: Kuznetsova, A., Christensen, R.H.B., Bavay, C., Brockhoff, P.B., Automated Mixed

ANOVA Modelling of sensory and consumer data, Food Quality and Preference (2014), doi: http://dx.doi.org/ 10.1016/j.foodqual.2014.08.004

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Automated Mixed ANOVA Modelling of sensory and1 consumer data2

Alexandra Kuznetsovaa,∗, Rune H.B. Christensena, Cecile Bavayb, Per3

Bruun Brockhoffa4 aDTU Compute, Statistical section, Technical University of Denmark, Richard Petersens5

Plads, Building 324, DK-2800 Kongens Lyngby, Denmark6 bGroupe ESA, UPSP GRAPPE 55, rue Rabelais BP30748, 49007 Angers, Cedex 01,7

France8

Abstract9

Mixed effects models have become increasingly prominent in sensory and con-10 sumer science. Still applying such models may be challenging for a sensory11 practitioner due the challenges associated with the choosing the random ef-12 fects, selecting an appropriate model, interpreting the results. In this paper13 we introduce an approach for automated mixed ANOVA/ANCOVA mod-14 elling together with the open source R package lmerTest developed by the15 authors that can perform automated complex mixed-effects modeling. The16 package can in an automated way investigate and incorporate the necessary17 random-effects by sequentially removing non-significant random terms in the18 mixed model, and similarly test and remove fixed effects. Tables and figures19 provide an overview of the structure and present post-hoc analysis. With20 this approach, complex error structures can be investigated, identified and21 incorporated whenever necessary. The package provides type-3 ANOVA out-22 put with degrees of freedom corrected F -tests for fixed-effects, which makes23 the package unique in open source implementations of mixed models. The24 approach together with the user-friendliness of the package allow to analyze25 a broad range of mixed effects models in a fast and efficient way. The bene-26 fits of the approach and the package are illustrated on four data sets coming27 from consumer/sensory studies.28

Keywords:29 mixed-effects models, automated model building, R program, conjoint,30 consumer preference, ANOVA31 ∗Corresponding author. E-mail address: alku@dtu.dk (A. Kuznetsova).

Preprint submitted to Elsevier August 21, 2014 1. Introduction32

Mixed models are used extensively for analysing sensory and consumer33 data. Sensory quantitative descriptive analysis (QDA) data are typically34 analysed attribute by attribute using analysis of variance (ANOVA) tech-35 niques to extract the important attribute-wise product difference information36 (Lawless & Heymann, 2010). The proper analysis will typically evaluate the37 statistical significance of product differences by using the assessor-by-product38 interaction as error structure (Lawless & Heymann, 2010). This is, what39 generally in statistics is called a mixed model as both fixed-effects (product40 differences) as random-effects (assessor differences and assessor-by-product41 interactions) are present in the modelling and analysis approach. Incorpo-42 rating random consumer effects for the analysis of e.g. consumer preference43 data or data from conjoint experiments is on one hand necessary to obtain the44 proper conclusions from such data and on the other hand similarly leads to45 mixed models. In the simplest of cases a mixed-effects model (mixed model)46 analysis can be handled by simple averaging combined with the use of the47 proper error term coming from a simple ANOVA decomposition of the data.48

Two often occurring examples of this situation are:49 1. Complete consumer preference data with just a single product factor,50 that is, just a collection of different products coded in a single variable51 (as opposed to a multifactorial setting), calling for a two-way (block)52

ANOVA, where the error term is simply the residual error.53 2. Complete sensory profile data similarly with just a single product fac-54 tor, calling for either a 2-way or 3-way ANOVA mixed model depend-55 ing on the presence of a blocking (replication) factor such as session56 or product batch. And hence calling for using either the panellist-by-57 product mean square as the error term or a combination of this with58 blocking-by-product (Næs et al., 2010a).59

These cases are exactly those covered by the open source software pack-60 age PanelCheck (Nofima Mat, 2008). However, these simple approaches of61 analysis have their limitations. With missing values or with more complex62 study designs one would often benefit from a more detailed analysis. The63

PanelCheck tool can still be a valuable tool in that using missing values im-64 putation and considering all products together it will in most cases be able65 to provide some relevant ANOVA information for the situation at hand, and66 by the way the by-attribute ANOVA is only a small part of what PanelCheck67 2 has to offer. The more detailed univariate analysis of variance provided in68 this paper becomes relevant in the sensory context in the following example69 list of situations:70 • Unbalanced sensory profile data (for example due to missing observa-71 tions).72 • Incomplete consumer preference data.73 • 2-(or higher) way product structure in sensory profile data. (Beck et al.,74 2014)75 • 2-(or higher) way product structure in consumer preference data (Con-76 joint) (Jaeger et al., 2013).77 • Extending Conjoint to include consumer background/design variables78 or factors/covariates79 • Complex blocking, product replication, product batch structures in as80 well sensory as consumer preference data.81 • Extending external preference mapping to include product and con-82 sumer background/design factors/covariates.83