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Geological Factor Analysis
389
These topics have been chosen to illustrate the d i c h o t o m y t hat continues to prevail in Archaean studies. It serves t o illustrate the value of meetings such as that held in Leicester where these differences can be debated. For those unable to attend in person, the present volume goes a long way towards compensating for their absence. Its publication will lead to a furt her burgeoning of e f f o r t and stimulate all those who are attempting, with varying degrees of success, to unlock the secrets of the early history of the Earth. D.R. H u n t e r University of Natal Pietermaritzburg
Geological Factor Analysis. K.G. JBreskog, J.E. Klovan and R.A. R e y m e n t . Elsevier, Amsterdam, 1976, xii + 178 pp, U.S.$ 23.25 (paperback). One may well w o n d e r w h e t h e r there is such a thing as a specifically
geological form of factor analysis. There is now nevertheless a book by that title and it is in m a n y respects a very good book. As might be expected, the first chapter tells w hy geologists ought to be interested in the subject. The concluding chapter reviews, very briefly and often rather uncritically, the work o f some geologists who are or have been interested in it. The intervening chapters say very little a bout geology. Chapter 2 is a splendid, though in places overcondensed, resum~ of those parts of matrix algebra directly applicable to factor analysis. Chapter 3 outlines the aims of factor analysis; Chapters 4 and 5 treat, respectively, R- and Q-mode analysis; and Chapter 6 is a blow-by-blow account of the kind o f thinking a naturalist should use in deciding w h e t h e r and how factor analysis should be applied to a specific problem. The b o o k would be a good t e x t for a one-semester advanced undergraduate or beginning graduate course taught by an instructor capable of fleshing o u t some o f its over-lean explications with classroom discussion, exercises, and extensive reading assignments. Mature readers who have already had some indoctrination in the statistical r e d u ctio n o f data will find the whole b o o k interesting and m uch of it helpful, but its utility for this class o f reader would have been vastly increased by inclusion o f a good index, for which even the rather full table of contents provided by the authors is n o t a viable substitute. In its present form I do n o t think the b o o k will be of m uc h use to the com pl et e autodidact, and that, alas, is still the class to which the current educational system assigns -- perhaps " c o n d e m n s " would be a more appropriate term -- most e m b r y o n i c statistical geologists. If its price can be br ought within reason -- even nowadays, $23.25 for a 178-p paperback seems unreasonable -- Geological Factor Analysis may well become a standard h a n d b o o k in this rapidly burgeoning field. Established geological workers should bear this in mind and feel no hesitation in
:~90 communicating suggestions to the authors for consideration in future editions~ The two currently uppermost in m y own mind are: (1) The desirability of a more perceptive treatment of the pros and cons of basing c o m p o n e n t or factor analyses on correlation as opposed to covariance matrices. In particular, the former are often said to be essential when the scales of measurement of the variables differ widely. The obverse of the coin, viz., that it is in fact reasonable to homogenize variances in this fashion, as for instance, in studies involving trace and major elements, is ordinarily accepted w i t h o u t discussion. It should not be, for it is often quite unreasonable. (2) The need for careful discussion of the extensive sampling variance of the coefficients of such functions as factors or principal components. The lack of a complete or readily understandable theory is no longer sufficient justification for evading this exceedingly important issue; its elucidation by simulation experiments is now entirely feasible. Geological Factor Analysis is the first volume of a planned series on Methods in Geomathematics. May succeeding volumes of the series maintain the same high standards of form and content! Felix Chayes Washington, D.C.
These topics have been chosen to illustrate the d i c h o t o m y t hat continues to prevail in Archaean studies. It serves t o illustrate the value of meetings such as that held in Leicester where these differences can be debated. For those unable to attend in person, the present volume goes a long way towards compensating for their absence. Its publication will lead to a furt her burgeoning of e f f o r t and stimulate all those who are attempting, with varying degrees of success, to unlock the secrets of the early history of the Earth. D.R. H u n t e r University of Natal Pietermaritzburg
Geological Factor Analysis. K.G. JBreskog, J.E. Klovan and R.A. R e y m e n t . Elsevier, Amsterdam, 1976, xii + 178 pp, U.S.$ 23.25 (paperback). One may well w o n d e r w h e t h e r there is such a thing as a specifically
geological form of factor analysis. There is now nevertheless a book by that title and it is in m a n y respects a very good book. As might be expected, the first chapter tells w hy geologists ought to be interested in the subject. The concluding chapter reviews, very briefly and often rather uncritically, the work o f some geologists who are or have been interested in it. The intervening chapters say very little a bout geology. Chapter 2 is a splendid, though in places overcondensed, resum~ of those parts of matrix algebra directly applicable to factor analysis. Chapter 3 outlines the aims of factor analysis; Chapters 4 and 5 treat, respectively, R- and Q-mode analysis; and Chapter 6 is a blow-by-blow account of the kind o f thinking a naturalist should use in deciding w h e t h e r and how factor analysis should be applied to a specific problem. The b o o k would be a good t e x t for a one-semester advanced undergraduate or beginning graduate course taught by an instructor capable of fleshing o u t some o f its over-lean explications with classroom discussion, exercises, and extensive reading assignments. Mature readers who have already had some indoctrination in the statistical r e d u ctio n o f data will find the whole b o o k interesting and m uch of it helpful, but its utility for this class o f reader would have been vastly increased by inclusion o f a good index, for which even the rather full table of contents provided by the authors is n o t a viable substitute. In its present form I do n o t think the b o o k will be of m uc h use to the com pl et e autodidact, and that, alas, is still the class to which the current educational system assigns -- perhaps " c o n d e m n s " would be a more appropriate term -- most e m b r y o n i c statistical geologists. If its price can be br ought within reason -- even nowadays, $23.25 for a 178-p paperback seems unreasonable -- Geological Factor Analysis may well become a standard h a n d b o o k in this rapidly burgeoning field. Established geological workers should bear this in mind and feel no hesitation in
:~90 communicating suggestions to the authors for consideration in future editions~ The two currently uppermost in m y own mind are: (1) The desirability of a more perceptive treatment of the pros and cons of basing c o m p o n e n t or factor analyses on correlation as opposed to covariance matrices. In particular, the former are often said to be essential when the scales of measurement of the variables differ widely. The obverse of the coin, viz., that it is in fact reasonable to homogenize variances in this fashion, as for instance, in studies involving trace and major elements, is ordinarily accepted w i t h o u t discussion. It should not be, for it is often quite unreasonable. (2) The need for careful discussion of the extensive sampling variance of the coefficients of such functions as factors or principal components. The lack of a complete or readily understandable theory is no longer sufficient justification for evading this exceedingly important issue; its elucidation by simulation experiments is now entirely feasible. Geological Factor Analysis is the first volume of a planned series on Methods in Geomathematics. May succeeding volumes of the series maintain the same high standards of form and content! Felix Chayes Washington, D.C.