stata multivariate statistics reference manual release 10

Title

intro Introduction to multivariate statistics manual

DescriptionThis entry describes this manual and what has changed since Stata 9.

RemarksThis manual documents Statas multivariate analysis features and is referred to as the [MV] manual

in cross-references.

Following this entry, [MV] multivariate provides an overview of the multivariate analysis featuresin Stata and Statas multivariate analysis commands. The other parts of this manual are arrangedalphabetically.

Stata is continually being updated, and Stata users are always writing new commands. To find outabout the latest multivariate analysis features, type search multivariate analysis after installingthe latest official updates; see [R] update.

Whats new

This section is intended for previous Stata users. If you are new to Stata, you may as well skip it.

1. New estimation commands discrim and candisc provide several discriminant analysis techniques,including linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), logistic discrim-inant analysis, and kth-nearest-neighbor (KNN) discrimination. See [MV] discrim, [MV] discrimestat, and [MV] candisc.

2. Existing estimation commands mds, mdslong, and mdsmat now provide modern as well as classicalmultidimensional scaling (MDS), including metric and nonmetric MDS. Available loss functionsinclude stress, normalized stress, squared stress, normalized squared stress, and Sammon. Availabletransformations include identity, power, and monotonic. mdslong also now allows aweights andfweights, and mdsmat has a weight() option. See [MV] mds, [MV] mdslong, and [MV] mdsmat.

3. New estimation command mca provides multiple correspondence analysis (MCA) and joint cor-respondence analysis (JCA); see [MV] mca and [MV] mca postestimation. You can use existingcommand screeplot afterward to graph principal inertias; see [MV] screeplot.

4. Concerning existing estimation command ca (correspondence analysis),

a. ca now allows crossed (stacked) variables. This provides a way to automatically combinetwo or more categorical variables into one crossed variable and perform correspondenceanalysis with it.

b. cas existing option normalize() now allows normalize(standard) to provide normal-ization of the coordinates by singular vectors divided by the square root of the mass.

c. cas new option length() allows you to customize the length of labels with crossed variablesin output.

d. New postestimation command estat loadings, used after ca and camat, displays corre-lations of profiles and axes.

1

2 intro Introduction to multivariate statistics manual

e. Existing postestimation command cabiplot has new option origin that displays the originwithin the plot. cabiplot also now accepts originlopts(line options) to customize theappearance of the origin on the graph.

f. Existing postestimation commands cabiplot and caprojection now allow row and columnmarker labels to be specified using the mlabel() suboption of rowopts() and colopts().

See [MV] ca and [MV] ca postestimation.

5. Existing commands cluster, matrix dissimilarity, and mds now allow the Gower measurefor a mix of binary and continuous data; see [MV] measure option.

6. Existing command biplot has new options. dim() specifies the dimensions to be displayed.negcol specifies that negative column (variable) arrows be plotted. negcolopts(col options)provides graph options for the negative column arrows. norow and nocolumn suppress the rowpoints or column arrows. See [MV] biplot.

7. New postestimation command estat rotate after canon performs orthogonal varimax rotationof the raw coefficients, standard coefficients, or canonical loadings. After estat rotate, newpostestimation command estat rotatecompare displays the rotated and unrotated coefficients orloadings and the most recently rotated coefficients or loadings. See [MV] canon postestimation.

8. Existing commands pcamat and factormat now allow singular correlation or covariance structures.New option forcepsd modifies a matrix to be positive semidefinite and thus to be a proper covariancematrix. See [MV] pca and [MV] factor.

9. Existing commands rotate and rotatemat now refer to Kaiser normalization rather thanHorst normalization. A search of the literature indicates that Kaiser normalization is the preferredterminology. Previously option horst was a synonym for normalize. Now option horst is notdocumented. See [MV] rotate and [MV] rotatemat.

10. Existing command procrustes now saves the number of y variables in scalar e(ny); see[MV] procrustes.

For a complete list of all the new features in Stata 10, see [U] 1.3 Whats new.

Also See[U] 1.3 Whats new

[R] intro Introduction to base reference manual

Title

multivariate Introduction to multivariate commands

DescriptionThe Multivariate Reference Manual organizes the commands alphabetically, which makes it easy

to find individual command entries if you know the name of the command. This overview organizesand presents the commands conceptually, that is, according to the similarities in the functions thatthey perform.

The commands listed under the heading Cluster analysis perform cluster analysis on variables or thesimilarity or dissimilarity values within a matrix. An introduction to cluster analysis and a descriptionof the cluster and clustermat subcommands is provided in [MV] cluster and [MV] clustermat.

The commands listed under the heading Discriminant analysis provide both descriptive andpredictive linear discriminant analysis (LDA), as well as predictive quadratic discriminant analysis (QDA),logistic discriminant analysis, and kth-nearest-neighbor (KNN) discriminant analysis. An introductionto discriminant analysis and the discrim command is provided in [MV] discrim.

The commands listed under the heading Factor analysis and principal component analysis providefactor analysis of a correlation matrix and principal component analysis (PCA) of a correlation orcovariance matrix. The correlation or covariance matrix can be provided directly or computed fromvariables.

The commands listed under the heading Rotation provide methods for rotating a factor or PCAsolution or for rotating a matrix. Also provided is Procrustean rotation analysis for rotating a set ofvariables to best match another set of variables.

The commands listed under Multivariate analysis of variance and related techniques providecanonical correlation analysis, multivariate regression, multivariate analysis of variance (MANOVA),and comparison of multivariate means.

The commands listed under Multidimensional scaling and biplots provide classic and modern(metric and nonmetric) MDS and two-dimensional biplots. MDS can be performed on the variables oron proximity data in a matrix or as proximity data in long format.

The commands listed under Correspondence analysis provide simple correspondence analysis(CA) on the cross-tabulation of two categorical variables or on a matrix and multiple correspondenceanalysis (MCA) and joint correspondence analysis (JCA) on two or more categorical variables.

Cluster analysis

cluster Introduction to cluster-analysis commandscluster (See [MV] cluster for details)clustermat Introduction to clustermat commandsmatrix dissimilarity Compute similarity or dissimilarity measures; may be used

by clustermat

3

4 multivariate Introduction to multivariate commands

Discriminant analysis

discrim Introduction to discriminant-analysis commandsdiscrim lda Linear discriminant analysis (LDA)candisc Canonical (descriptive) linear discriminant analysisdiscrim qda Quadratic discriminant analysis (QDA)discrim logistic Logistic discriminant analysisdiscrim knn kth-nearest-neighbor (KNN) discriminant analysisdiscrim estat Common postestimation tools for discrimdiscrim . . . postestimation Postestimation tools for discrim subcommands

Factor analysis and principal component analysis

factor Factor analysisfactor postestimation Postestimation tools for factor and factormatpca Principal component analysispca postestimation Postestimation tools for pca and pcamatrotate Orthogonal and oblique rotations after factor and pcascreeplot Scree plotscoreplot Score and loading plots

Rotation

rotate Orthogonal and oblique rotations after factor and pcarotatemat Orthogonal and oblique rotation of a Stata matrixprocrustes Procrustes transformationprocrustes postestimation Postestimation tools for procrustes

Multivariate analysis of variance and related techniques

canon Canonical correlationscanon postestimation Postestimation tools for canonmvreg See [R] mvreg Multivariate regressionmvreg postestimation See [R] mvreg postestimation Postestimation tools

for mvregmanova Multivariate analysis of variance and covariancemanova postestimation Postestimation tools for manovahotelling Hotellings T -squared generalized means test

Multidimensional scaling and biplots

mds Multidimensional scaling for two-way datamds postestimation Postestimation tools for mds, mdsmat, and mdslongmdslong Multidimensional scaling of proximity data in long formatmdsmat Multidimensional scaling of proximity data in a matrixbiplot Biplots

multivariate Introduction to multivariate commands 5

Correspondence analysis

ca Simple correspondence analysisca postestimation Postestimation tools for ca and camatmca Multiple and joint correspondence analysismca postestimation Postestimation tools for mca

RemarksRemarks are presented under the following headings:

Cluster analysisDiscriminant analysisFactor analysis and principal component analysisRotationMultivariate analysis of variance and related techniquesMultidimensional scaling and biplotsCorrespondence analysis

Cluster analysis

Cluster analysis is concerned with finding natural groupings, or clusters. Statas cluster-analysiscommands provide several hierarchical and partition clustering methods, postclustering summarizationmethods, and cluster-management tools. The hierarchical clustering methods may be applied to thedata with the cluster command or to a user-supplied dissimilarity matrix with the clustermatcommand. See [MV] cluster for an introduction to cluster analysis and the cluster and clustermatsuite of commands.

A wide variety of similarity and dissimilarity measures are available for comparing observations;see [MV] measure option. Dissimilarity matrices, for use with clustermat, are easily obtained usingthe matrix dissimilarity command; see [MV] matrix dissimilarity. This provides the buildingblocks necessary for clustering variables instead of observations or for clustering using a dissimilaritynot automatically provided by Stata; [MV] clustermat provides examples.

Discriminant analysis

Discriminant analysis may be used to describe differences between groups and to exploit thosedifferences in allocating (classifying) observations to the groups. These two purposes of discriminantanalysis are often called descriptive discriminant analysis and predictive discriminant analysis.

discrim has both descriptive and predictive LDA; see [MV] discrim lda. The candisc commandcomputes the same thing as discrim lda, but with output tailored for the descriptive aspects of thediscrimination; see [MV] candisc.

The remaining discrim subcommands provide alternatives to linear discriminant analysis forpredictive discrimination. [MV] discrim qda provides quadratic discriminant analysis. [MV] discrimlogistic provides logistic discriminant analysis. [MV] discrim knn provides kth-nearest-neighbordiscriminant analysis.

Postestimation commands provide classification tables (confusion matrices), error-rate estimates,classification listings, and group summarizations. In addition, postestimation tools for LDA andQDA include display of Mahalanobis distances between groups, correlations, and covariances. LDApostestimation tools also include discriminant-function loading plots, discriminant-function score plots,


scree plots, display of canonical correlations, eigenvalues, proportion of variance, likelihood-ratio testsfor the number of nonzero eigenvalues, classification functions, loadings, structure matrix, standardizedmeans, and ANOVA and MANOVA tables. See [MV] discrim estat, [MV] discrim lda postestimation,and [MV] discrim qda postestimation.

Factor analysis and principal component analysis

Factor analysis and principal component analysis (PCA) have dual uses. They may be used as adimension-reduction technique, and they may be used in describing the underlying data.

In PCA, the leading eigenvectors from the eigen decomposition of the correlation or covariancematrix of the variables describe a series of uncorrelated linear combinations of the variables thatcontain most of the variance. For data reduction, a few of these leading components are retained. Fordescribing the underlying structure of the data, the magnitudes and signs of the eigenvector elementsare interpreted in relation to the original variables (rows of the eigenvector).

pca uses the correlation or covariance matrix computed from the dataset. pcamat allows thecorrelation or covariance matrix to be directly provided. The vce(normal) option provides standarderrors for the eigenvalues and eigenvectors, which aids in their interpretation. See [MV] pca for details.

Factor analysis finds a few common factors that linearly reconstruct the original variables. Recon-struction is defined in terms of prediction of the correlation matrix of the original variables, unlikePCA, where reconstruction means minimum residual variance summed across all variables. Factorloadings are examined for interpretation of the structure of the data.

factor computes the correlation from the dataset, whereas factormat is supplied the matrixdirectly. They both display the eigenvalues of the correlation matrix, the factor loadings, and theuniqueness of the variables. See [MV] factor for details.

To perform factor analysis or PCA on binary data, compute the tetrachoric correlations and use thesewith factormat or pcamat. Tetrachoric correlations are available with the tetrachoric command;see [R] tetrachoric.

After factor analysis and PCA, a suite of commands are available that provide for rotation of theloadings; generation of score variables; graphing of scree plots, loading plots, and score plots; displayof matrices and scalars of interest such as anti-image matrices, residual matrices, KaiserMeyerOlkin measures of sampling adequacy, squared multiple correlations; and more. See [MV] factorpostestimation, [MV] pca postestimation, [MV] rotate, [MV] screeplot, and [MV] scoreplot fordetails.

Rotation

Rotation provides a modified solution that is rotated from an original multivariate solution suchthat interpretation is enhanced. Rotation is provided through three commands: rotate, rotatemat,and procrustes.

rotate works directly after pca, pcamat, factor, and factormat. It knows where to obtainthe component- or factor-loading matrix for rotation, and after rotating the loading matrix, it placesthe rotated results in e() so that all the postestimation tools available after pca and factor may beapplied to the rotated results. See [MV] rotate for details.

Perhaps you have the component or factor loadings from a published source and want to investigatevarious rotations, or perhaps you wish to rotate a loading matrix from some other multivariatecommand. rotatemat provides rotations for a specified matrix. See [MV] rotatemat for details.


A large selection of orthogonal and oblique rotations are provided for rotate and rotatemat.These include varimax, quartimax, equamax, parsimax, minimum entropy, Comreys tandem 1 and 2,promax power, biquartimax, biquartimin, covarimin, oblimin, factor parsimony, CrawfordFergusonfamily, Bentlers invariant pattern simplicity, oblimax, quartimin, target, and weighted target rotations.Kaiser normalization is also available.

The procrustes command provides Procrustean analysis. The goal is to transform a set of sourcevariables to be as close as possible to a set of target variables. The permitted transformations are anycombination of dilation (uniform scaling), rotation and reflection (orthogonal and oblique transforma-tions), and translation. Closeness is measured by the residual sum of squares. See [MV] procrustesfor details.

A set of postestimation commands are available after procrustes for generating fitted values andresiduals; for providing fit statistics for orthogonal, oblique, and unrestricted transformations; and forproviding a Procrustes overlay graph. See [MV] procrustes postestimation for details.

Multivariate analysis of variance and related techniques

The first canonical correlation is the maximum correlation that can be obtained between a linearcombination of one set of variables and a linear combination of another set of variables. The secondcanonical correlation is the maximum correlation that can be obtained between linear combinations ofthe two sets of variables subject to the constraint that these second linear combinations are orthogonalto the first linear combinations, and so on.

canon estimates these canonical correlations and provides the loadings that describe the linearcombinations of the two sets of variables that produce the correlations. Standard errors of the loadingsare provided, and tests of the significance of the canonical correlations are available. See [MV] canonfor details.

Postestimation tools are available after canon for generating the variables corresponding to thelinear combinations underlying the canonical correlations. Various matrices and correlations may alsobe displayed. See [MV] canon postestimation for details.

In canonical correlation, there is no real distinction between the two sets of original variables.In multivariate regression, however, the two sets of variables take on the roles of dependent andindependent variables. Multivariate regression is an extension of regression that allows for multipledependent variables. See [R] mvreg for multivariate regression, and see [R] mvreg postestimationfor the postestimation tools available after multivariate regression.

Just as analysis of variance (ANOVA) can be formulated in terms of regression where the categoricalindependent variables are represented by indicator (sometimes called dummy) variables, multivariateanalysis of variance (MANOVA), a generalization of ANOVA that allows for multiple dependent variables,can be formulated in terms of multivariate regression where the categorical independent variables arerepresented by indicator variables. Multivariate analysis of covariance (MANCOVA) allows for bothcontinuous and categorical independent variables.

The manova command fits MANOVA and MANCOVA models for balanced and unbalanced designs,including designs with missing cells, and for factorial, nested, or mixed designs, or designs involving re-peated measures. Four multivariate test statisticsWilks lambda, Pillais trace, the LawleyHotellingtrace, and Roys largest rootare computed for each term in the model. See [MV] manova for details.

Postestimation tools are available after manova that provide for univariate Wald tests of expressionsinvolving the coefficients of the underlying regression model and that provide for multivariate testsinvolving terms or linear combinations of the underlying design matrix. Linear combinations of thedependent variables are also supported. See [MV] manova postestimation for details.


Related to MANOVA is Hotellings T -squared test of whether a set of means is zero or whether twosets of means are equal. It is a multivariate test that reduces to a standard t test if only one variableis involved. The hotelling command provides Hotellings T -squared test; see [MV] hotelling.

Multidimensional scaling and biplots

Multidimensional scaling (MDS) is a dimension-reduction and visualization technique. Dissimi-larities (for instance, Euclidean distances) between observations in a high-dimensional space arerepresented in a lower-dimensional space (typically two dimensions) so that the Euclidean distancein the lower-dimensional space approximates the dissimilarities in the higher-dimensional space.

The mds command provides classical and modern (metric and nonmetric) MDS for dissimilaritiesbetween observations with respect to the variables; see [MV] mds. A wide variety of similarityand dissimilarity measures are allowed (the same ones available for the cluster command); see[MV] measure option.

mdslong and mdsmat provide MDS directly on the dissimilarities recorded either as data in longformat (mdslong) or as a dissimilarity matrix (mdsmat); see [MV] mdslong and [MV] mdsmat.

Postestimation tools available after mds, mdslong, and mdsmat provide MDS configuration plotsand Shepard diagrams; generation of the approximating configuration or the disparities, dissimilarities,distances, raw residuals and transformed residuals; and various matrices and scalars, such as Kruskalstress (loss), quantiles of the residuals per object, and correlations between disparities or dissimilaritiesand approximating distances. See [MV] mds postestimation for details.

Biplots are two-dimensional representations of data. Both the observations and the variables arerepresented. The observations are represented by marker symbols, and the variables are representedby arrows from the origin. Observations are projected to two dimensions so that the distance betweenthe observations is approximately preserved. The cosine of the angle between arrows approximatesthe correlation between the variables. A biplot aids in understanding the relationship between thevariables, the observations, and the observations and variables jointly. The biplot command producesbiplots; see [MV] biplot.

Correspondence analysis

Simple correspondence analysis (CA) is a technique for jointly exploring the relationship betweenrows and columns in a cross-tabulation. It is known by many names, including dual scaling, reciprocalaveraging, and canonical correlation analysis of contingency tables.

ca performs CA on the cross-tabulation of two integer-valued variables or on two sets of crossed(stacked) integer-valued variables. camat performs CA on a matrix with nonnegative entriesperhapsfrom a published table. See [MV] ca for details.

A suite of commands are available following ca and camat. These include commands for producingCA biplots and dimensional projection plots; for generating fitted values, row coordinates, and columncoordinates; and for displaying distances between row and column profiles, individual cell inertiacontributions, 2 distances between row and column profiles, and the fitted correspondence table.See [MV] ca postestimation for details.

mca performs multiple (MCA) or joint (JCA) correspondence analysis on two or more categoricalvariables and allows for crossing (stacking).

Postestimation tools available after mca provide graphing of category coordinate plots, dimensionalprojection plots, and plots of principal inertias; display of the category coordinates, optionally withcolumn statistics; the matrix of inertias of the active variables after JCA; and generation of row scores.


Also See[R] intro Introduction to base reference manual

442 mds Multidimensional scaling for two-way data

Matricese(D) dissimilarity matrixe(Disparities) disparity matrix for nonmetric MDSe(Y) approximating configuration coordinatese(Ev) eigenvaluese(idcoding) coding for integer identifier variablee(coding) variable standardization values; first column has value

to subtract and second column has divisore(norm stats) normaliztion statisticse(linearf) two element vector defining the linear transformation; distance

equals first element plus second element times dissimilarity

Functionse(sample) marks estimation sample

Methods and Formulasmds is implemented as an ado-file.

mds creates a dissimilarity matrix D according to the measure specified in option measure(). See[MV] measure option for descriptions of these measures. Subsequently, mds uses the same subroutinesas mdsmat to compute the MDS solution for D. See [MV] mdsmat for information on the methodsand formulas.

ReferencesBorg, I., and P. J. F. Groenen. 2005. Modern Multidimensional Scaling: Theory and Applications. 2nd ed. New York:

Springer.

Cox, T. F., and M. A. A. Cox. 2001. Multidimensional Scaling. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC.

Gifi, A. 1990. Nonlinear Multivariate Analysis. New York: Wiley.

Kendall, D. G. 1971. Seriation from abundance matrices. Mathematics in the Archaeological and Historical Sciences.Edinburgh: Edinburgh University Press.

Kruskal, J. B., and M. Wish. 1978. Multidimensional Scaling. Newbury Park, CA: Sage.

Lingoes, J. C. 1971. Some boundary conditions for a monotone analysis of symmetric matrices. Psychometrika 36:195203.

Mardia, K. V., J. T. Kent, and J. M. Bibby. 1979. Multivariate Analysis. New York: Academic Press.

Pearson, K. 1900. Mathematical contributions to the theory of evolution VII: On the correlation of characters notquantitatively measureable. Philosophical Transactions of the Royal Society. Series A 195: 147.

Sammon, J. W. 1969. A nonlinear mapping for data structure analysis. IEEE Transactions on Computers. 18(5):401-409.

Smullyan, R. 1986. This Book Needs No Title: A Budget of Living Paradoxes. New York: Touchstone.

Torgerson, W. S. 1952. Multidimensional scaling: I. Theory and method. Psychometrika 17: 401419.

Yang, K., and J. Trewn. 2004. Multivariate Statistical Methods in Quality Management. New York: McGrawHill.

Young, F. W., and R. M. Hamer. 1994. Theory and Applications of Multidimensional Scaling. Hillsdale, NJ: ErlbaumAssociates.

Young, G., and A. S. Householder. 1938. Discussion of a set of points in terms of their mutual distances. Psychometrika3: 1922.

See [MV] mdsmat for more references.

mds Multidimensional scaling for two-way data 443

Also See[MV] mds postestimation Postestimation tools for mds, mdsmat, and mdslong

[MV] biplot Biplots

[MV] ca Simple correspondence analysis

[MV] factor Factor analysis

[MV] mdslong Multidimensional scaling of proximity data in long format

[MV] mdsmat Multidimensional scaling of proximity data in a matrix

[MV] pca Principal component analysis

[U] 20 Estimation and postestimation commands

Title

mds postestimation Postestimation tools for mds, mdsmat, and mdslong

DescriptionThe following postestimation commands are of special interest after mds, mdslong, and mdsmat:

command description

estat config coordinates of the approximating configurationestat correlations correlations between disparities and distancesestat pairwise pairwise disparities, distances, and residualsestat quantiles quantiles of the residuals per objectestat stress Kruskal stress (loss) measure (only after classical MDS)

estat summarize estimation sample summarymdsconfig plot of approximating configurationmdsshepard Shepard diagramscreeplot plot eigenvalues (only after classical MDS)

estat summarize is not available after mdsmat.

For more information on these commands, except screeplot, see below. For information onscreeplot, see [MV] screeplot.

The following standard postestimation commands are also available:

command description

estimates cataloging estimation resultspredict approximating configuration, disparities, dissimilarities, distances, and

residuals

All estimates subcommands except table and stats are available.

See the corresponding entries in the Stata Base Reference Manual for more information.

Special-interest postestimation commands

estat config lists the coordinates of the approximating configuration.

estat correlations lists the Pearson and Spearman correlations between the disparities ordissimilarities and the Euclidean distances for each object.

estat pairwise lists the pairwise statistics: the disparities, the distances, and the residuals.

estat quantiles lists the quantiles of the residuals per object.

estat stress displays the Kruskal stress (loss) measure between the (transformed) dissimilaritiesand fitted distances per object (only after classical MDS).

444

mds postestimation Postestimation tools for mds, mdsmat, and mdslong 445

estat summarize summarizes the variables in the MDS over the estimation sample. After mds,estat summarize also reports whether and how variables were transformed before computingsimilarities or dissimilarities.

mdsconfig produces a plot of the approximating Euclidean configuration. By default, dimensions1 and 2 are plotted.

mdsshepard produces a Shepard diagram of the disparities against the Euclidean distances. Ideally,the points in the plot should be close to the y = x line. Optionally, separate plots are generated foreach row (value of id()).

Syntax for predict

predict[

type] {stub* | newvarlist} [ if ] [ in ] [ , statistic options ]

statistic description

Main

config approximating configuration; specify dimension() or fewervariables

pairwise(pstats) selected pairwise statistics; specify same number of variables

pstats description

disparities disparities = transformed(dissimilarities)dissimilarities dissimilaritiesdistances Euclidean distances between configuration pointsrresiduals raw residual = dissimilarity distancetresiduals transformed residual = disparity distanceweights weights

options description

Main saving(filename, replace) save results to filename; use replace to overwrite existing filenamefull create predictions for all pairs of objects; pairwise() only

saving() is required after mdsmat, after mds if pairwise() is selected, and after mdslong if config isselected.

Options for predict

Main

config generates variables containing the approximating configuration in Euclidean space. Specifyas many new variables as approximating dimensions (as determined by the dimension() optionof mds, mdsmat, or mdslong), though you may specify fewer. estat config displays the sameinformation but does not store the information in variables. After mdsmat and mdslong, you mustalso specify the saving() option.

446 mds postestimation Postestimation tools for mds, mdsmat, and mdslong

pairwise(pstats) generates new variables containing pairwise statistics. The number of new variablesshould be the same as the number of specified statistics. The following statistics are allowed:

disparities generates the disparities, i.e., the transformed dissimilarities. If no transformationis applied (modern MDS with transform(identity)), disparities are the same as dissimilarities.

dissimilarities generates the dissimilarities used in MDS. If mds, mdslong, or mdsmat wasinvoked on similarity data, the associated dissimilarities are returned.

distances generates the (unsquared) Euclidean distances between the fitted configuration points.

rresiduals generates the raw residuals: dissimilarities distances.tresiduals generates the transformed residuals: disparities distances.weights generates the weights. Missing proximities are represented by zero weights.

estat pairwise displays some of the same information but does not store the information invariables.

After mds and mdsmat, you must also specify the saving() option. With n objects, the pairwisedataset has n(n1)/2 observations. In addition to the three requested variables, predict producesvariables id1 and id2, which identify pairs of objects. With mds, id is the name of the identificationvariable (id() option), and with mdsmat it is Category.

saving(filename[, replace

]) is required after mdsmat, after mds if pairwise is selected, and

after mdslong if config is selected. saving() indicates that the generated variables are to becreated in a new Stata dataset and saved in the file named filename. Unless saving() is specified,the variables are generated in the current dataset.

replace indicates that filename specified in saving() may be overwritten.

full creates predictions for all pairs of objects (j1, j2). The default is to generate predictions onlyfor pairs (j1, j2) where j1 > j2. full may be specified only with pairwise.

Syntax for estat

List the coordinates of the approximating configuration

estat config[, maxlength(#) format(% fmt)

]List the Pearson and Spearman correlations

estat correlations[, maxlength(#) format(% fmt) notransform nototal

]List the pairwise statistics: disparities, distances, and residuals

estat pairwise[, maxlength(#) notransform full separator

]List the quantiles of the residuals

estat quantiles[, maxlength(#) format(% fmt) nototal notransform

]Display the Kruskal stress (loss) measure per point (only after classical MDS)

estat stress[, maxlength(#) format(% fmt) nototal notransform

]


Summarize the variables in MDS

estat summarize[, labels

]options description

maxlength(#) maximum number of characters for displaying object names; default is 12format(% fmt) display formatnototal suppress display of overall summary statisticsnotransform suppress the linear transformation of the dissimilaritiesfull display all pairs (j1, j2); default is (j1 > j2) onlyseparator draw separating lineslabels display variable labels

Options for estat

maxlength(#), an option used with all but estat summarize, specifies the maximum number ofcharacters of the object names to be displayed; the default is maxlength(12).

format(% fmt), an option used with estat config, estat correlations, estat quantiles, andestat stress, specifies the display format; the default differs between the subcommands.

nototal, an option used with estat correlations, estat quantiles, and estat stress,suppresses the overall summary statistics.

notransform, an option used with estat correlations, estat pairwise, estat quantiles, andestat stress, specifies that the untransformed dissimilarities be used instead of the transformeddissimilarities (disparities).

full, an option used with estat pairwise, displays a row for all pairs (j1, j2). The default is todisplay rows only for pairs where j1 > j2.

separator, an option used with estat pairwise, draws separating lines between blocks of rowscorresponding to changes in the first of the pair of objects.

labels, an option used with estat summarize, displays variable labels.

(Continued on next page)


Syntax for mdsconfig

mdsconfig[, options


Main

dimensions(# #) two dimensions to be displayed; default is dimensions(2 1)xnegate negate data relative to the x axisynegate negate data relative to the y axisautoaspect adjust aspect ratio on the basis of the data; default aspect ratio is 1maxlength(#) maximum number of characters used in marker labelscline options affect rendition of the lines connecting pointsmarker options change look of markers (color, size, etc.)marker label options change look or position of marker labels

Y axis, X axis, Titles, Legend, Overall

twoway options any options other than by() documented in [G] twoway options

Options for mdsconfig

Main

dimensions(# #) identifies the dimensions to be displayed. For instance, dimensions(3 2) plotsthe third dimension (vertically) versus the second dimension (horizontally). The dimension numbercannot exceed the number of extracted dimensions. The default is dimensions(2 1).

xnegate specifies that the data be negated relative to the x axis.

ynegate specifies that the data be negated relative to the y axis.

autoaspect specifies that the aspect ratio be automatically adjusted based on the range of the data tobe plotted. This option can make some plots more readable. By default, mdsconfig uses an aspectratio of one, producing a square plot. Some plots will have little variation in the y-axis direction,and use of the autoaspect option will better fill the available graph space while preserving theequivalence of distance in the x and y axes.

As an alternative to autoaspect, the twoway option aspectratio() can be used to overridethe default aspect ratio. mdsconfig accepts the aspectratio() option as a suggestion only andwill override it when necessary to produce plots with balanced axes; i.e., distance on the x axisequals distance on the y axis.

twoway options, such as xlabel(), xscale(), ylabel(), and yscale(), should be used withcaution. These options are accepted but may have unintended side effects on the aspect ratio.

maxlength(#) specifies the maximum number of characters for object names used to mark thepoints; the default is maxlength(12).

cline options affect the rendition of the lines connecting the plotted points; see [G] cline options. Ifyou are drawing connected lines, the appearance of the plot depends on the sort order of the data.

marker options affect the rendition of the markers drawn at the plotted points, including their shape,size, color, and outline; see [G] marker options.

marker label options specify if and how the markers are to be labeled; see [G] marker label options.



twoway options are any of the options documented in [G] twoway options, excluding by(). Theseinclude options for titling the graph (see [G] title options) and for saving the graph to disk (see[G] saving option). See autoaspect above for a warning against using options such as xlabel(),xscale(), ylabel(), and yscale().

Syntax for mdsshepard

mdsshepard[, options


Main

notransform use dissimilarities instead of disparitiesautoaspect adjust aspect ratio on the basis of the data; default aspect ratio is 1separate draw separate Shepard diagrams for each objectmarker options change look of markers (color, size, etc.)


twoway options any options other than by() documented in [G] twoway optionsbyopts(by option) affect the rendition of combined graphs; separate only

Options for mdsshepard

Main

notransform uses dissimilarities instead of disparities, i.e., suppresses the transformation of thedissimilarities.

autoaspect specifies that the aspect ratio be automatically adjusted based on the range of the datato be plotted. By default, mdsshepard uses an aspect ratio of one, producing a square plot.

See the description of the autoaspect option of mdsconfig for more details.

separate displays separate plots of each value of the ID variable. This may be time consuming ifthe number of distinct ID values is not small.

marker options affect the rendition of the markers drawn at the plotted points, including their shape,size, color, and outline; see [G] marker options.


twoway options are any of the options documented in [G] twoway options, excluding by(). Theseinclude options for titling the graph (see [G] title options) and for saving the graph to disk (see[G] saving option). See the autoaspect option of mdsconfig for a warning against using optionssuch as xlabel(), xscale(), ylabel(), and yscale().

byopts(by option) is documented in [G] by option. This option affects the appearance of thecombined graph and is allowed only with the separate option.


RemarksRemarks are presented under the following headings:

Postestimation statisticsMatching configuration plot and the Shepard diagramPredictions

Postestimation statistics

After an MDS analysis, several facilities can help you better understand the analysis and, inparticular, to assess the quality of the lower-dimensional Euclidean representation. We display resultsafter classical MDS. All are available after modern MDS except for estat stress.

Example 1

We illustrate the MDS postestimation facilities with the Morse code digit-similarity dataset; seeexample 1 in [MV] mdslong.

. use http://www.stata-press.com/data/r10/morse_long(Morse data (Rothkopf 1957))

. gen sim = freqsame/100

. mdslong sim, id(digit1 digit2) s2d(standard) noplot(output omitted )

MDS has produced a two-dimensional configuration with Euclidean distances approximating thedissimilarities between the Morse codes for digits. This configuration may be examined using theestat config command; see mdsconfig if you want to plot the configuration.

. estat config

Approximating configuration in 2-dimensional Euclidean space

digit1 dim1 dim2

0 0.5690 -0.01621 0.4561 0.33842 0.0372 0.58543 -0.3878 0.45164 -0.5800 0.07705 -0.5458 0.01966 -0.3960 -0.41877 -0.0963 -0.59018 0.3124 -0.38629 0.6312 -0.0608

This configuration is not unique. A translation, a reflection, and an orthonormal rotation ofthe configuration do not affect the interpoint Euclidean distances. All such transformations areequally reasonable MDS solutions. Thus you should not interpret aspects of these numbers (or of theconfiguration plot) that are not invariant to these transformations.

We now turn to the three estat subcommands that analyze the MDS residuals, i.e., the differencesbetween the disparities or dissimilarities and the matching Euclidean distances. There is a catch here.The raw residuals of MDS are not well behaved. For instance, the sum of the raw residuals is notzerooften it is not even close. The MDS solution does not minimize the sum of squares of the rawresiduals (Mardia, Kent, and Bibby 1979, 406408). To create reasonable residuals with MDS, thedissimilarities can be transformed to disparities approximating the Euclidean distances. In classicalMDS we use a linear transform f , fitted by least squares. This is equivalent to Kruskals Stress1loss function. The modified residuals are defined as the differences between the linearly transformeddissimilarities and the matching Euclidean distances.


In modern MDS we have three types of transformations from dissimilarities to disparities to choosefrom: the identity (which does not transform the dissimilarities), a power transformation, and amonotonic transformation.

The three estat subcommands summarize the residuals in different ways. After classical MDS,estat stress displays the Kruskal loss or stress measures for each object and the overall total.

. estat stress

Stress between adjusted dissimilarities and Euclidean distances

digit1 Kruskal

0 0.13391 0.12552 0.19723 0.20284 0.20405 0.27336 0.19267 0.19218 0.17159 0.1049

Total 0.1848

Second, after classical or modern MDS, the quantiles of the residuals are available, both overalland for the subgroup of object pairs in which an object is involved.

. estat quantiles

Quantiles of adjusted residuals

digit1 N min p25 q50 q75 max

0 9 -.111732 -.088079 -.028917 .11202 .2203991 9 -.170063 -.137246 -.041244 .000571 .112022 9 -.332717 -.159472 -.072359 .074999 .2348663 9 -.136251 -.120398 -.072359 .105572 .3658334 9 -.160797 -.014099 .03845 .208215 .3550535 9 -.09971 -.035357 .176337 .325043 .3658336 9 -.137246 -.113564 -.075008 .177448 .3250437 9 -.332717 -.170063 -.124129 .03845 .1763378 9 -.186452 -.134831 -.041244 .075766 .2203999 9 -.160797 -.104403 -.088079 -.064316 -.030032

Total 90 -.332717 -.113564 -.041244 .105572 .365833

The dissimilarities for the Morse code of digit 5 are fitted considerably worse than for all otherMorse codes. Digit 5 has the largest Kruskal stress (0.273) and median residual (0.176).



Finally, after classical or modern MDS, estat correlations displays the Pearson and Spearmancorrelations between the (transformed or untransformed) dissimilarities and the Euclidean distances.

. estat correlations

Correlations of dissimilarities and fitted distances

digit1 N Pearson Spearman

0 9 0.9510 0.95401 9 0.9397 0.77822 9 0.7674 0.40173 9 0.7922 0.78154 9 0.9899 0.92895 9 0.9412 0.91216 9 0.8226 0.86677 9 0.8444 0.42688 9 0.8505 0.70009 9 0.9954 0.9333

Total 90 0.8602 0.8301

Matching configuration plot and the Shepard diagram

The matching configuration plot and Shepard diagram are easily obtained after an MDS analysis.

Example 2

By default, mds, mdsmat, and mdslong display the MDS matching configuration plot. If you wantto exercise control over the graph, you can specify the noplot option of mds, mdsmat, or mdslongand then use the mdsconfig postestimation graph command.

Continuing with the Morse code digit example: we produce a configuration plot with an addedtitle and subtitle.

. mdsconfig, title(Morse code digit dissimilarity) subtitle(data: Rothkopf 1957)

0

1

2

3

45

6

7

8

9

.6

.4

.2

0.2

.4.6

.8D

imen

sion

2

.6 .4 .2 0 .2 .4 .6 .8Dimension 1

Classical MDS

data: Rothkopf 1957Morse code digit dissimilarity


The plot has an aspect ratio of one so that 1 unit on the horizontal dimension equals 1 unit onthe vertical dimension. Thus the straight-line distance in the plot is really (proportional to) theEuclidean distance between the points in the configuration and hence approximates the dissimilaritiesbetween the objectshere the Morse codes for digits.

Example 3

A second popular plot for MDS is the Shepard diagram. This is a plot of the Euclidean distances inthe matching configuration against the observed dissimilarities. As we explained before, in classicalMDS a linear transformation is applied to the dissimilarities to fit the Euclidean distances as closeas possible (in the least-squares sense). In modern MDS the transformation may be the identity (notransformation), a power function, or a monotonic function. A Shepard diagram is a plot of then(n 1)/2 transformed dissimilarities, called disparities, against the Euclidean distances.

. mdsshepard

0.2

.4.6

.81

1.2

1.4

dist

ance

s

.2 0 .2 .4 .6 .8 1 1.2disparities

Classical MDS

Shepard diagram

If the Euclidean configuration is close to the disparities between the objects, all points would beclose to the y = x line. Deviations indicate lack of fit. To simplify the diagnosis of whether thereare specific objects that are poorly represented, Shepard diagrams can be produced for each objectseparately. Such plots consist of n small plots with n 1 points each, namely, the disparities andEuclidean distances to all other objects.



. mdsshepard, separate(mdsshepard is producing a separate plot for each obs; this may take a while)

0.2

.4.6

.81

1.21

.40

.2.4

.6.8

11.

21.4

0.2

.4.6

.81

1.21

.4

.2 0 .2 .4 .6 .8 1 1.2.2 0 .2 .4 .6 .8 1 1.2

0 1 2 3

4 5 6 7

8 9

dist

ance

s

disparitiesClassical MDS

Shepard diagrams

Other examples of mdsconfig are found in [MV] mds, [MV] mdslong, and [MV] mdsmat.

Predictions

It is possible to generate variables containing the results from the MDS analysis. MDS operates attwo levels: first at the level of the objects and second at the level of relations between the objects orpairs of objects. You can generate variables at both of these levels.

The config option of predict after an MDS requests that the coordinates of the objects in thematching configuration be stored in variables. You may specify as many variables as there are retaineddimensions. You may also specify fewer variables. The first variable will store the coordinates fromthe first dimension. The second variable, if any, will store the coordinates from the second dimension,and so on.

The pairwise() option specifies that a given selection of the pairwise statistics are stored invariables. The statistics available are the disparities, dissimilarities, fitted distances, raw residuals,transformed residuals, and weights. The raw residuals are the difference between dissimilarities andthe fitted distances, and the transformed residuals are the difference between the disparities and thefitted distances.

There is a complicating issue. With n objects, there are n(n 1)/2 pairs of objects. So, to storeproperties of objects, you need n observations, but to store properties of pairs of objects, you needn(n 1)/2 observations. So, where do you store the variables? predict after MDS commands cansave the predicted variables in a new dataset. Specify the option saving(filename). Such a datasetwill automatically have the appropriate object identification variable or variables.

Sometimes it is also possible to store the variables in the dataset you have in memory: object-levelvariables in an object-level dataset and pairwise-level variables in a pairwise-level dataset.

After mds you have a dataset in memory in which the observations are associated with the MDSobjects. Here you can store object-level variables directly in the dataset in memory. To do so, youjust omit the saving() option. Here it is not possible to store the pairwise statistics in the datasetin memory. The pairwise statistics have to be stored in a new dataset.


After mdslong, the dataset in memory is in a pairwise form, so the variables predicted with theoption pairwise() can be stored in the dataset in memory. It is, of course, also possible to store thepairwise variables in a new dataset; the choice is yours. With pairwise data in memory, you cannotstore the object-level predicted variables into the data in memory; you need to specify the name of anew dataset.

After mdsmat, you always need to save the predicted variables in a new dataset.

Example 4

Continuing with our Morse code example that used mdslong: the dataset in memory is in longform. Thus we can store the pairwise statistics with the dataset in memory.

. predict tdissim eudist resid, pairwise

. list in 1/10

digit1 digit2 freqsame sim tdissim eudist resid

1. 2 1 62 .62 .3227682 .4862905 -.16352242. 3 1 16 .16 .957076 .851504 .10557193. 3 2 59 .59 .3732277 .4455871 -.07235944. 4 1 6 .06 1.069154 1.068583 .00057095. 4 2 23 .23 .8745967 .7995979 .0749989

6. 4 3 38 .38 .6841489 .4209922 .26315677. 5 1 12 .12 1.002667 1.051398 -.0487318. 5 2 8 .08 1.047234 .8123672 .23486659. 5 3 27 .27 .8257753 .4599419 .365833510. 5 4 56 .56 .4218725 .0668193 .3550532

Since we used mdslong, the object-level statistics must be saved in a file.

. predict d1 d2, config saving(digitdata)

. describe digit* d1 d2 using digitdata

Contains data unit statistics for MDS(method=classical,dim=2)

obs: 10 1 Mar 2007 10:07vars: 3size: 130

storage display valuevariable name type format label variable label

digit1 str1 %9sd1 float %9.0g MDS dimension 1d2 float %9.0g MDS dimension 2

Sorted by: digit1

The information in these variables was already shown with estat config. The dataset createdhas variables d1 and d2 with the coordinates of the Morse digits on the two retained dimensionsand an identification variable digit1. Use merge to add these variables to the data in memory; see[D] merge.


Saved Resultsestat correlations saves the following in r():

Matricesr(R) statistics per object; columns with # of obs., Pearson corr., and Spearman corr.r(T) overall statistics; # of obs., Pearson corr., and Spearman corr.

estat quantiles saves the following in r():

Macrosr(dtype) adjusted or raw; dissimilarity transformation

Matricesr(Q) statistics per object; columns with # of obs., min., p25, p50, p75, and max.r(T) overall statistics; # of obs., min., p25, p50, p75, and max.

estat stress saves the following in r():

Macrosr(dtype) adjusted or raw; dissimilarity transformation

Matricesr(S) Kruskals stress/loss measure per objectr(T) 11 matrix with the overall Kruskal stress/loss measure

Methods and FormulasAll postestimation commands listed above are implemented as ado-files.

See [MV] mdsmat for information on the methods and formulas for multidimensional scaling.

For classical MDS, let Dij be the dissimilarity between objects i and j, 1 i, j n. Weassume Dii = 0 and Dij = Dji. Let Eij be the Euclidean distance between rows i and j of thematching configuration Y. In classical MDS, DE is not a well-behaved residual matrix. We followthe approach used in metric and nonmetric MDS to transform Dij to optimally match Eij , with

Dij = a+ bDij, where a and b are chosen to minimize the residual sum of squares. This is a simpleregression problem and is equivalent to minimizing Kruskals stress measure (Kruskal 1964; Cox andCox 2001, 63)

Kruskal(D,E) ={

(Eij Dij)2E2ij

}1/2

with summation over all pairs (i, j). We call the Dij the adjusted or transformed dissimilarities. Ifthe transformation step is skipped by specifying the option notransform, we set Dij = Dij .

In estat stress, the decomposition of Kruskals stress measure over the objects is displayed.Kruskal(D,E)i is defined analogously with summation over all j = i.

For modern MDS, the optimal transformation to disparities, f(D) D, is calculated during theestimation. See [MV] mdsmat for details. For transform(power) the power is saved in e(alpha).For transform(monotonic) the disparities themselves are saved as e(Disparities).


ReferencesBorg, I., and P. J. F. Groenen. 2005. Modern Multidimensional Scaling: Theory and Applications. 2nd ed. New York:

Springer.

Cox, T. F., and M. A. A. Cox. 2001. Multidimensional Scaling. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC.

Kruskal, J. B. 1964. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika29: 127.

Mardia, K. V., J. T. Kent, and J. M. Bibby. 1979. Multivariate Analysis. New York: Academic Press.

See [MV] mdsmat for additional references.

Also See[MV] mds Multidimensional scaling for two-way data

[MV] mdslong Multidimensional scaling of proximity data in long format

[MV] mdsmat Multidimensional scaling of proximity data in a matrix

[MV] screeplot Scree plot

Subject and author index 613

Subject and author indexThis is the subject and author index for theStata Multivariate Statistics Reference Manual. Readersinterested in topics other than cluster analysis should seethe combined subject index (and the combined authorindex) in the Stata Quick Reference and Index. Thecombined index indexes the Getting Started manuals,the Users Guide, and all the Reference manuals exceptthe Mata Reference Manual.

Semicolons set off the most important entries from therest. Sometimes no entry will be set off with semicolons,meaning that all entries are equally important.

Aabsolute value dissimilarity measure,

[MV] measure optionAkaike, H., [MV] factor postestimationAlbert, A., [MV] discrim, [MV] discrim logisticAldenderfer, M. S., [MV] clusterAllison, M. J., [MV] manovaAnderberg coefficient similarity measure,

[MV] measure optionAnderberg, M. R., [MV] cluster,

[MV] measure optionAnderson, E., [MV] clustermat, [MV] discrim

estat, [MV] discrim lda, [MV] discrim ldapostestimation

Anderson, T. W., [MV] discrim, [MV] manova,[MV] pca

Andrews, D. F., [MV] discrim lda postestimation,[MV] discrim qda, [MV] discrim qdapostestimation, [MV] manova

angular similarity measure, [MV] measure optionanova, estat subcommand, [MV] discrim lda

postestimationanti, estat subcommand, [MV] factor

postestimation, [MV] pca postestimationanti-image

correlation matrix, [MV] factor postestimation,[MV] pca postestimation

covariance matrix, [MV] factor postestimation,[MV] pca postestimation

approximating Euclidean distances, [MV] mdspostestimation

Arnold, S. F., [MV] manovaArseven, E., [MV] discrim ldaaverage-linkage clustering, [MV] cluster, [MV] cluster

linkage, [MV] clustermataveragelinkage, cluster subcommand,

[MV] cluster linkage

BBartlett, M. S., [MV] factor, [MV] factor

postestimation

Bartlett scoring, [MV] factor postestimationBasilevsky, A. T., [MV] pcaBeerstecher, E., [MV] manovaBentler, P. M., [MV] rotate, [MV] rotatematBentler rotation, [MV] rotate, [MV] rotatematBernaards, C. A., [MV] rotatematBibby, J. M., [MV] discrim, [MV] discrim lda,

[MV] factor, [MV] manova, [MV] matrixdissimilarity, [MV] mds, [MV] mdspostestimation, [MV] mdslong, [MV] mdsmat,[MV] pca, [MV] procrustes

biplot command, [MV] biplotbiplots, [MV] biplot, [MV] ca postestimationbiquartimax rotation, [MV] rotate, [MV] rotatematbiquartimin rotation, [MV] rotate, [MV] rotatematBlashfield, R. K., [MV] clusterBlasius, J., [MV] ca, [MV] mcaBollen, K. A., [MV] factor postestimationBorg, I., [MV] mds, [MV] mds postestimation,

[MV] mdslong, [MV] mdsmatBox, G. E. P., [MV] manovaBray, R. J., [MV] clustermatBrent, R., [MV] mdsmatBrown, J. D., [MV] manovaBrowne, M. W., [MV] procrustes

Cca command, [MV] cacabiplot command, [MV] ca postestimationCailliez, F., [MV] mdsmatCalinski and Harabasz index stopping rules,

[MV] cluster stopCalinski, T., [MV] cluster, [MV] cluster stopcamat command, [MV] caCanberra dissimilarity measure, [MV] measure optioncandisc command, [MV] candisccanon command, [MV] canoncanonical correlations, [MV] canon, [MV] canon

postestimationcanonical discriminant analysis, [MV] candisccanontest, estat subcommand, [MV] discrim lda

postestimationcaprojection command, [MV] ca postestimationCarroll, J. B., [MV] rotatematcategorical data, [MV] ca, [MV] manova, [MV] mcaCattell, R. B., [MV] factor postestimation,

[MV] pca postestimation, [MV] procrustes,[MV] screeplot

centroid-linkage clustering, [MV] cluster, [MV] clusterlinkage, [MV] clustermat

centroidlinkage, cluster subcommand,[MV] cluster linkage

Choi, S. C., [MV] discrim knnClarke, M. R. B., [MV] factorclassfunctions, estat subcommand, [MV] discrim

lda postestimation

614 Subject and author index

classification, see discriminant analysis or clusteranalysis

classtable, estat subcommand, [MV] discrimestat, [MV] discrim knn postestimation,[MV] discrim lda postestimation, [MV] discrimlogistic postestimation, [MV] discrim qdapostestimation

Cliff, N., [MV] canon postestimationcluster analysis, [MV] cluster, [MV] cluster

dendrogram, [MV] cluster generate,[MV] cluster kmeans and kmedians,[MV] cluster linkage, [MV] cluster stop,[MV] cluster utility

dendrograms, [MV] cluster dendrogramdir, [MV] cluster utilitydrop, [MV] cluster utilityhierarchical, [MV] cluster, [MV] cluster linkage,

[MV] clustermatkmeans, [MV] cluster kmeans and kmedianskmedians, [MV] cluster kmeans and kmedianslist, [MV] cluster utilitynotes, [MV] cluster notesprogramming, [MV] cluster programming

subroutines, [MV] cluster programmingutilities

rename, [MV] cluster utilityrenamevar, [MV] cluster utilitystopping rules, [MV] cluster, [MV] cluster stoptrees, [MV] cluster dendrogramuse, [MV] cluster utility

clustermat command, [MV] clustermatcommon, estat subcommand, [MV] factor

postestimationcommunalities, [MV] factor, [MV] factor

postestimationcompare, estat subcommand, [MV] procrustes

postestimationcomplete-linkage clustering, [MV] cluster,

[MV] cluster linkage, [MV] clustermatcompletelinkage, cluster subcommand,

[MV] cluster linkagecomponent

analysis, [MV] factor, [MV] pca, [MV] rotate,[MV] rotatemat

loading plot, [MV] scoreplotplot, [MV] scoreplot

Comrey, A. L., [MV] rotate, [MV] rotatematComreys tandem rotation, [MV] rotate,

[MV] rotatematconfig, estat subcommand, [MV] mds

postestimationconfiguration plot, [MV] mds postestimationcontingency tables, [MV] caCooper, M. C., [MV] cluster, [MV] cluster

programming subroutines, [MV] cluster stopcoordinates, estat subcommand, [MV] ca

postestimation, [MV] mca postestimationcorrelation matrix, anti-image, [MV] factor

postestimation, [MV] pca postestimation

correlation,canonical, [MV] canonfactoring of, [MV] factorprincipal components of, [MV] pcasimilarity measure, [MV] measure option

correlations, estat subcommand, [MV] canonpostestimation, [MV] discrim ldapostestimation, [MV] discrim qdapostestimation, [MV] mds postestimation

correspondence analysis, [MV] ca, [MV] mcacovariance, estat subcommand, [MV] discrim

lda postestimation, [MV] discrim qdapostestimation

covariance matrix, anti-image, [MV] factorpostestimation, [MV] pca postestimation

covariance, principal components of, [MV] pcacovarimin rotation, [MV] rotate, [MV] rotatematCox, M. A. A., [MV] biplot, [MV] ca, [MV] mds,

[MV] mds postestimation, [MV] mdsmat,[MV] procrustes

Cox, T. F., [MV] biplot, [MV] ca, [MV] mds,[MV] mds postestimation, [MV] mdsmat,[MV] procrustes

Cozad, J. B., [MV] discrim ldaCramer, E. M., [MV] procrustesCrawford, C. B., [MV] rotate, [MV] rotatematCrawfordFerguson rotation, [MV] rotate,

[MV] rotatematCritchley F., [MV] mdsmatCurtis, J. T., [MV] clustermatCzekanowski, J., [MV] measure option

Ddata reduction, [MV] ca, [MV] canon, [MV] factor,

[MV] mds, [MV] pcaDay, W. H. E., [MV] clusterdelete, cluster subcommand, [MV] cluster

programming utilitiesdendrogram, cluster subcommand, [MV] cluster

dendrogramdendrograms, [MV] cluster, [MV] cluster dendrogramDice coefficient similarity measure,

[MV] measure optionDice, L. R., [MV] measure optionDijksterhuis, G. B., [MV] procrustesdir, cluster subcommand, [MV] cluster utilitydiscrim

knn command, [MV] discrim, [MV] discrim knnlda command, [MV] discrim, [MV] discrim ldalogistic command, [MV] discrim, [MV] discrim

logisticqda command, [MV] discrim, [MV] discrim qda

discriminant analysis, [MV] candisc, [MV] discrim,[MV] discrim knn, [MV] discrim lda,[MV] discrim logistic, [MV] discrim qda

loading plot, [MV] scoreplotscore plot, [MV] scoreplot


dissimilaritymatrices, [MV] matrix dissimilaritymeasures, [MV] cluster, [MV] cluster

programming utilities, [MV] matrixdissimilarity, [MV] mds, [MV] measure optionabsolute value, [MV] measure optionBray and Curtis, [MV] clustermatCanberra, [MV] measure optionEuclidean, [MV] measure optiongower, [MV] measure optionmaximum value, [MV] measure optionMinkowski, [MV] measure option

dissimilarity, matrix subcommand, [MV] matrixdissimilarity

distance matrices, [MV] matrix dissimilaritydistances, see dissimilarity measuresdistances, estat subcommand, [MV] ca

postestimationDriver, H. E., [MV] measure optiondrop, cluster subcommand, [MV] cluster utilitydual scaling, [MV] caDubes, R. C., [MV] clusterDuda and Hart index stopping rules, [MV] cluster stopDuda, R. O., [MV] cluster, [MV] cluster stopDunn, G., [MV] discrim, [MV] discrim qda

postestimation, [MV] mca

EEdelsbrunner, H., [MV] clustereigenvalues, [MV] factor, [MV] factor postestimation,

[MV] pca, [MV] rotate, [MV] rotatemat,[MV] screeplot

eigenvectors, [MV] factor, [MV] factor postestimation,[MV] pca, [MV] rotate, [MV] rotatemat,[MV] scoreplot

Enas, G. G, [MV] discrim knnEnder, P. B., [MV] canonentropy rotation, [MV] rotate, [MV] rotatematequality of means tests, [MV] hotelling, [MV] manovaequamax rotation, [MV] rotate, [MV] rotatematerrorrate, estat subcommand, [MV] discrim

estat, [MV] discrim knn postestimation,[MV] discrim lda postestimation, [MV] discrimlogistic postestimation, [MV] discrim qdapostestimation

estat

anova command, [MV] discrim lda postestimationanti command, [MV] factor postestimation,

[MV] pca postestimationcanontest command, [MV] discrim lda

postestimationclassfunctions command, [MV] discrim lda

postestimationclasstable command, [MV] discrim


estat, continuedcommon command, [MV] factor postestimationcompare command, [MV] procrustes

postestimationconfig command, [MV] mds postestimationcoordinates command, [MV] ca postestimation,

[MV] mca postestimationcorrelations command, [MV] canon

postestimation, [MV] discrim ldapostestimation, [MV] discrim qdapostestimation, [MV] mds postestimation

covariance command, [MV] discrimlda postestimation, [MV] discrim qdapostestimation

distances command, [MV] ca postestimationerrorrate command, [MV] discrim estat,

[MV] discrim knn postestimation,[MV] discrim lda postestimation, [MV] discrimlogistic postestimation, [MV] discrim qdapostestimation

factors command, [MV] factor postestimationgrdistances command, [MV] discrim


grmeans command, [MV] discrim ldapostestimation

grsummarize command, [MV] discrimestat, [MV] discrim knn postestimation,[MV] discrim lda postestimation, [MV] discrimlogistic postestimation, [MV] discrim qdapostestimation

inertia command, [MV] ca postestimationkmo command, [MV] factor postestimation,

[MV] pca postestimationlist command, [MV] discrim estat, [MV] discrim

knn postestimation, [MV] discrim ldapostestimation, [MV] discrim logisticpostestimation, [MV] discrim qdapostestimation

loadings command, [MV] canon postestimation,[MV] discrim lda postestimation, [MV] pcapostestimation

manova command, [MV] discrim ldapostestimation

mvreg command, [MV] procrustes postestimationpairwise command, [MV] mds postestimationprofiles command, [MV] ca postestimationquantiles command, [MV] mds postestimationresiduals command, [MV] factor postestimation,

[MV] pca postestimationrotatecompare command, [MV] canon

postestimation, [MV] factor postestimation,[MV] pca postestimation

rotate command, [MV] canon postestimationsmc command, [MV] factor postestimation,

[MV] pca postestimationstress command, [MV] mds postestimationstructure command, [MV] discrim lda

postestimation, [MV] factor postestimation


estat, continuedsubinertia command, [MV] mca postestimationsummarize command, [MV] ca postestimation,

[MV] discrim estat, [MV] discrimknn postestimation, [MV] discrim ldapostestimation, [MV] discrim logisticpostestimation, [MV] discrim qdapostestimation, [MV] factor postestimation,[MV] mca postestimation, [MV] mdspostestimation, [MV] pca postestimation,[MV] procrustes postestimation

table command, [MV] ca postestimationEuclidean dissimilarity measure,

[MV] measure optionEveritt, B. S., [MV] cluster, [MV] cluster

stop, [MV] discrim, [MV] discrim qdapostestimation, [MV] mca, [MV] pca,[MV] screeplot

Ffactor

analysis, [MV] canon, [MV] factor, [MV] factorpostestimation

loading plot, [MV] scoreplotscore plot, [MV] scoreplotscores, [MV] factor postestimation

factor command, [MV] factorfactorial design, [MV] manovafactormat command, [MV] factorfactors, estat subcommand, [MV] factor

postestimationFerguson, G. A., [MV] rotate, [MV] rotatematFidell, L. S., [MV] discrim, [MV] discrim ldaFisher, L. D., [MV] factor, [MV] pcaFisher, R. A., [MV] clustermat, [MV] discrim,

[MV] discrim estat, [MV] discrim ldaFix, E., [MV] discrim knnFriedman, J., [MV] discrim knnFuller, W. A., [MV] factorfunctions, cluster generate, adding, [MV] cluster

programming subroutines

GGabriel, K. R., [MV] biplotgenerate, cluster subcommand, [MV] cluster

generategenerate functions, adding, [MV] cluster

programming subroutinesGifi, A., [MV] mdsGilbert, G. K., [MV] measure optionGirshick, M. A., [MV] pcaGnanadesikan, R., [MV] manovaGordon, A. D., [MV] biplot, [MV] cluster,

[MV] cluster stop, [MV] measure optionGorsuch, R. L., [MV] factor, [MV] rotate,

[MV] rotatemat

Gower coefficient similarity measure,[MV] measure option

Gower, J. C., [MV] biplot, [MV] ca, [MV] mca,[MV] measure option, [MV] procrustes

graphs,biplot, [MV] biplot, [MV] ca postestimationCA dimension projection, [MV] ca postestimationcluster tree, [MV] cluster dendrogramdendrogram, [MV] cluster dendrogrameigenvalue

after factor, [MV] screeplotafter pca, [MV] screeplot

loadingafter candisc, [MV] scoreplotafter discrim lda, [MV] scoreplotafter factor, [MV] scoreplotafter pca, [MV] scoreplot

MDS configuration, [MV] mds postestimationprocrustes overlay, [MV] procrustes postestimationscore

after candisc, [MV] scoreplotafter discrim lda, [MV] scoreplotafter factor, [MV] scoreplotafter pca, [MV] scoreplot

Shepard diagram, [MV] mds postestimationgrdistances, estat subcommand, [MV] discrim


Green, B. F., [MV] discrim lda, [MV] procrustesGreen, P. E., [MV] clusterGreenacre, M. J., [MV] ca, [MV] mcaGreenfield, S., [MV] factor, [MV] factor

postestimationgrmeans, estat subcommand, [MV] discrim lda

postestimationGroenen, P. J. F., [MV] mds, [MV] mds

postestimation, [MV] mdslong, [MV] mdsmatgrouping variables, generating, [MV] cluster generategrsummarize, estat subcommand, [MV] discrim


HHamann coefficient similarity measure,

[MV] measure optionHamann, U., [MV] measure optionHamer, R. M., [MV] mds, [MV] mdslong,

[MV] mdsmatHamilton, L. C., [MV] factor, [MV] screeplotHand, D. J., [MV] biplot, [MV] ca, [MV] discrim,

[MV] mcaHarabasz, J., [MV] cluster, [MV] cluster stopHarman, H. H., [MV] factor, [MV] factor

postestimation, [MV] rotate, [MV] rotatematHarris, E. K., [MV] discrim, [MV] discrim logistic


Harris, R., [MV] canon postestimationHart, P. E., [MV] cluster, [MV] cluster stopHastie, T., [MV] discrim knnHeagerty, P. J., [MV] factor, [MV] pcaHendrickson, A. E., [MV] rotate, [MV] rotatematHerzberg, A. M., [MV] discrim lda postestimation,

[MV] discrim qda, [MV] discrim qdapostestimation, [MV] manova

hierarchical cluster analysis, [MV] cluster,[MV] cluster linkage, [MV] clustermat

Hilbe, J., [MV] discrim lda, [MV] manova,[MV] measure option

Hodges, J. L., [MV] discrim knnHorst normalization, see Kaiser normalizationHorst, P., [MV] factor postestimation, [MV] rotate,

[MV] rotatemathotelling command, [MV] hotellingHotelling, H., [MV] canon, [MV] hotelling,

[MV] manova, [MV] pcaHotellings

T -squared, [MV] hotellinggeneralized T -squared statistic, [MV] manova

Householder, A. S., [MV] mds, [MV] mdslong,[MV] mdsmat

Hubalek, Z., [MV] measure optionHuberty, C. J., [MV] candisc, [MV] discrim,

[MV] discrim estat, [MV] discrim lda,[MV] discrim lda postestimation, [MV] discrimqda

Hughes, J. B., [MV] manovaHurley, J. R., [MV] procrustes

Iindex, stopping rules, see stopping rulesinertia, estat subcommand, [MV] ca postestimationISSP, [MV] mca, [MV] mca postestimation

JJaccard coefficient similarity measure,

[MV] measure optionJaccard, P., [MV] measure optionJackson, J. E., [MV] pca, [MV] pca postestimationJacoby, W. G., [MV] biplotJain, A. K., [MV] clusterJennrich, R. I., [MV] rotate, [MV] rotatematJohnson, D. E., [MV] manovaJohnson, R. A., [MV] canon, [MV] discrim,

[MV] discrim estat, [MV] discrim lda,[MV] discrim lda postestimation

Jolliffe, I. T., [MV] biplot, [MV] pcaJoreskog, K. G., [MV] factor postestimation

KKaiser, H. F., [MV] factor postestimation, [MV] pca

postestimation, [MV] rotate, [MV] rotatemat

KaiserMeyerOlkin sampling adequacy, [MV] factorpostestimation, [MV] pca postestimation

Kaiser normalization, [MV] factor postestimation,[MV] pca postestimation, [MV] rotate,[MV] rotatemat

Kaufman, L.,[MV] cluster, [MV] clustermat, [MV] matrixdissimilarity, [MV] measure option

Kendall, D. G., [MV] mdsKendall, M. G., [MV] measure optionKent, J. T., [MV] discrim, [MV] discrim lda,


Kerm, P. van, [MV] caKim, J. O., [MV] factorKimbrough, J. W., [MV] discrim knnKlecka, W. R., [MV] discrim, [MV] discrim ldakmeans, cluster subcommand, [MV] cluster kmeans

and kmedianskmeans clustering, [MV] cluster, [MV] cluster kmeans

and kmedianskmedians, cluster subcommand, [MV] cluster

kmeans and kmedianskmedians clustering, [MV] cluster, [MV] cluster

kmeans and kmedianskmo, estat subcommand, [MV] factor postestimation,

[MV] pca postestimationknn, discrim subcommand, [MV] discrim knnKohler, U., [MV] biplotKroeber, A. L., [MV] measure optionKrus, D., [MV] canon postestimationKruskal, J. B., [MV] mds, [MV] mds postestimation,

[MV] mdslong, [MV] mdsmatKruskal stress, [MV] mds postestimationKshirsagar, A. M., [MV] discrim lda, [MV] pcakth-nearest neighbor, [MV] discrim knnKulczynski coefficient similarity measure,

[MV] measure optionKulczynski, S., [MV] measure option

LLachenbruch, P. A., [MV] discrim, [MV] discrim estat,

[MV] discrim ldaLance and Williams formula, [MV] clusterLance, G. N., [MV] clusterLandau, S., [MV] cluster, [MV] cluster stopLatin square designs, [MV] manovaLawley, D. N., [MV] canon, [MV] factor, [MV] factor

postestimation, [MV] manova, [MV] pcaLawleyHotelling trace statistic, [MV] canon,

[MV] manovaLDA, [MV] discrim ldalda, discrim subcommand, [MV] discrim ldaLeese, M., [MV] cluster, [MV] cluster stopLeeuw, J. de, [MV] ca postestimationLesaffre, E., [MV] discrim logistic


Lincoff, G. H., [MV] discrim knnlinear discriminant analysis, [MV] candisc,

[MV] discrim ldaLingoes, J. C., [MV] mds, [MV] mdslong,

[MV] mdsmatlist,

cluster subcommand, [MV] cluster utilityestat subcommand, [MV] discrim estat,

[MV] discrim knn postestimation,[MV] discrim lda postestimation, [MV] discrimlogistic postestimation, [MV] discrim qdapostestimation

loading plot, [MV] scoreplotloadingplot command, [MV] discrim lda

postestimation, [MV] factor postestimation,[MV] pca postestimation, [MV] scoreplot

loadings, estat subcommand, [MV] canonpostestimation, [MV] discrim ldapostestimation, [MV] pca postestimation

Loftsgaarden, D. O., [MV] discrim knnlogistic, discrim subcommand, [MV] discrim

logisticlogistic discriminant analysis, [MV] discrim logisticLumley, T., [MV] factor, [MV] pcaLuniak, M., [MV] biplotLurie, M. B., [MV] manova

MMahalanobis, P. C., [MV] discrim lda, [MV] hotellingmain effects, [MV] manovaMANCOVA, [MV] manovaManly, B. F. J., [MV] discrim qda postestimationMANOVA, [MV] manovamanova command, [MV] manovamanova, estat subcommand, [MV] discrim lda

postestimationmanovatest command, [MV] manova postestimationMardia, K. V., [MV] discrim, [MV] discrim lda,


matching coefficient similarity measure,[MV] measure option

matrices,correlation, [MV] pcacovariance, [MV] pcadissimilarity, [MV] matrix dissimilaritydistances, [MV] matrix dissimilaritysimilarity, [MV] matrix dissimilarity

matrix command, [MV] matrix dissimilaritymaximum likelihood estimation, [MV] factormaximum value dissimilarity measure,

[MV] measure optionMaxwell, A. E., [MV] factor, [MV] factor

postestimationmca command, [MV] mcamcaplot command, [MV] mca postestimation

mcaprojection command, [MV] mca postestimationMcLachlan, G. J., [MV] discrim, [MV] discrim estat,

[MV] discrim knn, [MV] discrim ldamds command, [MV] mdsmdsconfig, estat subcommand, [MV] mds

postestimationmdslong command, [MV] mdslongmdsmat command, [MV] mdsmatmdsshepard, estat subcommand, [MV] mds

postestimationmeans, testing equality, [MV] hotelling, [MV] manovameasures, cluster subcommand, [MV] cluster

programming utilitiesmedian-linkage clustering, [MV] cluster, [MV] cluster

linkage, [MV] clustermatmedianlinkage, cluster subcommand, [MV] cluster

linkageMichener, C. D., [MV] measure optionMickey, M. R., [MV] discrim estatMilan, L., [MV] ca, [MV] factor, [MV] mca,

[MV] pcaMilligan, G. W., [MV] cluster, [MV] cluster

programming subroutines, [MV] cluster stopMilliken, G. A., [MV] manovaMinkowski dissimilarity measure,

[MV] measure optionmixed designs, [MV] manovaMorrison, D. F., [MV] clustermat, [MV] discrim lda,

[MV] discrim logistic, [MV] discrim logisticpostestimation, [MV] manova

Mosier, C. I., [MV] procrustesMueller, C. W., [MV] factorMueller, R. O., [MV] discrim ldaMuirhead, R. J., [MV] pcaMulaik, S. A., [MV] factormultidimensional scaling, [MV] mds, [MV] mds

postestimation, [MV] mdslong, [MV] mdsmatmultivariate analysis, [MV] canon, [MV] hotelling

of covariance, [MV] manovaof variance, [MV] manova

Murrill, W. A., [MV] discrim knnmvreg, estat subcommand, [MV] procrustes

postestimation

NN-way multivariate analysis of variance, [MV] manovaNagel, R., [MV] discrim ldanearest neighbor, [MV] discrim knnNelson, E. C., [MV] factor, [MV] factor

postestimationnested

designs, [MV] manovaeffects, [MV] manova

Nevels, K., [MV] procrustesNiemann, H., [MV] mdsmatNordlund, D. J., [MV] discrim lda


notes, cluster analysis, [MV] cluster notesnotes, cluster subcommand, [MV] cluster notes

Ooblimax rotation, [MV] rotate, [MV] rotatematoblimin rotation, [MV] rotate, [MV] rotatematoblique rotation, [MV] factor postestimation,

[MV] rotate, [MV] rotatematOchiai, A., [MV] measure optionOchiai coefficient similarity measure,

[MV] measure optionOdum, E. P., [MV] clustermatOlkin, I., [MV] hotellingorthogonal rotation, [MV] factor postestimation,

[MV] rotate, [MV] rotatemat

Ppairwise, estat subcommand, [MV] mds

postestimationparsedistance, cluster subcommand, [MV] cluster

programming utilitiesparsimax rotation, [MV] rotate, [MV] rotatematpartial target rotation, [MV] rotate, [MV] rotatematpartition cluster-analysis methods, [MV] cluster kmeans

and kmedianspca command, [MV] pcapcamat command, [MV] pcaPearson coefficient similarity measure,

[MV] measure optionPearson, K., [MV] mds, [MV] measure option,

[MV] pcaPeen, C., [MV] procrustesPerrin, E., [MV] factor, [MV] factor postestimationPillai, K. C. S., [MV] canon, [MV] manovaPillais trace statistic, [MV] canon, [MV] manovapredict command, [MV] factor postestimation,

[MV] pca postestimationprincipal

component analysis, [MV] pcafactors analysis, [MV] factor

procoverlay command, [MV] procrustespostestimation

procrustes, [MV] procrustesrotation, [MV] procrustes

procrustes command, [MV] procrustesrotation, profiles, estat subcommand, [MV] ca

postestimationprogramming

cluster subcommands, [MV] cluster programmingsubroutines

cluster utilities, [MV] cluster programmingsubroutines

rotations, [MV] rotateprogramming, cluster analysis, [MV] cluster

programming utilitiespromax rotation, [MV] rotate, [MV] rotatemat

QQDA, [MV] discrim qdaqda, discrim subcommand, [MV] discrim qdaquadratic discriminant analysis, [MV] discrim qdaquantiles, estat subcommand, [MV] mds

postestimationquartimax rotation, [MV] rotate, [MV] rotatematquartimin rotation, [MV] rotate, [MV] rotatematquery, cluster subcommand, [MV] cluster

programming utilitiesQuesenberry, C. P., [MV] discrim knn

RRabe-Hesketh, S., [MV] pca, [MV] screeplotRao, C. R., [MV] factor, [MV] hotelling,

[MV] manovaRao, T. R., [MV] measure optionRaos canonical-factor method, [MV] factorreciprocal averaging, [MV] careconstructed correlations, [MV] factor postestimationregression scoring, [MV] factor postestimationreliability, [MV] factorrename, cluster subcommand, [MV] cluster utilityrenamevar, cluster subcommand, [MV] cluster

utilityRencher, A., [MV] mcaRencher, A. C., [MV] biplot, [MV] ca, [MV] candisc,

[MV] canon, [MV] canon postestimation,[MV] cluster, [MV] discrim, [MV] discrimestat, [MV] discrim knn, [MV] discrim lda,[MV] discrim lda postestimation, [MV] discrimlogistic, [MV] discrim qda, [MV] discrim qdapostestimation, [MV] factor, [MV] manova,[MV] pca, [MV] screeplot

repeated measures MANOVA, [MV] manovaresiduals, estat subcommand, [MV] factor

postestimation, [MV] pca postestimationRogers and Tanimoto similarity measure,

[MV] measure optionRogers, D. J., [MV] measure optionRohlf, F. J., [MV] clusterRomney, A. K., [MV] caRose, D. W., [MV] discrim knnrotate command, [MV] factor postestimation,

[MV] pca postestimation, [MV] rotate,[MV] rotatemat

rotate, estat subcommand, [MV] canonpostestimation

rotatecompare, estat subcommand, [MV] canonpostestimation, [MV] factor postestimation,[MV] pca postestimation

rotated factor loadings, [MV] factor postestimationrotated principal components, [MV] pca postestimationrotation, [MV] factor postestimation, [MV] pca

postestimation, [MV] rotate, [MV] rotatematprocrustes, [MV] procrustes


rotation, continuedtoward a target, [MV] procrustes, [MV] rotate,

[MV] rotatematRothkopf, E. Z., [MV] mdslongRousseeuw, P. J.,

[MV] cluster, [MV] clustermat, [MV] matrixdissimilarity, [MV] measure option

Roy, S. N., [MV] canon, [MV] manovaRoys

largest root test, [MV] canon, [MV] manovaunion-intersection test, [MV] canon, [MV] manova

Russell and Rao coefficient similarity measure,[MV] measure option

Russell, P. F., [MV] measure option

SSammon, J. W., [MV] mds, [MV] mdslong,

[MV] mdsmatSampson, A. R., [MV] hotellingscaling, [MV] mds, [MV] mds postestimation,

[MV] mdslong, [MV] mdsmatSchaffer, C. M., [MV] clusterSchwarz, G., [MV] factor postestimationscore plot, [MV] scoreplotscoreplot command, [MV] discrim lda

postestimation, [MV] factor postestimation,[MV] pca postestimation, [MV] scoreplot

scoring, [MV] factor postestimation, [MV] pcapostestimation

scree plot, [MV] screeplotscreeplot command, [MV] discrim lda

postestimation, [MV] factor postestimation,[MV] mca postestimation, [MV] pcapostestimation, [MV] screeplot

Seber, G. A. F., [MV] biplot, [MV] manovaset, cluster subcommand, [MV] cluster

programming utilitiesShepard

diagram, [MV] mds postestimationplot, [MV] mds postestimation

Sibson, R., [MV] clustersimilarity

matrices, [MV] matrix dissimilaritymeasures, [MV] cluster, [MV] cluster

programming utilities, [MV] matrixdissimilarity, [MV] measure optionAnderberg coefficient, [MV] measure optionangular, [MV] measure optioncorrelation, [MV] measure optionDice coefficient, [MV] measure optionGower coefficient, [MV] measure optionHamann coefficient, [MV] measure optionJaccard coefficient, [MV] measure optionKulczynski coefficient, [MV] measure optionmatching coefficient, [MV] measure optionOchiai coefficient, [MV] measure option

similarity, continuedPearson coefficient, [MV] measure optionRogers and Tanimoto coefficient,

[MV] measure optionRussell and Rao coefficient,

[MV] measure optionSneath and Sokal coefficient,

[MV] measure optionYule coefficient, [MV] measure option

single-linkage clustering, [MV] cluster, [MV] clusterlinkage, [MV] clustermat

singlelinkage, cluster subcommand, [MV] clusterlinkage

smc, estat subcommand, [MV] factor postestimation,[MV] pca postestimation

Smith, C. A. B., [MV] discrim estat, [MV] discrimqda

Smith, H., [MV] manovaSmith-Vikos, T., [MV] discrim knnSmullyan, R., [MV] mdsSneath and Sokel coefficient similarity measure,

[MV] measure optionSneath, P. H. A., [MV] measure optionSokal, R. R., [MV] measure optionSorbom, D., [MV] factor postestimationSrensen, T., [MV] measure optionSpath, H., [MV] clusterSpearman, C., [MV] factorspecificity, [MV] factorsplit-plot designs, [MV] manovasquared multiple correlations, [MV] factor

postestimationstopping rules

adding, [MV] cluster programming subroutinesCalinski and Harabasz index, [MV] cluster,

[MV] cluster stopDuda and Hart index, [MV] cluster, [MV] cluster

stopstepsize, [MV] cluster programming subroutines

stress, [MV] mds postestimationstress, estat subcommand, [MV] mds

postestimationstructure, estat subcommand, [MV] discrim lda

postestimation, [MV] factor postestimationsubinertia, estat subcommand, [MV] mca

postestimationsubroutines, adding, [MV] cluster programming

utilitiessummarize, estat subcommand, [MV] ca

postestimation, [MV] discrim estat,[MV] discrim knn postestimation,[MV] discrim lda postestimation, [MV] discrimlogistic postestimation, [MV] discrim qdapostestimation, [MV] factor postestimation,[MV] mca postestimation, [MV] mdspostestimation, [MV] pca postestimation,[MV] procrustes postestimation

summary variables, generating, [MV] cluster generate


TTabachnick, B. G., [MV] discrim, [MV] discrim ldatable command, [MV] ca postestimationTanimoto, T. T., [MV] measure optiontarget rotation, [MV] procrustes, [MV] rotate,

[MV] rotatematTarlov, A. R., [MV] factor, [MV] factor postestimationten Berge, J. M. F., [MV] procrustesThompson, B., [MV] canon postestimationThomson, G. H, [MV] factor postestimationThomson scoring, [MV] factor postestimationThurstone, L. L., [MV] rotateTibshirani, R., [MV] discrim knnTimm, N. H., [MV] manovaTorgerson, W. S., [MV] mds, [MV] mdslong,

[MV] mdsmattransformation, [MV] procrustestrees, [MV] cluster, [MV] cluster dendrogramTrewn, J., [MV] mdsttest command, [MV] hotellingtwo-way multivariate analysis of variance,

[MV] manovaTyler, D. E., [MV] pca

Uuse, cluster subcommand, [MV] cluster utilityutilities, programming, [MV] cluster utility

Vvan Belle, G., [MV] factor, [MV] pcaVan der Heijden, P. G. M., [MV] ca postestimationvariables, generate, summary, or grouping, [MV] cluster

generatevariance analysis, [MV] manovavarimax rotation, [MV] rotate, [MV] rotatemat

WWard, J. H., Jr., [MV] clusterWards linkage clustering, [MV] cluster linkagewards-linkage clustering, [MV] cluster,

[MV] clustermatwards method clustering, [MV] cluster,

[MV] clustermatwardslinkage, cluster subcommand, [MV] cluster

linkageWare, J. E., Jr., [MV] factor, [MV] factor

postestimationwaveragelinkage, cluster subcommand,

[MV] cluster linkageWeesie, J., [MV] ca postestimation, [MV] pcaweighted-average linkage clustering, [MV] cluster,

[MV] cluster linkage, [MV] clustermatWeiss, J., [MV] mdsmatWeller, S. C., [MV] ca

White, P. O., [MV] rotate, [MV] rotatematWhittaker, J., [MV] ca, [MV] factor, [MV] mca,

[MV] pcaWichern, D. W., [MV] canon, [MV] discrim,

[MV] discrim estat, [MV] discrim lda,[MV] discrim lda postestimation

Wilkslambda, [MV] canon, [MV] manovalikelihood-ratio test, [MV] canon, [MV] manova

Wilks, S. S., [MV] canon, [MV] hotelling,[MV] manova

Williams, W. T., [MV] clusterWilliams, B. K., [MV] discrim ldaWish, M., [MV] mds, [MV] mdslong, [MV] mdsmatWoodard, D. E., [MV] manova

YYang, K., [MV] mdsYoung, F. W., [MV] mds, [MV] mdslong,

[MV] mdsmatYoung, G., [MV] mds, [MV]

stata multivariate statistics reference manual release 10

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