Package MExPosition. R topics documented: February 19, Type Package Title Multi-table ExPosition Version 2.0.

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1 Type Package Title Multi-table ExPosition Version Date Package MExPosition February 19, 2015 Author Cherise R. Chin Fatt, Derek Beaton, Herve Abdi. Maintainer Cherise R. Chin Fatt MExPosition is for descriptive (i.e., fixed-effects) multi-table multivariate analysis the singular value decomposition. License GPL-2 Depends prettygraphs (>= 2.0.0), ExPosition (>= 2.0.0) NeedsCompilation no Repository CRAN Date/Publication :39:41 R topics documented: MExPosition-package mpanisostatis mpanisostatis.core mpcanostatis mpcanostatis.core mpcovstatis mpcovstatis.core mpdistatis mpdistatis.core mpdoact.statis mpdoact.statis.core mpgraphs mpkplus1statis mpkplus1statis.core mpmahalanobis

2 2 R topics documented: mpmfa mpmultitable mppta mppta.core mpstatis mpstatis.columnpreproc mpstatis.core mpstatis.optimize mpstatis.preprocess mpstatis.rowpreproc mpstatis.tablepreproc mpsumpca mptablecheck print.covstatis.compromise print.covstatis.innerproduct print.covstatis.overview print.covstatis.table print.distatis.compromise print.distatis.innerproduct print.distatis.overview print.distatis.table print.doact.statis.compromise print.doact.statis.innerproduct print.doact.statis.overview print.doact.statis.table print.kplus1.statis.compromise print.kplus1.statis.innerproduct print.kplus1.statis.overview print.kplus1.statis.table print.mexposition.output print.mpanisostatis print.mpcovstatis print.mpdistatis print.mpdoact.statis print.mpgraphs print.mpkplus1statis print.mpmfa print.mpstatis print.statis.compromise print.statis.innerproduct print.statis.overview print.statis.table Index 77

3 MExPosition-package 3 MExPosition-package Multi-table Exploratory Analysis with the Singular Value DecomPosition with the STATIS family. Details MExPosition is multi-table ExPosition and includes the family of STATIS method, such as Plain STATIS, DISTATIS, Dual STATIS and ANISOSTATIS. The core of MExPosition is ExPosition and the svd. Package: MExPosition Type: Package Version: Date: Depends: R (>=2.15.0), prettygraphs (>= 2.0.0), ExPosition (>= 2.0.0) License: GPL-2 Questions, comments, compliments, and complaints go to Cherise R. Chin Fatt <cherise.chinfatt@utdallas.edu>. The following people are contributors to MExPosition code, data, or examples: Derek Beaton and Hervé Abdi. References Abdi, H., Valentin, D., Chollet, S., & Chrea, C. (2007). Analyzing assessors and products in sorting tasks: DISTATIS, theory and applications. Food Quality and Preference, 18, Abdi, H., & Valentin, D. (2005). DISTATIS: the analysis of multiple distance matrices. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. pp Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4. Abdi, H., & Valentin, D. (2007). STATIS. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Sage. pp

4 4 mpanisostatis See Also mpstatis, mpdistatis Examples #For more examples, see each individual function (as noted above). mpanisostatis mpanisostatis.core: ANISOSTATIS via MExPositio All ANISOSTATIS steps are combined in this function. It enables preparation of the data, processing and graphing. mpanisostatis(data, anisostatis.option = ANISOSTATIS_Type1, column.design, make.columndesign.nominal = TRUE, DESIGN =NULL, make.design.nominal = TRUE, graphs = TRUE) data Data Matrix anisostatis.option ANISOSTATIS string ptions: ANISOSTATIS_Type1 or ANISOSTATIS_Type2 column.design Matrix used to identify tables of data matrix make.columndesign.nominal a boolean. If TRUE (default), table is a vector that indicates groups (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. DESIGN a design matrix to indicate if rows belong to groups. make.design.nominal Boolean option. If TRUE (default), table is a vector that indicates groups (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. graphs Boolean option. If TRUE (default), graphs are displayed Details mpanisostatis computes Anisotropic STATIS, where the one weight is assigned per variable.

5 mpanisostatis 5 Value Returns a large list of items which are divided into four categories: $Overview $InnerProduct $Compromise $Table Overview of Results Results for the Inner Product Results for the Compromise Results for the Tables The results for Overview are bundled inside of $Overview. $Overview$data Data Matrix $Overview$groupmatrix Matrix used to identify the different tables of the data matrix $Overview$preprocess.data Preprocessed data matrix $Overview$num.groups Number of Tables $Overview$num.obs Number of Observations $Overview$row.preprocess Row Preprocess Option used $Overview$column.preprocess Column Preprocess Option used $Overview$Table.preprocess Table Preprocess Option used The results for InnerProduct are bundled inside of $InnerProduct $InnerProduct$S Inner Product: Scalar Product Matrices $InnerProduct$C Inner Product: C Matrix $InnerProduct$RVMatrix Inner Product: RV Matrix $InnerProduct$eigs.vector Inner Product: Eigen Vectors $InnerProduct$eigs Inner Product: Eigen Values $InnerProduct$fi Inner Product: Factor Scores $InnerProduct$t Inner Product: Percent Variance Explained $InnerProduct$ci Inner Product: Contribution of the Rows $InnerProduct$cj Inner Product: Contribution of the Columns

6 6 mpanisostatis $InnerProduct$alphaWeights Alpha Weights The results for the Compromise are bundled inside of $Compromise compromise Compromise Matrix compromise.eigs Compromise: Eigen Values compromise.eigs.vector Compromise: Eigen Vector compromise.fi Compromise.t compromise.ci compromise.cj Compromise: Factor Scores Compromise: Percent Variance Explained Compromise: Contributions of the rows Compromise: Contributions of the Columns The results for the Tables are bundled inside of $Table. $m Table: masses $Table$eigs Table: Eigen Values $Table$eigs.vector Table: Eigen Vectors $Table$Q Table: Loadings $Table$fi Table: Factor Scores $Table$partial.fi Table: Partial Factor Scores $Table$partial.fi.array Table: Arrray of Partial Factor Scores Table$ci $Table$cj $Table$t Table: Contribition of the Rows Table: Contribution of the Columns Table: Percent Variance Explained Cherise R. Chin Fatt References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, Abdi, H., Valentin, D., Chollet, S., & Chrea, C. (2007). Analyzing assessors and products in sorting tasks: DISTATIS, theory and applications. Food Quality and Preference, 18, Abdi, H., & Valentin, D. (2005). DISTATIS: the analysis of multiple distance matrices. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. pp

7 mpanisostatis.core 7 See Also mpanisostatis.core Examples # ANOISTATIS Type 1 data( wines2012 ) data = wines2012$data column.design = wines2012$table row.design= c( NZ, NZ, NZ, NZ, FR, FR, FR, FR, CA, CA, CA, CA ) demo.anisostatis1 <- mpanisostatis(data,anisostatis.option= ANISOSTATIS_Type1, column.design = column.design) # ANISOSTATISType 2 data( wines2012 ) data = wines2012$data column.design = wines2012$table row.design = c( NZ, NZ, NZ, NZ, FR, FR, FR, FR, CA, CA, CA, CA ) demo.anisostatis2 <- mpanisostatis(data,anisostatis.option= ANISOSTATIS_Type2, column.design = column.design) mpanisostatis.core mpanisostatis.core: Core Function for ANISOSTATIS via MExPosition Performs the core of ANISOSTATIS on the data mpanisostatis.core(data, num.obs, column.design, num.groups, optimization.option= ANISOSTATIS_Type1 ) data Details num.obs column.design Matrix of preprocessed data Number of observations Table Matrix- used to identifty the tables of the data matrix num.groups Number of groups optimization.option String option of either ANISOSTATIS_Type1 (DEFAULT), or ANISOSTATIS_Type2 Computation of Anisotropic STATIS (ANISOSTATIS), where the one weight is assigned per variable.

8 8 mpanisostatis.core Value S RVMatrix C ci cj eigs eigs.vector eigenvalue fi tau alphaweights Inner Product: Scalar Product Matrices Inner Product: RV Matrix Inner Product: C Matrix Inner Product: Contribution of the rows of C Inner Product: Contribuition of the columns of C Inner Product: Eigen Values of C Inner Product: Eigen Vectors of S Inner Product: Eigen Value Inner Product: Factor Scores Inner Product: Percent Variance Explained Inner Product: Alpha Weights compromise Compromise Matrix compromise.eigs Compromise: Eigen Values compromise.eigs.vector Compromise: Eigen Vector compromise.fi Compromise: Factor Scores Compromise.tau Compromise: Percent Variance Explained compromise.ci compromise.cj masses Compromise: Contributions of the rows Compromise: Contributions of the Columns Table: masses table.eigs Table: Eigen Values table.eigs.vector Table: Eigen Vectors table.loadings Table: Loadings table.fi Table: Factor Scores table.partial.fi Table: Partial Factor Scores table.partial.fi.array Table: Array of Partial Factor Scores table.tau Table: Percent Variance Explained Cherise R. Chin Fatt and Hervé Abdi. References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4,

9 mpcanostatis 9 See Also mpdistatis, mpstatis, mpanisostatis mpcanostatis mpcanostatis: Canonical STATIS (CANOSTATIS) via MExPosition All CANOSTATIS steps are combined in this function. It enables preparation of the data, processing and graphing. mpcanostatis(data, column.design, row.design, normalization = MFA, row.preprocess = None, column.preprocess = Center_1Norm, table.preprocess = Sum_PCA, make.columndesign.nominal = TRUE, make.rowdesign.nominal = TRUE, DESIGN = NULL, make.design.nominal = TRUE, graphs = TRUE) data Details column.design row.design normalization Matrix of data Column Design- used to identifty the tables of the data matrix Row Design - used to identify the groups of the data matrix String option: None, MFA (default), or Sum_PCA row.preprocess String option: None (default), Profile, Hellinger, Center or Center_Hellinger column.preprocess String option: None, Center, 1Norm, Center_1Norm (default) or Z_Score table.preprocess String option: None, Num_Columns, Tucker, Sum_PCA (default), RV_Normalization or MFA_Normalization make.columndesign.nominal Boolean option. If TRUE (default), the matrix will be nominalized make.rowdesign.nominal Boolean option. If TRUE (default), the matrix will be nominalized DESIGN a design matrix to indicate if rows belong to groups. make.design.nominal Boolean option. If TRUE (default), table is a vector that indicates groups (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. graphs Boolean option. If TRUE (default), graphs are displayed Computation of Canonical STATIS (CANOOSTATIS), where the observations come from predefined groups and tables.

10 10 mpcanostatis Value Returns a large list of items which are divided into four categories: $Overview $InnerProduct $Compromise $Table Overview of Results Results for the Inner Product Results for the Compromise Results for the Tables The results for Overview are bundled inside of $Overview. $Overview$data Data Matrix $Overview$groupmatrix Matrix used to identify the different tables of the data matrix $Overview$row.design Matrix used to identify the groups of the data matrix $Overview$preprocess.data Preprocessed data matrix $Overview$num.groups Number of Tables $Overview$num.obs Number of Observations $Overview$row.preprocess Row Preprocess Option used $Overview$column.preprocess Column Preprocess Option used $Overview$Table.preprocess Table Preprocess Option used The results for InnerProduct are bundled inside of $InnerProduct mahalanobis Mahalanobis distance matrices $InnerProduct$S Inner Product: Scalar Product Matrices $InnerProduct$C Inner Product: C Matrix $InnerProduct$RVMatrix Inner Product: RV Matrix $InnerProduct$eigs.vector Inner Product: Eigen Vectors $InnerProduct$eigs Inner Product: Eigen Values $InnerProduct$fi Inner Product: Factor Scores $InnerProduct$t Inner Product: Percent Variance Explained $InnerProduct$ci Inner Product: Contribution of the Rows

11 mpcanostatis 11 $InnerProduct$cj Inner Product: Contribution of the Columns $InnerProduct$alphaWeights Alpha Weights The results for the Compromise are bundled inside of $Compromise $Compromise$compromise Compromise Matrix $Compromise$compromise.eigs Compromise: Eigen Values $Compromise$compromise.eigs.vector Compromise: Eigen Vector $Compromise$compromise.fi Compromise: Factor Scores $Compromise$compromise.t Compromise: Percent Variance Explained $Compromise$compromise.ci Compromise: Contributions of the rows $Compromise$compromise.cj Compromise: Contributions of the Columns The results for the Tables are bundled inside of $Table. $Table$m Table: masses $Table$eigs Table: Eigen Values $Table$eigs.vector Table: Eigen Vectors $Table$Q Table: Loadings $Table$fi Table: Factor Scores $Table$partial.fi Table: Partial Factor Scores $Table$partial.fi.array Table: Arrray of Partial Factor Scores $Table$ci $Table$cj $Table$t Table: Contribition of the Rows Table: Contribution of the Columns Table: Percent Variance Explained Cherise R. Chin Fatt and Hervé Abdi. References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4,

12 12 mpcanostatis.core See Also mpcanostatis.core, mpcanostatis Examples # CANOSTATIS data( wines2012 ) row.design = c( NZ, NZ, NZ, NZ, FR, FR, FR, FR, CA, CA, CA, CA ) column.design = wines2012$table demo.canostatis.2012 <- mpcanostatis(wines2012$data,column.design, row.design, DESIGN = row.design) mpcanostatis.core mpcanostatis.core: Core Function for Canonical STATIS (CANO- STATIS) via MExPosition Performs the core of CANOSTATIS on the given dataset mpcanostatis.core(data, num.obs = num.obs, column.design, row.design, num.groups = num.groups, normalization = MFA, masses = NULL) data num.obs column.design row.design num.groups normalization masses Matrix of preprocessed data Number of observations Column Design- used to identifty the tables of the data matrix Row Design - used to identify the groups of the data matrix Number of groups String option of either None, MFA (DEFAULT), or Sum_PCA Masses Details Computation of Canonical STATIS (CANOSTATIS), where the observations come from predefined groups and tables.

13 mpcanostatis.core 13 Value mahalanobis normalization column.design row.design S rvmatrix C ci cj eigs eigs.vector eigenvalue fi tau alphaweights Mahalanobis distance matrices Inner Product: Normalization option selected Column Design- used to identifty the tables of the data matrix Row Design - used to identify the groups of the data matrix Inner Product: Scalar Product Matrices Inner Product: RV Matrix Inner Product: C Matrix Inner Product: Contribution of the rows of C Inner Product: Contribuition of the columns of C Inner Product: Eigen Values of C Inner Product: Eigen Vectors of S Inner Product: Eigen Value Inner Product: Factor Scores Inner Product: Percent Variance Explained Inner Product: Alpha Weights compromise Compromise Matrix compromise.eigs Compromise: Eigen Values compromise.eigs.vector Compromise: Eigen Vector compromise.fi Compromise: Factor Scores Compromise.tau Compromise: Percent Variance Explained compromise.ci compromise.cj masses Compromise: Contributions of the rows Compromise: Contributions of the Columns Table: masses table.eigs Table: Eigen Values table.eigs.vector Table: Eigen Vectors table.q Table: Loadings table.fi Table: Factor Scores table.partial.fi Table: Partial Factor Scores table.partial.fi.array Table: Array of Partial Factor Scores table.tau Table: Percent Variance Explained Cherise R. Chin Fatt and Hervé Abdi.

14 14 mpcovstatis References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, See Also mpdistatis, mpstatis, mpcanostatis mpcovstatis mpcovstatis: Core Function for COVSTATIS via MExPosition All COVSTATIS steps are combined in this function. It enables preparation of the data, processing and graphing. mpcovstatis(data, normalization = None, masses = NULL, table = NULL, make.table.nominal = TRUE, DESIGN = NULL, make.design.nominal = TRUE, graphs = TRUE) data normalization masses table Matrix of preprocessed data String option of either None, MFA (DEFAULT), or Sum_PCA Masses Design Matrix - used to identifty the tables of the data matrix make.table.nominal a boolean. If TRUE (default), table is a vector that indicates tables (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. DESIGN a design matrix to indicate if rows belong to groups. make.design.nominal Boolean option. If TRUE (default), table is a vector that indicates groups (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. graphs Boolean option. If TRUE (default), graphs are displayed Details COVSTATIS is used to analysis covariance matrices. It is an extension of three-way multidimensional scaling.

15 mpcovstatis 15 Value Returns a large list of items which are divided into four categories: $Overview $InnerProduct $Compromise $Table Overview of Results Results for the Inner Product Results for the Compromise Results for the Tables The results for Overview are bundled inside of $Overview. $Overview$data Data Matrix $Overview$normalization Type of normalization used $Overview$table Matrix used to identify the different tables of the data matrix $Overview$num.groups Number of Tables The results for InnerProduct are bundled inside of $InnerProduct $InnerProduct$S Inner Product: Scalar Product Matrices $InnerProduct$C Inner Product: C Matrix $InnerProduct$rvMatrix Inner Product: RV Matrix $InnerProduct$eigs.vector Inner Product: Eigen Vectors $InnerProduct$eigs Inner Product: Eigen Values $InnerProduct$fi Inner Product: Factor Scores $InnerProduct$t Inner Product: Percent Variance Explained $InnerProduct$ci Inner Product: Contribution of the Rows $InnerProduct$cj Inner Product: Contribution of the Columns $InnerProduct$alphaWeights Alpha Weights The results for the Compromise are bundled inside of $Compromise compromise Compromise Matrix compromise.eigs Compromise: Eigen Values compromise.eigs.vector Compromise: Eigen Vector

16 16 mpcovstatis compromise.fi Compromise.t compromise.ci compromise.cj Compromise: Factor Scores Compromise: Percent Variance Explained Compromise: Contributions of the rows Compromise: Contributions of the Columns The results for the Tables are bundled inside of $Table. $m Table: masses $Table$eigs Table: Eigen Values $Table$eigs.vector Table: Eigen Vectors $Table$Q Table: Loadings $Table$fi Table: Factor Scores $Table$partial.fi Table: Partial Factor Scores $Table$partial.fi.array Table: Arrray of Partial Factor Scores Table$ci $Table$cj $Table$t Table: Contribition of the Rows Table: Contribution of the Columns Table: Percent Variance Explained Cherise R. Chin Fatt and Hervé Abdi. References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, See Also mpcanostatis Examples #COVSTATIS data( faces2005 ) table = c( pixel, pixel, pixel, pixel, pixel, pixel, distance, distance, distance, distance, distance, distance, ratings, ratings, ratings, ratings, ratings, ratings, similarity, similarity, similarity, similarity, similarity, similarity ) demo.covstatis.2005 <- mpcovstatis(faces2005$data, table = table)

17 mpcovstatis.core 17 mpcovstatis.core mpcovstatis.core: Core Function for COVSTATIS via MExPosition Performs the core of CANOSTATIS on the given dataset mpcovstatis.core(data, normalization = None, masses = NULL, table = NULL, make.table.nominal = TRUE) data Details Value normalization masses Matrix of preprocessed data String option of either None, MFA (DEFAULT), or Sum_PCA Masses table Design Matrix - used to identifty the tables of the data matrix make.table.nominal a boolean. If TRUE (default), table is a vector that indicates tables (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. COVSTATIS is used to analysis covariance matrices. It is an extension of three-way multidimensional scaling. data normalization table S rvmatrix C ci cj eigs eigs.vector eigenvalue fi tau Data matrix Inner Product: Normalization option selected Design matrix used to identifty the tables of the data matrix Inner Product: Scalar Product Matrices Inner Product: RV Matrix Inner Product: C Matrix Inner Product: Contribution of the rows of C Inner Product: Contribuition of the columns of C Inner Product: Eigen Values of C Inner Product: Eigen Vectors of S Inner Product: Eigen Value Inner Product: Factor Scores Inner Product: Percent Variance Explained

18 18 mpcovstatis.core alphaweights Inner Product: Alpha Weights compromise Compromise Matrix compromise.eigs Compromise: Eigen Values compromise.eigs.vector Compromise: Eigen Vector compromise.fi Compromise: Factor Scores Compromise.tau Compromise: Percent Variance Explained compromise.ci compromise.cj masses Compromise: Contributions of the rows Compromise: Contributions of the Columns Table: masses table.eigs Table: Eigen Values table.eigs.vector Table: Eigen Vectors table.q Table: Loadings table.fi Table: Factor Scores table.partial.fi Table: Partial Factor Scores table.partial.fi.array Table: Array of Partial Factor Scores table.tau Table: Percent Variance Explained Cherise R. Chin Fatt and Hervé Abdi. References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, See Also mpcanostatis

19 mpdistatis 19 mpdistatis mpdistatis: DISTATIS via MExPosition All DISTATIS steps are combined in this function. It enables preparation of the data, processing and graphing. mpdistatis(data, sorting = No, normalization = None, masses = NULL, table=null, make.table.nominal = TRUE, DESIGN = NULL, make.design.nominal = TRUE, graphs = TRUE) data Details Value sorting normalization Data Matrix a boolean. If YES, DISTATIS will by processed as a sorting task. Default is NO Normaliztion string option: None (default), Sum_PCA, or MFA table Table which identifies the different tables. make.table.nominal a boolean. If TRUE (default), table is a vector that indicates groups (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. masses graphs Masses: if NULL, 1/num.obs would be set by default. For customized masses, enter the matrix of customized masses a boolean. If TRUE (default), graphs are displayed DESIGN a design matrix to indicate if rows belong to groups. make.design.nominal a boolean. If TRUE (default), DESIGN is a vector that indicates groups (and will be dummy-coded). If FALSE, DESIGN is a dummy-coded matrix. mpdistatis performs DISTATIS on a set of data matrices measured on the same set of observations. Returns a large list of items which are divided into three categories: $Overview $InnerProduct $Compromise $Table Overview of Results Results for the Inner Product Results for the Compromise Results for the Tables The results for Overview are bundled inside of $Overview.

20 20 mpdistatis $Overview$data Data Matrix $Overview$normalization Type of Normalization used. $Overview$sorting Indicates if the task is a sorting task $Overview$table Table which indicates the tables $num.groups Number of groups The results for InnerProduct are bundled inside of $InnerProduct $InnerProduct$S Inner Product: Scalar Product Matrices $norm.s Normalized Scalar Product Matrices $InnerProduct$C Inner Product: C Matrix $InnerProduct$eigs.vector Inner Product: Eigen Vectors $InnerProduct$eigs Inner Product: Eigen Values $InnerProduct$fi Inner Product: Factor Scores $InnerProduct$t Inner Product: Percent Variance Explained (tau) $InnerProduct$alphaWeights Alpha Weights The results for the Compromise are bundled inside of $Compromise $Compromise$compromise Compromise Matrix $Compromise$compromise.eigs Compromise: Eigen Values $Compromise$compromise.eigs.vector Compromise: Eigen Vector $Compromise$compromise.fi Compromise: Factor Scores $Compromise$compromise.t Compromise: Percent Variance Explained $Compromise$compromise.ci Compromise: Contributions of the rows $Compromise$compromise.cj Compromise: Contributions of the Columns The results for the Tables are bundled inside of $Table. $Table$m $Table$eigs Table: Masses Table: Eigen Values

21 mpdistatis 21 $Table$eigs.vector Table: Eigen Vectors $Table$Q Table: Loadings $Table$fi Table: Factor Scores $Table$partial.fi Table: Partial Factor Scores $Table$partial.fi.array Table: Array of Partial Factor Scores $Table$cj $Table$cj $Table$t Table:Contribution for the rows Table: Contribution for the columns Table:Percent Variance Explained Cherise R. Chin Fatt References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, Abdi, H., Valentin, D., Chollet, S., & Chrea, C. (2007). Analyzing assessors and products in sorting tasks: DISTATIS, theory and applications. Food Quality and Preference, 18, Abdi, H., & Valentin, D. (2005). DISTATIS: the analysis of multiple distance matrices. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. pp See Also mpstatis Examples data( faces2005 ) table = c( pixel, pixel, pixel, pixel, pixel, pixel, distance, distance, distance, distance, distance, distance, ratings, ratings, ratings, ratings, ratings, ratings, similarity, similarity, similarity, similarity, similarity, similarity ) face.data <- faces2005$data demo.distatis <- mpdistatis(face.data, sorting = No, normalization = MFA, table = table)

22 22 mpdistatis.core mpdistatis.core mpdistatis.core mpdistatis.core performs the core functions of DISTATIS. mpdistatis.core(data, table, sorting = No, normalization = None, masses = NULL, make.table.nominal=true) data Details Value table sorting normalization Matrix of preprocessed data Table which identifies the different tables. a boolean. If YES, DISTATIS will by processed as a sorting task. Default is NO Normaliztion string option: None (default), Sum_PCA, or MFA masses Masses: if NULL, 1/num.obs would be set by default. For customized masses, enter the vector of customized masses make.table.nominal a boolean. If TRUE (default), table is a vector that indicates groups (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. This function should not be used directly. Please use mpdistatis Returns a large list of items which are also returned in mpdistatis. data table normalization sorting S C ci cj eigs.vector eigs fi Data Matrix Design Matrix Type of Normalization used. Indicates if the task is a sorting task Inner Product: Scalar Product Matrices Inner Product: C Matrix Inner Product: Contribution of the rows of C Inner Product: Contribuition of the columns of C Inner Product: Eigen Vectors Inner Product: Eigen Values Inner Product: Factor Scores

23 mpdistatis.core 23 tau alphaweights Inner Product: Percent Variance Explained Alpha Weights compromise Compromise Matrix compromise.eigs Compromise: Eigen Values compromise.eigs.vector Compromise: Eigen Vector compromise.fi Compromise: Factor Scores Compromise.tau Compromise: Percent Variance Explained compromise.ci compromise.cj masses Compromise: Contributions of the rows Compromise: Contributions of the Columns Table: masses table.eigs Table: Eigen Values table.eigs.vector Table: Eigen Vectors table.q Table: Loadings table.fi Table: Factor Scores table.partial.fi Table: Partial Factor Scores table.partial.fi.array Table: Array of Partial Factor Scores table.tau Table: Percent Variance Explained Cherise R. Chin Fatt and Hervé Abdi. References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, Abdi, H., Valentin, D., Chollet, S., & Chrea, C. (2007). Analyzing assessors and products in sorting tasks: DISTATIS, theory and applications. Food Quality and Preference, 18, Abdi, H., & Valentin, D. (2005). DISTATIS: the analysis of multiple distance matrices. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. pp See Also mpstatis, mpstatis.core, mpdistatis

24 24 mpdoact.statis mpdoact.statis mpdoact.statis: Function for Dual STATIS (DO-ACT) via MExPosition All DO-ACT steps are combined in this function. It enables preparation of the data, processing and graphing. mpdoact.statis(data1, column.design.1, make.columndesign.1.nominal = TRUE, data2, column.design.2, make.columndesign.2.nominal = TRUE, row.preprocess.data1 = None, column.preprocess.data1 = Center, table.preprocess.data1 = Sum_PCA, row.preprocess.data2 = None, column.preprocess.data2 = Center, table.preprocess.data2 = Sum_PCA, DESIGN = NULL, make.design.nominal = TRUE, graphs = TRUE) data1 Matrix of dataset 1 column.design.1 Column Design for dataset 1 - used to identifty the tables of the data matrix make.columndesign.1.nominal Boolean option. If TRUE (default), the matrix will be nominalized data2 Matrix of dataset 2 column.design.2 Column Design for dataset 2 - used to identifty the tables of the data matrix make.columndesign.2.nominal Boolean option. If TRUE (default), the matrix will be nominalized row.preprocess.data1 String option: None (default), Profile, Hellinger, Center or Center_Hellinger column.preprocess.data1 String option: None, Center, 1Norm, Center_1Norm (default) or Z_Score table.preprocess.data1 String option: None, Num_Columns, Tucker, Sum_PCA (default), RV_Normalization or MFA_Normalization row.preprocess.data2 String option: None (default), Profile, Hellinger, Center or Center_Hellinger column.preprocess.data2 String option: None, Center, 1Norm, Center_1Norm (default) or Z_Score table.preprocess.data2 String option: None, Num_Columns, Tucker, Sum_PCA (default), RV_Normalization or MFA_Normalization

25 mpdoact.statis 25 Details Value DESIGN a design matrix to indicate if rows belong to groups. make.design.nominal Boolean option. If TRUE (default), table is a vector that indicates groups (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. graphs Boolean option. If TRUE (default), graphs are displayed Computation of DualSTATIS (DOSTATIS). Returns a large list of items which are divided into four categories: $Overview $InnerProduct $Compromise $Table Overview of Results Results for the Inner Product Results for the Compromise Results for the Tables The results for Overview are bundled inside of $Overview. $Overview$data1 Data Matrix for dataset 1 $Overview$column.design.1 Column Design for dataset1 $Overview$row.preprocess.data1 Row Preprocess Option used for dataset1 $Overview$column.preprocess.data1 Column Preprocess Option used for dataset1 $Overview$Table.preprocess.data1 Table Preprocess Option used for dataset1 $Overview$num.groups.1 Number of Groups in dataset1 $Overview$data2 Data Matrix for dataset 2 $Overview$column.design.2 Column Design for dataset2 $Overview$row.preprocess.data2 Row Preprocess Option used for dataset2 $Overview$column.preprocess.data2 Column Preprocess Option used for dataset2 $Overview$Table.preprocess.data2 Table Preprocess Option used for dataset2 $Overview$num.groups.2 Number of Groups in dataset 2 The results for InnerProduct are bundled inside of $InnerProduct

26 26 mpdoact.statis $InnerProduct$S.1 Inner Product: Scalar Product Matrices for dataset 1 $InnerProduct$S.2 Inner Product: Scalar Product Matrices for dataset 2 $InnerProduct$C Inner Product: C Matrix $InnerProduct$RVMatrix Inner Product: RV Matrix $InnerProduct$eigs.vector Inner Product: Eigen Vectors $InnerProduct$eigs Inner Product: Eigen Values $InnerProduct$fi Inner Product: Factor Scores $InnerProduct$t Inner Product: Percent Variance Explained $InnerProduct$ci Inner Product: Contribution of the Rows $InnerProduct$cj Inner Product: Contribution of the Columns $InnerProduct$alphaWeights Inner Product: Alpha Weights $InnerProduct$betaWeights Inner Product: Beta Weights The results for the Compromise are bundled inside of $Compromise $Compromise$compromiseMatrix.1 Compromise Matrix for dataset 1 $Compromise$compromise.eigs.1 Compromise: Eigen Values for dataset 1 $Compromise$compromise.eigs.vector.1 Compromise: Eigen Vector for dataset 1 $Compromise$compromise.fi.1 Compromise: Factor Scores for dataset 1 $Compromise$compromise.t.1 Compromise: Percent Variance Explained for dataset 1 $Compromise$compromise.ci.1 Compromise: Contributions of the rows for dataset 1 $Compromise$compromise.cj.1 Compromise: Contributions of the Columns for dataset 1 $Compromise$compromiseMatrix.2 Compromise Matrix for dataset 2 $Compromise$compromise.eigs.2 Compromise: Eigen Values for dataset 2 $Compromise$compromise.eigs.vector.2 Compromise: Eigen Vector for dataset 2

27 mpdoact.statis 27 $Compromise$compromise.fi.2 Compromise: Factor Scores for dataset 2 $Compromise$compromise.t.2 Compromise: Percent Variance Explained for dataset 2 $Compromise$compromise.ci.2 Compromise: Contributions of the rows for dataset 2 $Compromise$compromise.cj.2 Compromise: Contributions of the Columns for dataset 2 The results for the Tables are bundled inside of $Table. $Table$m.1 Table: masses for dataset 1 $Table$eigs.1 Table: Eigen Values for dataset 1 $Table$eigs.vector.1 Table: Eigen Vectors for dataset 1 $Table$Q.1 Table: Loadings for dataset 1 $Table$fi.1 Table: Factor Scores for dataset 1 $Table$partial.fi.1 Table: Partial Factor Scores for dataset 1 $Table$partial.fi.array.1 Table: Arrray of Partial Factor Scores for dataset 1 $Table$ci.1 Table: Contribition of the Rows for dataset 1 $Table$cj.1 Table: Contribution of the Columns for dataset 1 $Table$t.1 Table: Percent Variance Explained for dataset 1 $Table$m.2 Table: masses for dataset 2 $Table$eigs.2 Table: Eigen Values for dataset 2 $Table$eigs.vector.2 Table: Eigen Vectors for dataset 2 $Table$Q.2 Table: Loadings for dataset 2 $Table$fi.2 Table: Factor Scores for dataset 2 $Table$partial.fi.2 Table: Partial Factor Scores for dataset 2 $Table$partial.fi.array.2 Table: Arrray of Partial Factor Scores for dataset 2 $Table$ci.2 Table: Contribition of the Rows for dataset 2 $Table$cj.2 Table: Contribution of the Columns for dataset 2 $Table$t.2 Table: Percent Variance Explained for dataset 2 Cherise R. Chin Fatt and Hervé Abdi.

28 28 mpdoact.statis.core References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, See Also mpstatis, mpdoact.statis Examples #DO-ACT data( wines2012 ) design=c( NZ, NZ, NZ, NZ, FR, FR, FR, FR, CA, CA, CA, CA ) data1 <- wines2012$data data2 <- wines2012$data design.1 <- wines2012$table design.2 <- wines2012$table demo.double <- mpdoact.statis(data1=data1,column.design.1=design.1, data2=data2, column.design.2=design.2, DESIGN=design) mpdoact.statis.core mpdoact.statis.core: Core Function for Dual STATIS (DO-ACT) via MExPosition Performs the core of Dual STATIS on two given dataset mpdoact.statis.core(dataset1, column.design.1, dataset2, column.design.2) Details dataset1 Matrix of dataset 1 column.design.1 Column Design for dataset 1 - used to identifty the tables of the data matrix dataset2 Matrix of dataset 2 column.design.2 Column Design for dataset 2 - used to identifty the tables of the data matrix Computation of DualSTATIS (DOSTATIS). This function should not be used independently. It should be used with mpdoact.statis

29 mpdoact.statis.core 29 Value S.1 Inner Product: Scalar Product Matrices of dataset1 S.2 Inner Product: Scalar Product Matrices of dataset2 C ci cj eigs eigs.vector eigenvalue fi tau alphaweights Inner Product: C Matrix Inner Product: Contribution of the rows of C Inner Product: Contribuition of the columns of C Inner Product: Eigen Values of C Inner Product: Eigen Vectors of S Inner Product: Eigen Value Inner Product: Factor Scores Inner Product: Percent Variance Explained Inner Product: Alpha Weights betaweights Inner Product: Beta Weights compromisematrix.1 Compromise Matrix for dataset 1 compromise.eigs.1 Compromise: Eigen Values for dataset 1 compromise.eigs.vector.1 Compromise: Eigen Vector for dataset 1 compromise.fi.1 Compromise: Factor Scores for dataset 1 Compromise.tau.1 Compromise: Percent Variance Explained for dataset 1 compromise.ci.1 Compromise: Contributions of the rows for dataset 1 compromise.cj.1 Compromise: Contributions of the Columns for dataset 1 compromisematrix.2 Compromise Matrix for dataset 2 compromise.eigs.2 Compromise: Eigen Values for dataset 2 compromise.eigs.vector.2 Compromise: Eigen Vector for dataset 2 compromise.fi.2 Compromise: Factor Scores for dataset 2 Compromise.tau.2 Compromise: Percent Variance Explained for dataset 2 compromise.ci.2 Compromise: Contributions of the rows for dataset 2 compromise.cj.2 Compromise: Contributions of the Columns for dataset 2

30 30 mpdoact.statis.core masses.1 Table: masses for dataset 1 table.eigs.1 Table: Eigen Values for dataset 1 table.eigs.vector.1 Table: Eigen Vectors for dataset 1 table.loadings.1 Table: Loadings for dataset 1 table.fi.1 Table: Factor Scores for dataset 1 table.partial.fi.1 Table: Partial Factor Scores for dataset 1 table.partial.fi.array.1 Table: Array of Partial Factor Scores for dataset 1 table.tau.1 Table: Percent Variance Explained for dataset 1 masses.2 Table: masses for dataset 2 table.eigs.2 Table: Eigen Values for dataset 2 table.eigs.vector.2 Table: Eigen Vectors for dataset 2 table.loadings.2 Table: Loadings for dataset 2 table.fi.2 Table: Factor Scores for dataset 2 table.partial.fi.2 Table: Partial Factor Scores for dataset 2 table.partial.fi.array.2 Table: Array of Partial Factor Scores for dataset 2 table.tau.2 Table: Percent Variance Explained for dataset 2 Cherise R. Chin Fatt and Hervé Abdi. References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, See Also mpstatis, mpdoact.statis

31 mpgraphs 31 mpgraphs mpgraphs: MExPosition plotting function MExPosition plotting function which is an interface to prettygraphs. mpgraphs(res, table, DESIGN = NULL, x_axis = 1, y_axis = 2, fi.col = NULL, fj.col = NULL, table.col = NULL, col.offset = NULL, constraints = NULL, xlab = NULL, ylab = NULL, main = NULL, graphs = TRUE) res table DESIGN x_axis y_axis fi.col fj.col table.col col.offset constraints xlab ylab main graphs results from MExPosition (i.e., $mexposition.data) results from mpgraphs (i.e., $Plotting.Data) Design Matrix which differentiates the tables which component should be on the x axis? which component should be on the y axis? Colors for the rows Colors for the columns Colors for the tables Color Offset Plotting Constraints x axis label y axis label main label for the graph window Boolean option. If TRUE (default), graphs will be plotted else, there will be graphical output Details mpgraphs is an interface between MExPosition and prettygraphs. Value The following items are bundled inside of $Plotting.Data: $fi.col $fj.col the colors that are associated to the groups. the colors that are associated to the column items.

32 32 mpkplus1statis Cherise R. Chin Fatt and Derek Beaton See Also prettygraphs mpkplus1statis mpkplus1statis: Function for (K+1) STATIS via MExPosition All (K+1) STATIS steps are combined in this function. It enables preparation of the data, processing and graphing. mpkplus1statis(data, plus1data, column.design, make.columndesign.nominal = TRUE, row.preprocess = None, column.preprocess = Center, table.preprocess = Sum_PCA, optimization.option = STATIS, DESIGN = NULL, make.design.nominal = TRUE, graphs = TRUE) data plus1data Data Matrix External table column.design Column Design for data - used to identifty the tables of the data matrix make.columndesign.nominal Boolean option. If TRUE (default), table is a vector that indicates groups (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. row.preprocess String option: None (default), Profile, Hellinger, Center or Center_Hellinger column.preprocess String option: None, Center (default), 1Norm, Center_1Norm or Z_Score table.preprocess String option: None, Num_Columns, Tucker, Sum_PCA (default), RV_Normalization or MFA_Normalization optimization.option String option of either None, Multiable, RV_Matrix, STATIS (DEFAULT), or STATIS_Power1 DESIGN a design matrix to indicate if rows belong to groups. make.design.nominal Boolean option. If TRUE (default), table is a vector that indicates groups (and will be dummy-coded). If FALSE, table is a dummy-coded matrix. graphs Boolean option. If TRUE (default), graphs are displayed

33 mpkplus1statis 33 Details Computation of (K+1) STATIS. Value Returns a large list of items which are divided into four categories: $Overview $InnerProduct $Compromise $Table Overview of Results Results for the Inner Product Results for the Compromise Results for the Tables The results for Overview are bundled inside of $Overview. $Overview$data Data Matrix $Overview$plus1data Preprocessed external table $Overview$column.design Column Design for dataset $Overview$row.preprocess Row Preprocess Option used $Overview$column.preprocess Column Preprocess Option used $Overview$Table.preprocess Table Preprocess Option used $Overview$num.groups Number of Groups in dataset The results for InnerProduct are bundled inside of $InnerProduct $InnerProduct$S Inner Product: Scalar Product Matrices of dataset $InnerProduct$S.star Inner Product: Scalar Product Matrices * of dataset $InnerProduct$rvMatrix.star Inner Product: RV Matrix * $InnerProduct$C Inner Product: C Matrix of S* $InnerProduct$ci Inner Product: Contribution of the rows of C* $InnerProduct$cj Inner Product: Contribuition of the columns of C* $InnerProduct$eigs Inner Product: Eigen Values of C* $InnerProduct$eigs.vector Inner Product: Eigen Vectors of C* $InnerProduct$eigs Inner Product: Eigen Value of C*

34 34 mpkplus1statis $InnerProduct$fi Inner Product: Factor Scores of C* $InnerProduct$t Inner Product: Percent Variance Explained of C* $InnerProduct$alphaWeights Inner Product: Alpha Weights * The results for the Compromise are bundled inside of $Compromise $Compromise$compromise Compromise Matrix $Compromise$compromise.eigs Compromise: Eigen Values $Compromise$compromise.eigs.vector Compromise: Eigen Vector $Compromise$compromise.fi Compromise: Factor Scores $Compromise$compromise.t Compromise: Percent Variance Explained $Compromise$compromise.ci Compromise: Contributions of the rows $Compromise$compromise.cj Compromise: Contributions of the Columns The results for the Tables are bundled inside of $Table. $Table$m Table: masses $Table$eigs Table: Eigen Values $Table$eigs.vector Table: Eigen Vectors $Table$Q Table: Loadings $Table$fi Table: Factor Scores $Table$partial.fi Table: Partial Factor Scores $Table$partial.fi.array Table: Arrray of Partial Factor Scores $Table$ci $Table$cj $Table$t Table: Contribition of the Rows Table: Contribution of the Columns Table: Percent Variance Explained Cherise R. Chin Fatt and Hervé Abdi. References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4,

35 mpkplus1statis.core 35 See Also mpkplus1statis, mpstatis Examples #(K+1) STATIS data( wines2012 ) data=wines2012$data chemical <- wines2012$supplementary design=c( NZ, NZ, NZ, NZ, FR, FR, FR, FR, CA, CA, CA, CA ) demo.plus1 <- mpkplus1statis(wines2012$data,chemical,wines2012$table) mpkplus1statis.core mpkplus1statis.core: Core Function for (K+1) STATIS via MExPosition Performs the core of (K+1) STATIS mpkplus1statis.core(data, plus1data, num.obs, column.design, num.groups, optimization.option = STATIS ) data plus1data num.obs column.design num.groups Matrix of preprocessed data Matrix of preprocessed external table Number of observations Column Design for data - used to identifty the tables of the data matrix Number of groups optimization.option String option of either None, Multiable, RV_Matrix, STATIS (DEFAULT), or STATIS_Power1 Details Computation of (K+1) STATIS. This function should not be used independently. It should be used with mpkplus1statis

36 36 mpkplus1statis.core Value S S.star Inner Product: Scalar Product Matrices of dataset Inner Product: Scalar Product Matrices * of dataset rvmatrix.star Inner Product: RV Matrix * C Inner Product: C Matrix of S* ci Inner Product: Contribution of the rows of C* cj Inner Product: Contribuition of the columns of C* eigs Inner Product: Eigen Values of C* eigs.vector Inner Product: Eigen Vectors of C* eigenvalue Inner Product: Eigen Value of C* fi Inner Product: Factor Scores of C* tau Inner Product: Percent Variance Explained of C* alphaweights Inner Product: Alpha Weights * compromise Compromise Matrix compromise.eigs Compromise: Eigen Values compromise.eigs.vector Compromise: Eigen Vector compromise.fi Compromise: Factor Scores Compromise.tau Compromise: Percent Variance Explained compromise.ci compromise.cj masses Compromise: Contributions of the rows Compromise: Contributions of the Columns Table: masses table.eigs Table: Eigen Values table.eigs.vector Table: Eigen Vectors table.loadings Table: Loadings table.fi Table: Factor Scores table.partial.fi Table: Partial Factor Scores table.partial.fi.array Table: Array of Partial Factor Scores table.tau Table: Percent Variance Explained Cherise R. Chin Fatt and Hervé Abdi. References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4,

37 mpmahalanobis 37 See Also mpkplus1statis, mpstatis mpmahalanobis mpmahalanobis: Mahalanobis Distance Computation of Mahalanobis Distance mpmahalanobis(data, row.design) data row.design Data Matrix Design Matrix which identifies the groups of the data matrix Details Computation of Mahalanobis Distance which is used in mpcanostatis. Value D Matrix of Mahalanobis Distances Cherise R. Chin Fatt and Hervé Abdi. References Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, See Also mpcanostatis Examples #Mahalanobis Example data( wines2012 ) data <- as.matrix(wines2012$data[,1:6]) design <- makenominaldata(as.matrix(c( NZ, NZ, NZ, NZ, FR, FR, FR, FR, CA, CA, CA, CA ))) demo <- mpmahalanobis(data,design)