References

Akaike, H. (1974), "A New Look at the Statistical Identification Model," IEEE Transactions on Automatic Control, 19, 716–723.

Akaike, H. (1987), "Factor Analysis and AIC," Psychometrika, 52, 317–332.

Beale, E. M. L. (1972), "A Derivation of Conjugate Gradients," in Numerical Methods for Nonlinear Optimization, ed. F. A. Lootsma, London: Academic Press.

Bentler, P. M. (1985), Theory and Implementation of EQS: A Structural Equations Program, Manual for Program Version 2.0, Los Angeles: BMDP Statistical Software.

Bentler, P. M. (1986), Lagrange Multiplier and Wald Tests for EQS and EQS/PC, Los Angeles: BMDP Statistical Software.

Bentler, P. M. (1995), EQS, Structural Equations Program Manual, Program Version 5.0, Encino, CA: Multivariate Software.

Bentler, P. M. and Bonett, D. G. (1980), "Significance Tests and Goodness of Fit in the Analysis of Covariance Structures," Psychological Bulletin, 88, 588–606.

Bentler, P. M. and Freeman, E. H. (1983), "Test for Stability in Linear Structural Equation Systems," Psychometrika, 48, 143–145.

Bentler, P. M. and Weeks, D. G. (1980), "Linear Structural Equations with Latent Variables," Psychometrika, 45, 289–308.

Bishop, Y. M. M. , Fienberg, S. E., and Holland, P. W. (1977), Discrete Multivariate Analysis: Theory and Practice, Cambridge and London: MIT Press.

Bollen, K. A. (1986), "Sample Size and Bentler and Bonett’s Nonnormed Fit Index," Psychometrika, 51, 375–377.

Bollen, K. A. (1989a), "A New Incremental Fit Index for General Structural Equation Models," Sociological Methods and Research, 17, 303–316.

Bollen, K. A. (1989b), Structural Equations with Latent Variables, New York: John Wiley & Sons.

Box, G. E. P. (1949), "A General Distribution Theory for a Class of Likelihood Criteria," Biometrika, 36, 317–346.

Bozdogan, H. (1987), "Model Selection and Akaike’s Information Criterion (AIC): The General Theory and its Analytical Extensions," Psychometrika, 52, 345–370.

Browne, M. W. (1974), "Generalized Least Squares Estimators in the Analysis of Covariance Structures," South African Statistical Journal, 8, 1–24.

Browne, M. W. (1982), "Covariance Structures," in Topics in Multivariate Analyses, ed. D. M. Hawkins, New York: Cambridge University Press.

Browne, M. W. (1984), "Asymptotically Distribution-Free Methods for the Analysis of Covariance Structures," British Journal of Mathematical and Statistical Psychology, 37, 62–83.

Browne, M. W. and Cudeck, R. (1993), "Alternative Ways of Assessing Model Fit," in Testing Structural Equation Models, ed. K. A. Bollen and S. Long, Newbury Park, CA: Sage Publications.

Browne, M. W. and Du Toit, S. H. C. (1992), "Automated Fitting of Nonstandard Models," Multivariate Behavioral Research, 27, 269–300.

Browne, M. W. and Shapiro, A. (1986), "The Asymptotic Covariance Matrix of Sample Correlation Coefficients under General Conditions," Linear Algebra and Its Applications, 82, 169–176.

Bunch, J. R. and Kaufman, K. (1977), "Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems," Mathematics of Computation, 31, 162–179.

Buse, A. (1982), "The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note," The American Statistician, 36, 153–157.

Chamberlain, R. M., Powell, M. J. D., Lemarechal, C., and Pedersen, H. C. (1982), "The Watchdog Technique for Forcing Convergence in Algorithms for Constrained Optimization," Mathematical Programming, 16, 1–17.

Crawford, C. B. and Ferguson, G. A. (1970), "A General Rotation Criterion and Its Use in Orthogonal Rotation," Psychometrika, 35, 321–332.

DeLeeuw, J. (1983), "Models and Methods for the Analysis of Correlation Coefficients," Journal of Econometrics, 22, 113–137.

Dennis, J. E. and Mei, H. H. W. (1979), "Two New Unconstrained Optimization Algorithms Which Use Function and Gradient Values," Journal of Optimization Theory and Applications, 28, 453–482.

Dijkstra, T. K. (1992), "On Statistical Inference with Parameter Estimates on the Boundary of the Parameter Space," British Journal of Mathematical and Statistical Psychology, 45, 289–309.

Everitt, B. S. (1984), An Introduction to Latent Variable Methods, London: Chapman & Hall.

Fletcher, R. (1980), Practical Methods of Optimization, Vol. 1, Chichester: John Wiley & Sons.

Fletcher, R. (1987), Practical Methods of Optimization, Second Edition, Chichester: John Wiley & Sons.

Fuller, W. A. (1987), Measurement Error Models, New York: John Wiley & Sons.

Gay, D. M. (1983), "Subroutines for Unconstrained Minimization," ACM Transactions on Mathematical Software, 9, 503–524.

Gill, E. P., Murray, W., Saunders, M. A., and Wright, M. H. (1984), "Procedures for Optimization Problems with a Mixture of Bounds and General Linear Constraints," ACM Transactions on Mathematical Software, 10, 282–298.

Guttman, L. (1957), "Empirical Verification of the Radex Structure of Mental Abilities and Personality Traits," Educational and Psychological Measurement, 17, 391–407.

Hägglund, G. (1982), "Factor Analysis by Instrumental Variable Methods," Psychometrika, 47, 209–222.

Harman, H. H. (1976), Modern Factor Analysis, Third Edition, Chicago: University of Chicago Press.

Hoelter, J. W. (1983), "The Analysis of Covariance Structures: Goodness-of-Fit Indices," Sociological Methods and Research, 11, 325–344.

Holzinger, K. J. and Swineford, F. (1937), "The Bi-Factor Method," Psychometrika, 2, 41–54.

James, L. R., Mulaik, S. A., and Brett, J. M. (1982), Causal Analysis: Assumptions, Models, and Data, Beverly Hills, CA: Sage Publications.

Jennrich, R. I. (1973), "Standard Errors for Obliquely Rotated Factor Loadings," Psychometrika, 38, 593–604.

Jennrich, R. I. (1987), "Tableau Algorithms for Factor Analysis by Instrumental Variable Methods," Psychometrika, 52, 469–476.

Jöreskog, K. G. (1973), "A General Method for Estimating a Linear Structural Equation System," in Structural Equation Models in the Social Sciences, ed. A. S. Goldberger and O. D. Duncan, New York: Seminar Press.

Jöreskog, K. G. (1978), "Structural Analysis of Covariance and Correlation Matrices," Psychometrika, 43, 443–477.

Jöreskog, K. G. and Sörbom, D. (1985), LISREL VI; Analysis of Linear Structural Relationships by Maximum Likelihood, Instrumental Variables, and Least Squares, Uppsala: University of Uppsala.

Jöreskog, K. G. and Sörbom, D. (1988), LISREL 7: A Guide to the Program and Applications, Chicago: SPSS Inc.

Keesling, J. W. (1972), "Maximum Likelihood Approaches to Causal Analysis," Ph. D. dissertation, University of Chicago, 1972.

Kmenta, J. (1971), Elements of Econometrics, New York: Macmillan.

Lawley, D. N. and Maxwell, A. E. (1971), Factor Analysis as a Statistical Method, New York: American Elsevier.

Lee, S. Y. (1985), "On Testing Functional Constraints in Structural Equation Models," Biometrika, 72, 125–131.

Loehlin, J. C. (2004), Latent Variable Models, An Introduction to Factor, Path, and Structural Analysis (4th ed.), Hillsdale, NJ: Lawrence Erlbaum Associates.

Long, J. S. (1983), Covariance Structure Models, an Introduction to LISREL, Beverly Hills, CA: Sage Publications.

MacCallum, R. (1986), "Specification Searches in Covariance Structure Modeling," Psychological Bulletin, 100, 107–120.

MacCallum, R. C., Roznowski, M., and Necowitz, L. B. (1992), "Model Modification in Covariance Structure Analysis: The Problem of Capitalization on Chance," Psychological Bulletin, 111, 490–504.

Mauchly, J. W. (1940), "Significance Test for Sphericity of a Normal N-Variate Distribution," Annals of Mathematical Statistics, 11, 204–209.

McArdle, J. J. (1980), "Causal Modeling Applied to Psychonomic Systems Simulation," Behavior Research Methods & Instrumentation, 12, 193–209.

McArdle, J. J. (1988), "Dynamic but Structural Equation Modeling of Repeated Measures Data," in The Handbook of Multivariate Experimental Psychology, ed. J. R. Nesselroade and R. B. Cattell, New York: Plenum Press.

McArdle, J. J. and McDonald, R. P. (1984), "Some Algebraic Properties of the Reticular Action Model," British Journal of Mathematical and Statistical Psychology, 37, 234–251.

McDonald, R. P. (1978), "A Simple Comprehensive Model for the Analysis of Covariance Structures," British Journal of Mathematical and Statistical Psychology, 31, 59–72.

McDonald, R. P. (1980), "A Simple Comprehensive Model for the Analysis of Covariance Structures: Some Remarks on Applications," British Journal of Mathematical and Statistical Psychology, 33, 161–183.

McDonald, R. P. (1985), Factor Analysis and Related Methods, Hillsdale, NJ: Lawrence Erlbaum Associates.

McDonald, R. P. (1989), "An Index of Goodness-of-Fit Based on Noncentrality," Journal of Classification, 6, 97–103.

McDonald, R. P. and Hartmann, W. (1992), "A Procedure for Obtaining Initial Values of Parameters in the RAM Model," Multivariate Behavioral Research, 27, 57–176.

Moré, J. J. (1978), "The Levenberg-Marquardt Algorithm: Implementation and Theory," in Numerical Analysis–Dundee 1977, ed. G. A. Watson, Lecture Notes in Mathematics 630, Berlin: Springer-Verlag.

Moré, J. J. and Sorensen, D. C. (1983), "Computing a Trust-Region Step," SIAM Journal on Scientific and Statistical Computing, 4, 553–572.

Mulaik, S. A., James, L. R., Van Alstine, J., Bennett, N., Lind, S., and Stilwell, C. D. (1989), "Evaluation of Goodness-of-Fit Indices for Structural Equation Models," Psychological Bulletin, 105, 430–445.

Mulaik, S. A. and Quartetti, D. A. (1997). "First Order or Higher Order General Factor," Structural Equation Modeling, 4, 193–211.

Polak, E. (1971), Computational Methods in Optimization, New York: Academic Press.

Powell, J. M. D. (1977), "Restart Procedures for the Conjugate Gradient Method," Mathematical Programming, 12, 241–254.

Powell, J. M. D. (1978a), "A Fast Algorithm for Nonlinearly Constraint Optimization Calculations," in Numerical Analysis, Dundee 1977, Lecture Notes in Mathematics 630, ed. G. A. Watson, Berlin: Springer Verlag, 144–175.

Powell, J. M. D. (1978b), "Algorithms for Nonlinear Constraints That Use Lagrangian Functions," Mathematical Programming, 14, 224–248.

Powell, M. J. D. (1982a), "Extensions to Subroutine VF02AD," in Systems Modeling and Optimization, Lecture Notes In Control and Information Sciences 38, ed. R. F. Drenick and F. Kozin, Berlin: Springer Verlag, 529–538.

Powell, J. M. D. (1982b), "VMCWD: A Fortran Subroutine for Constrained Optimization," DAMTP 1982/NA4, Cambridge, England.

Schmid, J. and Leiman, J. M. (1957), "The Development of Hierarchical Factor Solutions," Psychometrika, 22, 53–61.

Schwarz, G. (1978), "Estimating the Dimension of a Model," Annals of Statistics, 6, 461–464.

Sclove, L. S. (1987), "Application of Model-Selection Criteria to Some Problems in Multivariate Analysis," Psychometrika, 52, 333–343.

Steiger, J. H. (1998), "A Note on Multiple Sample Extensions of the RMSEA Fit Index," Structural Equation Modeling, 5, 411–419.

Steiger, J. H. and Lind, J. C. (1980), "Statistically Based Tests for the Number of Common Factors," paper presented at the annual meeting of the Psychometric Society, Iowa City, IA.

Swaminathan, H. (1974), "A General Factor Model for the Description of Change," Report LR-74-9, Laboratory of Psychometric and Evaluative Research, University of Massachusetts.

Tucker, L. R. and Lewis, C. (1973), "A Reliability Coefficient for Maximum Likelihood Factor Analysis," Psychometrika, 38, 1–10.

Wheaton, B., Muthèn, B., Alwin, D. F., and Summers, G. F. (1977), "Assessing Reliability and Stability in Panel Models," in Sociological Methodology, ed. D. R. Heise, San Francisco: Jossey Bass.

Wiley, D. E. (1973), "The Identification Problem for Structural Equation Models with Unmeasured Variables," in Structural Equation Models in the Social Sciences, ed. A. S. Goldberger and O. D. Duncan, New York: Seminar Press, 69–83.

Wilson, E. B. and Hilferty, M. M. (1931), "The Distribution of Chi-Square," Proceeding of the National Academy of Science, 17, 694.

Yung, Y. F., Thissen, D., and McLeod, L. D. (1999), "On the Relationship Between the Higher-order Factor Model and the Hierarchical Factor Model," Psychometrika, 64, 113–128.