The Theory and Application of Canonical Trend Surfaces

The theory of canonical correlation analysis has been combined with that of trend-surface analysis in order to construct a multivariate trend surface that is called a canonical trend surface. A canonical trend surface is a parsimonious summarization of areal variations of a set of geologic variates. This trend has a property of maximum correlation between variates and geographic coordinates. It does not show the absolute value of each variate, but it shows the nature of variation of a linear function of the variates. By use of this type of trend, it is possible to reveal the underlying pattern of geographic variation common to a set of variates. The Permian system in western Kansas and eastern Colorado was studied as a numerical example to illustrate the general procedures in solving practical problems and also to demonstrate the validity of this technique.

[1]  C. Pelto,et al.  Mapping of Multicomponent Systems , 1954, The Journal of Geology.

[2]  R. Cassie,et al.  Fauna and sediments of an intertidal mud flat: A multivariate analysis , 1968 .

[3]  H. Hotelling.  Relations Between Two Sets of Variates , 1936 .

[4]  H. Hotelling.  The relations of the newer multivariate statistical methods to factor analysis. , 1957 .

[5]  Frederick V. Waugh,et al.  Regressions between Sets of Variables , 1942 .

[6]  E. McKee,et al.  Paleotectonic investigations of the Permian system in the United States , 1967 .

[7]  P. Hsu,et al.  ON THE LIMITING DISTRIBUTION OF THE CANONICAL CORRELATIONS , 1941 .

[8]  S. C. Pearce,et al.  Some applications of multivariate methods in botany. , 1960 .

[9]  William Meredith,et al.  Canonical correlations with fallible data , 1964 .

[10]  A. E. Maxwell.  Canonical Variate Analysis When the Variables are Dichotomous , 1961 .

[11]  M. S. Bartlett,et al.  The General Canonical Correlation Distribution , 1947 .

[12]  M. Kendall.  A course in multivariate analysis , 1958 .

[13]  W. C. Krumbein.  Open and Closed Number Systems in Stratigraphic Mapping , 1962 .

[14]  G. Tintner.  Some Applications of Multivariate Analysis to Economic Data , 1946 .

[15]  A. G. Constantine,et al.  On the General Canonical Correlation Distribution , 1958 .

[16]  J. G. Skellam,et al.  Multivariate Statistical Analysis for Biologists , 1965 .

[17]  Harry R. Glahn,et al.  Canonical Correlation and Its Relationship to Discriminant Analysis and Multiple Regression , 1968 .

[18]  M. Buzas.  The discrimination of morphological groups of Elphidium (Foraminifer) in Long Island Sound through canonical analysis and invariant characters , 1966 .

[19]  Calyampudi R. Rao.  Estimation and tests of significance in factor analysis , 1955 .

[20]  William J. Hill,et al.  A Review of Response Surface Methodology: A Literature Survey* , 1966 .

[21]  Maxwell Ae,et al.  Differentiation of clinical groups using canonical variates. , 1958 .

[22]  John Imbrie,et al.  FACTOR AND VECTOR ANALYSIS PROGRAMS FOR ANALYZING GEOLOGIC DATA , 1963 .

[23]  K. Jöreskog.  Some contributions to maximum likelihood factor analysis , 1967 .

[24]  A. Kshirsagar.  A note on direction and collinearity factors in canonical analysis , 1962 .

[25]  S. Kullback,et al.  Some Aspects of Multivariate Analysis. , 1958 .

[26]  G. Thomson.  THE MAXIMUM CORRELATION OF TWO WEIGHTED BATTERIES: (HOTELLING'S “MOST PREDICTABLE CRITERION”) , 1947 .

[27]  A. E. Maxwell,et al.  Factor Analysis as a Statistical Method. , 1964 .

[28]  P. J. Ebertein,et al.  A Jacobi-Like Method for the Automatic Computation of Eigenvalues and Eigenvectors of an Arbitrary Matrix , 1962 .

[29]  D. Lawley,et al.  TESTS OF SIGNIFICANCE IN CANONICAL ANALYSIS , 1959 .

[30]  G. Dunteman,et al.  A Canonical Correlational Analysis of the Strong Vocational Interest Blank and the Minnesota Multiphasic Personality Inventory for a Female College Population1 , 1967 .