Relating Principal Component Analysis on Merged Data Sets to a Regression Approach

A method for calculating a consensus of several data matrices on the same samples using a PCA is based on a mathematical background. We propose a model to describe the data which might be obtained e. g. by means of a free choice profiling or a fixed vocabulary in a sensory profiling framework. A regression approach for this model leads to a Principal Component Analysis on Merged Data sets (PCAMD), which provides a simple method to calculate a consensus from the data. Since we use less restrictions on the variables under investigation, the model is claimed to be more general than the model induced by GPA respectively STATIS, which are widely accepted methods to analyse this kind of data. Furthermore, the PCAMD provides also additional opportunities to compare and interpret assessor performances with respect to the variables of the calculated consensus. An example from a sensory profiling study of cider is provided to illustrate these possibilities

Identifying assessor differences in weighting the underlying sensory dimensions

In a previous paper Kunert and Qannari (1999) discussed a simple alternative to Generalized Procrustes Analysis to analyze data derived from a sensory profiling study. After simple pretreatments of the individual data matrices, they propose to merge the data sets together and undergo Principal Components Analysis of the matrix thus formed. On the basis of two data sets, it was shown that the results slightly differ from those obtained by means of Generalized Procrustes Analysis. In this paper we give a mathematical justification to this approach by relating it to a statistical regression model. Furthermore, we obtain additional information from this method concerning the dimensions used by the assessors as well as the contribution of each assessor to the determination of these dimensions. This information may be useful to characterize the performance of the assessors and single out those assessors who downweight or overweight some dimensions. In particular, those assessors who overweight the last dimensions should arouse suspicion regarding their performance as, in general, the last dimensions in a principal components analysis are deemed to reflect random fluctuations

A simple alternative to generalized procrustes analysis

A statistical method for analysing sensory profiling data obtained by means of fixed vocabulary or free choice profiling is discussed. The most interesting feature of this method is that it involves only simple statistical treatment and can therefore be performed using standard software packages. The outcomes of this method are compared to those of Generalized Procrustes Analysis on the basis of two data sets obtained respectively by means of fixed vocabulary and free choice profiling. A significance test is also discussed in order to assess whether the overall configuration of the products is meaningful. This significance test is based upon a simulation study involving the permutation procedure

Biased power regression: a new biased estimation procedure in linear regression

In order to circumvent the effects of multicollinearity on the quality of a multiple linear regression, a new strategy of analysis is proposed. It is based on a biased estimation of the vector of coefficients. Properties of this approach of analysis are shown. Moreover, the link between this new strategy of analysis and existing strategies are discussed, particularly Ridge and Generalized Ridge regression. Illustrations on the basis of two datasets are also outlined and the outcomes are compared to those of Ridge regression

Understanding aroma release from model cheeses by a statistical multiblock approach on oral processing

For human beings, the mouth is the first organ to perceive food and the different signalling events associated to food breakdown. These events are very complex and as such, their description necessitates combining different data sets. This study proposed an integrated approach to understand the relative contribution of main food oral processing events involved in aroma release during cheese consumption. In vivo aroma release was monitored on forty eight subjects who were asked to eat four different model cheeses varying in fat content and firmness and flavoured with ethyl propanoate and nonan-2-one. A multiblock partial least square regression was performed to explain aroma release from the different physiological data sets ( masticatory behaviour, bolus rheology, saliva composition and flux, mouth coating and bolus moistening). This statistical approach was relevant to point out that aroma release was mostly explained by masticatory behaviour whatever the cheese and the aroma, with a specific influence of mean amplitude on aroma release after swallowing. Aroma release from the firmer cheeses was explained mainly by bolus rheology. The persistence of hydrophobic compounds in the breath was mainly explained by bolus spreadability, in close relation with bolus moistening. Resting saliva poorly contributed to the analysis whereas the composition of stimulated saliva was negatively correlated with aroma release and mostly for soft cheeses, when significant

Gait characterization in golden retriever muscular dystrophy dogs using linear discriminant analysis

Background: Accelerometric analysis of gait abnormalities in golden retriever muscular dystrophy (GRMD) dogs isof limited sensitivity, and produces highly complex data. The use of discriminant analysis may enable simpler andmore sensitive evaluation of treatment benefits in this important preclinical model.Methods: Accelerometry was performed twice monthly between the ages of 2 and 12 months on 8 healthy and20 GRMD dogs. Seven accelerometric parameters were analysed using linear discriminant analysis (LDA). Manipulationof the dependent and independent variables produced three distinct models. The ability of each model to detect gaitalterations and their pattern change with age was tested using a leave-one-out cross-validation approach.Results: Selecting genotype (healthy or GRMD) as the dependent variable resulted in a model (Model 1) allowing agood discrimination between the gait phenotype of GRMD and healthy dogs. However, this model was not sufficientlyrepresentative of the disease progression. In Model 2, age in months was added as a supplementary dependentvariable (GRMD_2 to GRMD_12 and Healthy_2 to Healthy_9.5), resulting in a high overall misclassification rate (83.2%).To improve accuracy, a third model (Model 3) was created in which age was also included as an explanatory variable.This resulted in an overall misclassification rate lower than 12%. Model 3 was evaluated using blinded data pertainingto 81 healthy and GRMD dogs. In all but one case, the model correctly matched gait phenotype to the actualgenotype. Finally, we used Model 3 to reanalyse data from a previous study regarding the effects ofimmunosuppressive treatments on muscular dystrophy in GRMD dogs. Our model identified significant effect ofimmunosuppressive treatments on gait quality, corroborating the original findings, with the added advantages ofdirect statistical analysis with greater sensitivity and more comprehensible data representation.Conclusions: Gait analysis using LDA allows for improved analysis of accelerometry data by applying adecision-making analysis approach to the evaluation of preclinical treatment benefits in GRMD dogs

A simple alternative to Generalized Procrustes Analysis. Application to sensory profiling data

A statistical method for analysing sensory profiling data obtained by means of fixed vocabulary or free choice profiling is discussed. The most interesting feature of this method is that it involves only simple statistical treatment and can therefore be performed using standard software packages. The outcomes of this method are compared to those of Generalized Procrustes Analysis on the basis of two data sets obtained respectively by means of fixed vocabulary and free choice profiling. A significance test is also discussed in order to assess whether the overall configuration of the products is meaningful. This significance test is based upon a simulation study involving the permutation procedure. Keywords : Sensory profiling, Principal Components Analysis, Generalized Procrustes Analysis, Isotropic scaling factors, Permutation test. 3 Introduction Generalized Procrustes Analysis (GPA) was introduced and popularized by Gower (1975). It is used for the analysis of sensory profiling da..

A continuum standardization of the variables. Application to principal components analysis and PLS-regression

International audienceA continuum standardization of the variables is proposed. It consists of dividing each variable by its standard deviation to the power α, where α is a scalar between 0 and 1. The non-standardized dataset and the standardized datasets appear as the two extreme points of this continuum and the Pareto standardization is its mid-point. Properties related to this standardization are discussed. Application to principal components analysis and PLS-regression is outlined and illustrated on the basis of real datasets