• ###### 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)
• ###### Vectors
• The definition of elliptical distributions for real random-vectors has been extended to accommodate random vectors in Euclidean spaces over the field of complex numbers, so facilitating applications in time-series analysis. (wikipedia.org)
• ###### multidimensional
• In Multidimensional Scaling, Volume 1, Cox and Cox write that "Albert Gifi is the nom de plume of members, past and present, of the Department of Data Theory at the University of Leiden who devised a system of nonlinear multivariate analysis that extends various techniques, such as principal components analysis and canonical correlation analysis. (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)
• ###### canonical correlat
• Canonical correlation analysis: Uses and interpretation. (indiana.edu)
• ###### Observations
• Classification Analysis: Allocation of Observations to Groups. (ebooks.com)
• ###### 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)
• ###### latent
• Dr. Wallentin's program of research is on the theory and applications of latent variable modeling and other types of multivariate statistical analysis, particularly their applications in the social and behavioral sciences. (springer.com)
• ###### Data Analysis
• Hair, J. F. Jr. (1995) Multivariate Data Analysis with Readings, 4th ed. (wikipedia.org)
• Yet again Origin and OriginPro upholds its foremost status as the best purposeful and all-embracing data analysis and graphing software on the market. (adeptscience.co.uk)
• Although other software packages exist, few are as straightforward to use, flexible, and high-quality when it comes to performing challenging data analysis or creating publication superior graphs. (adeptscience.co.uk)
• ###### 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)
• ###### evaluate
• 2.To be able to objectively evaluate manuscripts in which selected MS analyses were employed. (indiana.edu)
• ###### extension
• A Multivariate Analysis and Extension of the Human Development Index ," Working Papers 2004-01, Utah State University, Department of Economics. (repec.org)
• ###### measurements
• The errors are usually assumed to be uncorrelated across measurements, and follow a multivariate normal distribution. (wikipedia.org)
• Linear and Nonlinear Models for the Analysis of Repeated Measurements. (wikipedia.org)
• ###### general
• The general linear model or multivariate regression model is a statistical linear model. (wikipedia.org)
• An application of the general linear model appears in the analysis of multiple brain scans in scientific experiments where Y contains data from brain scanners, X contains experimental design variables and confounds. (wikipedia.org)
• ###### measures
• A multivariate technique called principal component analysis is used to combine measures of human development. (repec.org)
• ###### thesis
• In 1973 he received his PhD cum laude with a thesis entitled "Canonical Analysis of Categorical Data" advised by John P. van de Geer. (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)
• ###### tests
• This analysis tests two models: model I excludes variables based on worker perceptions that were suspected to be endogenous with job satisfaction ( HHA feels valued by organization, Aide feels involved in challenging work, Aide feels trusted with patient care decisions, Aide feels confident in ability to do job, Time for ADLs, Satisfaction with hours, Aide feels respected by supervisor, Aide feels respected by patients ), while model II includes these variables. (hhs.gov)
• 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)
• ###### results
• 3.To carry out MS analyses of data by SAS software and to interpret the analysis results in written reports. (indiana.edu)
• The results showed that inclusion of the covariate allowed improved estimates of the trend against time to be obtained, compared to analyses which omitted the covariate. (wikipedia.org)
• The gametic disequilibria between all possible pairs of loci were examined for a set of eight codominant loci in each of fifty Yanomama villages, using a multivariate correlation analysis which reduces the results to a single measure of departure from multiple-locus-gametic equilibrium. (genetics.org)
• ###### uses
• Uses for multivariate analysis include: design for capability (also known as capability-based design) inverse design, where any variable can be treated as an independent variable Analysis of Alternatives (AoA), the selection of concepts to fulfil a customer need analysis of concepts with respect to changing scenarios identification of critical design-drivers and correlations across hierarchical levels. (wikipedia.org)
• method uses a multivariate test statistic for the summary table. (ethz.ch)
• ###### variables
• In design and analysis, the technique is used to perform trade studies across multiple dimensions while taking into account the effects of all variables on the responses of interest. (wikipedia.org)
• ###### polynomial
• For representing a multivariate polynomial that takes only non-negative values over the reals as a sum of squares of rational functions, see Hilbert's seventeenth problem. (wikipedia.org)
• ###### practice
• Classic parametric methods, like Pearson correlation coefficient, or least squares method produce comparable results only for comparable distribution types (in practice multivariate normal distribution is being assumed). (wikipedia.org)
• ###### Variance
• Common spatial pattern (CSP) is a mathematical procedure used in signal processing for separating a multivariate signal into additive subcomponents which have maximum differences in variance between two windows. (wikipedia.org)
• ###### Proteomics
• Shotgun proteomics can be used for functional classification or comparative analysis of these protein products. (wikipedia.org)
• ###### control
• Regression analyses, which control in various ways for precipitation, technological change, soils, and location-specific unobserved factors, all show a similar nonlinear relationship between temperature and yields. (pnas.org)
• As reported in Journal of the National Cancer Institute , Mehta and colleagues found that subjects in the highest (5th) quintile of plasma MIC-1 as measured by enzyme-linked immunosorbent assay had significantly increased risk of colorectal cancer (relative risk [RR] = 1.93, P = .004 for trend) compared with the lowest quintile on multivariate analysis in a nested case-control study. (ascopost.com)
• ###### study
• We report here the analysis of the GC-MS and 1H-NMR metabolomes of serum samples from a randomized cross-over study in 11 healthy volunteers having consumed isocaloric amounts of milk, cheese, and a soy drink as non-dairy alternative. (mdpi.com)
• A multivariate analysis of the untargeted serum metabolomes, combined with a targeted analysis of candidate FIBs previously reported in urine samples from the same study, identified galactitol, galactonate, and galactono-1,5-lactone (milk), 3-phenyllactic acid (cheese), and pinitol (soy drink) as candidate FIBs for these products. (mdpi.com)
• Low baseline plasma HGF levels among 310 patients with advanced clear-cell RCC correlated with overall survival (OS) in the patients treated with interferon-α (IFN-α) with or without bevacizumab-and plasma HGF levels remained prognostic at 4 weeks in multivariate analyses, reported the lead study author of the first study (abstract 4522 ), Daniel J. George, MD, of the Duke Cancer Institute in Durham, North Carolina. (cancernetwork.com)
• ###### Studies
• Finally, an analysis of the postprandial behavior of candidate FIBs, in particular the dairy fatty acids pentadecanoic acid and heptadecanoic acid, revealed specific kinetic patterns of relevance to their detection in future validation studies. (mdpi.com)
• ###### Results
• Other cryptographic results of Courtois include algebraic attacks on stream ciphers, attacks on the KeeLoq and Hitag 2 systems used for remote keyless automobile entry systems, and an analysis of cryptographic weaknesses in public transit smart cards including the London Underground Oyster card and the Dutch OV-chipkaart. (wikipedia.org)
• ###### signal
• Let X 1 {\displaystyle \mathbf {X} _{1}} of size ( n , t 1 ) {\displaystyle (n,t_{1})} and X 2 {\displaystyle \mathbf {X} _{2}} of size ( n , t 2 ) {\displaystyle (n,t_{2})} be two windows of a multivariate signal, where n {\displaystyle n} is the number of signals and t 1 {\displaystyle t_{1}} and t 2 {\displaystyle t_{2}} are the respective number of samples. (wikipedia.org)
• ###### Principal
• If there is only one window, R 2 {\displaystyle \mathbf {R} _{2}} can be considered as the identity matrix and then CSP corresponds to Principal component analysis. (wikipedia.org)
• ###### Time Series A
• Her habilitation thesis, titled "Trend Estimation Problems in Time Series Analysis", was accepted in 1973. (wikipedia.org)
• ###### report
• Another report on RCC biomarker development (abstract 4523 ) involved an analysis of the correlation of PBRM1 and BAP1 mutations with angiogenesis expression signatures in patients on first-line tyrosine kinase inhibitor (TKI) therapy, by Martin H. Voss, MD, and colleagues at Memorial Sloan Kettering Cancer Center in New York. (cancernetwork.com)
• ###### According
• According to R. Blutner and E. Hochnadel, "socionics is not so much a theory of personalities per se, but much more a theory of type relations providing an analysis of the relationships that arise as a consequence of the interaction of people with different personalities. (wikipedia.org)