• Gaussian
• If the vector pd1 is Gaussian multivariate-distributed with zero mean and unit covariance matrix N(p01,pIp) and pMp is a p x p matrix with unit scale matrix and m degrees of freedom with a Wishart distribution W(pIp,m), then the Quadratic form m(1dT p M−1pd1) has a Hotelling T2(p,m) distribution with dimensionality parameter p and m degrees of freedom. (wikipedia.org)
• mathbf {X} )}} has a W − 1 ( A + Ψ , n + ν ) {\displaystyle {\mathcal {W}}^{-1}({\mathbf {A} }+{\mathbf {\Psi } },n+\nu )} distribution, where A = X X T {\displaystyle {\mathbf {A} }=\mathbf {X} \mathbf {X} ^{T}} . Because the prior and posterior distributions are the same family, we say the inverse Wishart distribution is conjugate to the multivariate Gaussian. (wikipedia.org)
• differences
• The multivariate aspect of the MANCOVA allows the characterisation of differences in group means in regards to a linear combination of multiple dependent variables, while simultaneously controlling for covariates. (wikipedia.org)
• This multivariate technique accounts for differences in the variances of component indexes as well as interdependence among the component indexes. (repec.org)
• multilevel analysis
• De Leeuw is coauthor of Introducing Multilevel Modeling (1998) and co-editor of the "Handbook of Multilevel Analysis" (2009). (wikipedia.org)
• Introducing Multilevel Modeling Handbook of Multilevel Analysis De Leeuw's Rpub Page De Leeuw's Research Gate Page homals on CRAN. (wikipedia.org)
• chapters
• Other chapters consider the topics of eigenstructures and linear transformations that are important to the understanding of multivariate techniques. (elsevier.com)
• Vector
• Representing a major improvement upon the standard "black box" approach to analyzing economic model structure, it introduces the powerful concept of parameter sensitivity analysis within a linear systems root/vector framework. (google.com)
• procedure
• As a multivariate procedure, it is used when there are two or more dependent variables, and is typically followed by significance tests involving individual dependent variables separately. (wikipedia.org)
• examples
• To illustrate multivariate applications, the author provides examples and exercises based on fifty-nine real data sets from a wide variety of scientific fields. (ebooks.com)
• researchers
• Multivariate analysis enables researchers to explore the joint performance of such variables and to determine the effect of each variable in the presence of the others. (ebooks.com)
• Longitudinal analysis-Repeated measure designs allow researchers to monitor how participants change over time, both long- and short-term situations. (wikipedia.org)
• Techniques
• Fully integrated model building combines Quality Analyst's exceptional database connectivity capabilities with Pirouette's comprehensive multivariate modeling techniques. (adeptscience.co.uk)