Some distance properties of latent root and vector methods used in multivariate analysis
Gower, J.C.
Some distance properties of latent root and vector methods used in multivariate analysis - United Kingdom : Oxford University Press, 1966. - Printed
This paper is concerned with the representation of a multivariate sample of size n as points P1, P2, …, Pn in a Euclidean space. The interpretation of the distance Δ(Pi, Pj) between the ith and jth members of the sample is discussed for some commonly used types of analysis, including both Q and R techniques. When all the distances between n points are known a method is derived which finds their co-ordinates referred to principal axes. A set of necessary and sufficient conditions for a solution to exist in real Euclidean sapce is found. Q and R techniques are defined as being dual to one another when they both lead to a set of n points with the same inter-point distances. Pairs of dual techniques are derived. In factor analysis the distances between points whose co-ordinrates are the estimated factor scores can be interpreted as D2 with a singular dispersion matrix.
Text in English
0006-3444 1464-3510 (Online)
https://doi.org/10.1093/biomet/53.3-4.325
Methods
Statistical data
Analysis of variance
Some distance properties of latent root and vector methods used in multivariate analysis - United Kingdom : Oxford University Press, 1966. - Printed
This paper is concerned with the representation of a multivariate sample of size n as points P1, P2, …, Pn in a Euclidean space. The interpretation of the distance Δ(Pi, Pj) between the ith and jth members of the sample is discussed for some commonly used types of analysis, including both Q and R techniques. When all the distances between n points are known a method is derived which finds their co-ordinates referred to principal axes. A set of necessary and sufficient conditions for a solution to exist in real Euclidean sapce is found. Q and R techniques are defined as being dual to one another when they both lead to a set of n points with the same inter-point distances. Pairs of dual techniques are derived. In factor analysis the distances between points whose co-ordinrates are the estimated factor scores can be interpreted as D2 with a singular dispersion matrix.
Text in English
0006-3444 1464-3510 (Online)
https://doi.org/10.1093/biomet/53.3-4.325
Methods
Statistical data
Analysis of variance