
Review of Short Phrases and Links 
This Review contains major "Multivariate" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 A multivariate is a vector each of whose elements is a variate.
 The term "multivariate" is also used as an adjective to mean involving many variables, as opposed to one ( univariate) or two ( bivariate).
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 Returned multivariate is a vector multivariate representing the cross product of the two given multivariates.
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 Multivariate is a concept from statistics.
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 The term "multivariate" is also used as an adjective to mean involving many variables, as opposed to one ( univariate) or two ( bivariate).
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 Jim Ramsay is Professor of Psychology at McGill University and is an international authority on many aspects of multivariate analysis.
 Variable selection, functional data analysis, nonparametric smoothing, multivariate analysis, and quasimonte carlo method.
 We could now perform a multivariate analysis of variance (MANOVA) to test this hypothesis.
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 A multivariate analysis of variance (MANOVA) approach is proposed for studies with two or more experimental conditions.
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 Multivariate analysis of variance (MANOVA) is used when there is more than one dependent variable.
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 In statistics, a latent class model (LCM) relates a set of observed discrete multivariate variables to a set of latent variables.
 Algina, J. (1994). Some alternative approximate tests for a split plot design: Multivariate Behavioral Research Vol 29(4) 1994, 365384.
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 Pln: Multivariate plane to free.
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 Index: To decompose into the different axes of the multivariate.
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 Increment the index of the control mesh of the multivariate function by one.
 The multivariate social scientist: Introductory statistics using generalized linear models.
 Handbook of multivariate experimental psychology (2nd ed.).
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 Anderson, T. W. (1984). An introduction to multivariate statistical analysis (2 nd ed.).
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 Raykov, T. (2001). Testing multivariate covariance structure and means hypotheses via structural equation modeling.
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 Multivariate regression and simultaneous equation models with some dependent variables truncated.
 Maas, C.J.M. & Hox, J.J. (2003). Multilevel structural equation models: The limited information and the multivariate multilevel approach.
 MV1, MV2: Two multivariate to multiply coordinatewise.
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 MV1, MV2: Two multivariate to subtract coordinatewise.
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 MV: Multivariate to increase its order in direction Dir.
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 MV: Multivariate to derive a cone bounding its normal spaace.
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 MvarMVStruct *: A multivariate with same geometry as MV but with one degree higher.
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 QSAR is often taken to be equivalent to chemometrics or multivariate statistical data analysis.
 Summary of univariate categorical data analysis; introduction to multivariate analysis of categorical epidemiologic data using multiplicative models.
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 Stevens, J. (1996). Applied multivariate statistics for the social sciences (3rd ed.).
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 Multivariate techniques commonly used in the social and behavioral sciences.
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 STAT 524 Applied Multivariate Analysis (3 cr.) P: 528 or equivalent, or consent of instructor.
 Steiger, J.H., Shapiro, A., & Browne, M.W. (1985). On the multivariate asymptotic distribution of sequential chisquare statistics.
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 Stevens, J. (1986). Applied multivariate statistics for the social sciences.
 Applications are given for vector autoregression (VAR) models of unknown order and multivariate spline models with unknown knot points.
 MVs: Vector of multivariate constraints.
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 Gower, J. C. 1966. Some distance properties of latent root and vector methods used in multivariate analysis.
 Each element of obs is then a vector (for univariate distributions) or a matrix (for multivariate distributions).
 Both approaches assume that the vector of log ratios of gene expression y(t) follows a multivariate normal distribution.
 Builds a gradient for the given scalar multivariate.
 MvarMVStruct *: A rational scalar multivariate that is equal to the reciprocal value of MV.
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 SHORT
suppresses all default output from the canonical analysis except the tables of canonical correlations and multivariate statistics.
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 In L. Grimm & P. Yarnold (eds.), Reading and understanding more multivariate statistics (pp.261284).
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 The level of the course is intermediate; basic understanding of matrix algebra and multivariate statistics is a prerequisite.
 Using Multivariate Statistics provides practical guidelines for conducting numerous types of multivariate statistical analyses.
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 In L. Grimm & P. Yarnold (eds.), Reading and understanding more multivariate statistics (pp.261284).
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 Dim: Number of dimensions of this multivariate.
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 NewDim: New dimension of the promoted multivariate.
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 Canonical correlation is a generalization of MANOVA, MANCOVA, and multivariate multiple regression.
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 Topics covered including multivariate analysis of variance, discriminant analysis, canonical correlation analysis and principal components analysis.
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 Canonical correlation is a generalization of MANOVA, MANCOVA, and multivariate multiple regression.
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 Canonical correlation, multivariate analysis of variance, and multivariate regressions.
 Canonical correlation is a well understood notion in multivariate statistics.
 MV: Bspline multivariate to convert to open end conditions.
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 Returns TRUE iff the given Bspline multivariate has open end coditions in all direction directions.
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 In multivariate designs, with multiple dependent measures, the homogeneity of variances assumption described earlier also applies.
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 Multivariate statistical testing for the homogeneity of covariance matrices by the Box's M.
 Overview. When there are multiple dependent variables in a design, the design is said to be multivariate.
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 Ttest, univariate ANOVA, and multivariate MANOVA.
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 The paper covers multivariate and univariate approaches to multiple comparison procedures, interactions, interaction contrasts, and mixed designs.
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 MvarPolyStruct *: Merged as possible multivariate polylines.
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 MvarPolyStruct *: Connected multivariate polylines, upto MaxTol tolerance.
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 Converts a surface into a multivariate function.
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 MV: A multivariate of dimension one to convert to a curve.
 Converts the given multivariate from Power basis functions to Bezier basis functions.
 Using Multivariate Statistics provides practical guidelines for conducting numerous types of multivariate statistical analyses.
 DataRevelation  Software for automatic, multivariate statistical modeling.
 Teaches how to understand more advanced multivariate statistical methods and how to use statistical software to get the correct results.
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 Therefore its methodology is appropriately complex and often, particularly in American sociology, dominated by multivariate statistical methods of analysis.
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 Factor analysis is mentioned here as one example of the many multivariate statistical methods used by educational psychologists.
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 Two main approaches have been used, which focus either on the amounts of variation or on covariance structures of multivariate features such as shape.
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 Fouladi, R.T. (2000) Performance of modified test statistics in covariance and correlation structure analysis under conditions of multivariate nonnormality.
 Multivariate distributions and notion of invariance in statistical inference.
 Multivariate analysis; linear models; statistical inference; biometrics.
 Engle, R.F., 2002, Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models.
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 Bollerslev, T., 1990, Modelling the coherence in shortrun nominal exchange rates: A multivariate generalized ARCH model.
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 Chameleon Statistics  Multivariate data analysis and visualisation software.
 To become familiar with the techniques for writing up reports of multivariate analyses using the format of the American Psychological Association.
 Returned multivariate is a vector multivariate representing the cross product of the two given multivariates.
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 This product and related ones from CAMO are proven tools that have enabled different organizations solve their Multivariate Analysis requirements.
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 Given a multivariate and a vector  computes their dot product.
 Extract an isoparametric sub multivariate out of the given tensor product multivariate, or expand its dimension by one.
 Bock, R. D., and Haggard, E. A. The use of multivariate analysis of variance in behavioral research.
 In this paper, multivariate analysis of variance (MANOVA) and discriminant analysis (DA) are used.
 Hummel, T. J., & Sligo, J. R. (1971) Empirical comparison of univariate and multivariate analysis of variance procedures.
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 Multivariate distributions Descriptive measures: cov() and cor() in stats will provide estimates of the covariance and correlation matrices respectively.
 Multivariate distributions with correlation matrices for nonlinear repeated measurements.
 Fouladi, R.T. (2000) Performance of modified test statistics in covariance and correlation structure analysis under conditions of multivariate nonnormality.
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 Polys: Multivariate polylines to merge, in place.
 Reverses a list of multivariate points, in place.
 Multivariate analysis of variance and repeated measures.
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 Doubly multivariate design are analyzed using a combination of univariate repeated measures and multivariate analysis techniques.
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 Thus it provides, e.g., a way to achieve a fully multivariate analysis of repeated measures with incomplete data.
 Overall, the analysis of these data, using both univariate and multivariate analyses, highlights a key point.
 There are three varieties of the general linear model available in SPSS: univariate, multivariate, and repeated measures.
 His statistical contributions can be divided into ways of arranging numerical facts  univariate and multivariate  estimation and testing.
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 GLM will compute all the standard results, including ANOVA tables with univariate and multivariate tests, descriptive statistics, etc.
 WERMUTH, N., COX, D. and PEARL, J. (1999). Explanations for multivariate structures derived from univariate recursive regressions.
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 The derivation of the maximumlikelihood estimator of the covariance matrix of a multivariate normal distribution is subtle.
 Introduction to multivariate normal distribution and linear models.
 Shrinkage preliminary test estimation in multivariate normal distributions.
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 The derivation of the maximumlikelihood estimator of the covariance matrix of a multivariate normal distribution is perhaps surprisingly subtle and elegant.
 Free a multivariate normal cone structure.
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 Some of the most common multivariate methods are cluster analysis, conjoint analysis, factor analysis, multidimensional scaling.
 Typical multivariate statistics and techniques include factor analysis, cluster analysis and multidimensional scaling.
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 Srf1, Srf2: The two surfaces, Srf1(u, v) and Srf2(r, t), to form their distance function square between them as a multivariate function.
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 Crv1, Srf2: The two entities, Crv1(t) and Srf2(u, v), to form their distance function square between them as a multivariate function.
 It is closely related to Hotelling's Tsquare distribution used for multivariate statistical testing.
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 Multivariate normal, Wishart's and Hotelling's distributions.
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 STATISTICA Partial Least Squares (PLS) offers a selection of algorithms for univariate and multivariate partial least squares problems.
 The dse1 and dse2 packages in the dse bundle provide a variety of more advanced estimation methods and multivariate time series analysis.
 This course focuses on regression modelling and multivariate analysis.
 The impact of general nonparametric volatility functions in multivariate GARCH models.
 Multivariate analysis, mathematical statistics.
 Because the x axis often represents time you may also view the analysis of these data as falling in the category of multivariate time series.
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 Estimating common trends in multivariate time series using dynamic factor analysis.
 Mahalanobis distance is a measure of distance relative to the variation in each direction of the multivariate space [48].
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 The used discriminant analysis is based on Principal Component Analysis with Mahalanobis Distance (PCAMD)  part of multivariate analysis.
 Mardia's statistic is a test for multivariate normality.
 Structural equation modeling and certain other procedures assume multivariate normality.
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 Little is known about the effects of violations of the multivariate normality assumption.
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 Mardia's statistic is a test for multivariate normality.
 This test is very sensitive to meeting also the assumption of multivariate normality.
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Multivariate
 Univariate methods examine the distribution of a single variable; multivariate methods describe relationships among two or more variables.
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 Free. Stata  Data analysis, management, graphics, matrix language, linear models, survey statistics, multivariate methods, multinomial and probit.
 The term "multivariate" is also used as an adjective to mean involving many variables, as opposed to one (univariate) or two (bivariate).
 Research interests: Analysis of discrete data, multivariate analysis, generalized linear modelling, SPlus, graphical methods, statistical consulting.
 PtsList: Point list to connect into multivariate polylines.
 Two closely related techniques, principal component analysis and factor analysis, are used to reduce the dimensionality of multivariate data.
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 Multivariate denoising using wavelets and principal component analysis.
 Gorsuch R., Common factor analysis versus component analysis: Some well and little known facts, Multivariate Behavioral Research, 25, 1990, 3339.
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 These distributions are of great importance in the estimation of covariance matrices in multivariate statistics.
 Relaxing the assumption of normality, nonparametric and robust methods in multivariate statistics.
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 Efron, B. and Morris, C. (1976). Multivariate empirical Bayes and estimation of covariance matrices.
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 Principal component analysis is a technique often found to be useful for identifying structure in multivariate data.
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 Multivariate data analysis (3rd ed.).
 Thompson (1999) also criticized researchers who perform several univariate analyses to analyze multivariate data.
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 The authors also estimate the likelihood of catastrophic expenditures using multivariate regression analysis.
 A range of Java, Fortran and C programs for multivariate analysis.
 Multivariate regression describes models that have more than one response variable.
 Structural Equation Modeling (Multivariate Regression) with PROC CALIS [2], assumes that both dependent variables are continuous.
 This statistic is useful in multivariate regression (i.e., multiple independent variables) when you want to describe the relationship between the variables.
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 The general linear model (or multivariate regression model) is a linear model with multiple measurements per object.
 See multiple regression and multivariate regression.
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 The procedure analyzes and forecasts multivariate time series using the state space model.
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 The state space approach to modeling a multivariate stationary time series is summarized in Akaike (1976).
 With multivariate testing, the system randomly selects a version of each variable every time a new visitor comes to the sales page.
 Doubly multivariate design are analyzed using a combination of univariate repeated measures and multivariate analysis techniques.
 Multivariate analysis techniques, a type of statistics incorporating many variables, are frequently used to examine landscape level vegetation patterns.
 Multivariate analysis techniques include cluster analysis, discriminant analysis, and multiple regression analysis.
 A multivariate technique of analysis that examines the ability of predictor variables to discriminate (i.e.
 In the multivariate case, a test about several parameters at once is carried out using a variance matrix [2].
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 That concept is extended to the multivariate case as follows.
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 The notion of the univariate divided differences is generalized to the multivariate case.
 Selected topics in multivariate distributions.
 Created by Brown, bsta provided a generic programming hierarchy (using templates) for both univariate and multivariate distributions.
 If a multivariate method fails to find a comprehensible pattern it may be because such a pattern does not exist within the data.
 Another, and possibly more robust, method of checking for multicollinearity is to carefully compare the results from bivariate and multivariate regressions.
 A new method for the elimination of uninformative variables in multivariate data sets is proposed.
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