Structural analysis of covariance and correlation matrices

A general approach to the analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.Several different types of covariance structures are considered as special cases of the general model. These include models for sets of congeneric tests, models for confirmatory and exploratory factor analysis, models for estimation of variance and covariance components, regression models with measurement errors, path analysis models, simplex and circumplex models. Many of the different types of covariance structures are illustrated by means of real data.

[1]  S. Wright.  The Method of Path Coefficients , 1934 .

[2]  J. Tukey,et al.  Multiple-Factor Analysis , 1947 .

[3]  L. Thurstone.  Primary mental abilities. , 1938, Science.

[4]  J. W. French.  The description of aptitude and achievement tests in terms of rotated factors. , 1951 .

[5]  F. Lord.  A study of speed factors in tests and academic grades , 1956 .

[6]  J. Guilford.  The structure of intellect. , 1956, Psychological bulletin.

[7]  H. Kaiser.  The varimax criterion for analytic rotation in factor analysis , 1958 .

[8]  D. Campbell,et al.  Convergent and discriminant validation by the multitrait-multimethod matrix. , 1959, Psychological bulletin.

[9]  H. Harman.  Modern factor analysis , 1961 .

[10]  R. D. Bock.  COMPONENTS OF VARIANCE ANALYSIS AS A STRUCTURAL AND DISCRIMINAL ANALYSIS FOR PSYCHOLOGICAL TESTS , 1960 .

[11]  F. Graybill.  An introduction to linear statistical models , 1961 .

[12]  Patrick Suppes,et al.  Mathematical Methods in the Social Sciences , 1962 .

[13]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[14]  T. W. Anderson,et al.  The use of factor analysis in the statistical analysis of multiple time series , 1963 .

[15]  P. O. White,et al.  PROMAX: A QUICK METHOD FOR ROTATION TO OBLIQUE SIMPLE STRUCTURE , 1964 .

[16]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[17]  R. D. Bock,et al.  Analysis of covariance structures , 1966, Psychometrika.

[18]  Donald M. Miller,et al.  ITEM DESIGN FOR AN INVENTORY OF TEACHING PRACTICES AND LEARNING SITUATIONS1 , 1966 .

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

[20]  L. Humphreys.  The fleeting nature of the prediction of college academic success. , 1968, Journal of educational psychology.

[21]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[22]  E. B. Andersen,et al.  Modern factor analysis , 1961 .

[23]  K. Jöreskog.  A general approach to confirmatory maximum likelihood factor analysis , 1969 .

[24]  Karl G. Jöreskog,et al.  ESTIMATION AND TESTING OF SIMPLEX MODELS , 1970 .

[25]  K. Jöreskog.  A general method for analysis of covariance structures , 1970 .

[26]  Karl G. Jöreskog,et al.  A COMPUTER PROGRAM FOR MINIMIZING A FUNCTION OF SEVERAL VARIABLES1 , 1970 .

[27]  Robert L. Linn,et al.  Path analysis: Psychological examples. , 1970 .

[28]  B. Mukherjee.  LIKELIHOOD RATIO TESTS OF STATISTICAL HYPOTHESES ASSOCIATED WITH PATTERNED COVARIANCE MATRICES IN PSYCHOLOGY , 1970 .

[29]  A. Goldberger,et al.  The Treatment of Unobservable Variables in Path Analysis , 1971 .

[30]  W. Kristof.  On the theory of a set of tests which differ only in length , 1971 .

[31]  J. C. Gower,et al.  Factor Analysis as a Statistical Method. 2nd ed. , 1972 .

[32]  A. Goldberger,et al.  Factor analysis by generalized least squares , 1972 .

[33]  M. Browne.  Generalized Least Squares Estimators in the Analysis of Covariance Structures. , 1973 .

[34]  W. Schmidt,et al.  Studies of a Class of Covariance Structure Models , 1973 .

[35]  R. Jennrich,et al.  Standard errors for rotated factor loadings , 1973 .

[36]  R. Jennrich.  Standard errors for obliquely rotated factor loadings , 1973 .

[37]  Roderick P. McDonald,et al.  Testing pattern hypotheses for covariance matrices , 1974 .

[38]  Karl G. Jöreskog,et al.  Analyzing psychological data by structural analysis of covariance matrices , 1974 .

[39]  W. Fuller,et al.  An Errors-In-Variables Analysis of Managerial Role Performance , 1974 .

[40]  R. McDonald,et al.  Testing pattern hypotheses for correlation matrices , 1975 .

[41]  A. Goldberger,et al.  Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable , 1975 .

[42]  P. Suppes,et al.  Contemporary Developments in Mathematical Psychology , 1976 .

[43]  R. Linn,et al.  A Maximum Likelihood Solution To The Errors In Variables And Errors In Equations Model. , 1977, Multivariate behavioral research.

[44]  M. Browne.  The analysis of patterned correlation matrices by generalized least squares , 1977 .

[45]  B. Muthén,et al.  Assessing Reliability and Stability in Panel Models , 1977 .

[46]  K. Jöreskog.  Factor analysis by least squares and maximum likelihood methods , 1977 .

[47]  P. Whittle,et al.  Latent Variables in Socio‐Economic Models , 1978 .

[48]  Anthony Ralston,et al.  Statistical Methods for Digital Computers. , 1980 .

[49]  K. Jöreskog,et al.  Reliability of College Grades From Longitudinal Data , 1978 .

[50]  Karl G. Jöreskog,et al.  Statistical estimation of structural models in longitudinal-developmental investigations , 1979 .