The CALIS Procedure

References

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

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

  • Bartlett, M. S. (1950), “Tests of Significance in Factor Analysis,” British Journal of Psychology, 3, 77–85.

  • Bartlett, M. S. (1954), “A Note on Multiplying Factors for Various Chi-Squared Approximations,” Journal of the Royal Statistical Society, Series B, 16, 296–298.

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

  • Belsley, D. A., Kuh, E., and Welsch, R. E. (1980), Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, New York: John Wiley & Sons.

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

  • 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. (1975), Discrete Multivariate Analysis: Theory and Practice, Cambridge, MA: 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 D. M. Hawkins, ed., Topics in Applied Multivariate Analysis, 72–141, Cambridge: 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 K. A. Bollen and S. Long, eds., Testing Structural Equation Models, 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,” American Statistician, 36, 153–157.

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

  • De Leeuw, 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.

  • Duncan, O. D., Haller, A. O., and Portes, A. (1968), “Peer Influences on Aspirations: A Reinterpretation,” American Journal of Sociology, 74, 119–137.

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

  • Fletcher, R. (1980), Practical Methods of Optimization, volume 1, Unconstrained Optimization, Chichester, UK: John Wiley & Sons.

  • Fletcher, R. (1987), Practical Methods of Optimization, 2nd Edition, Chichester, UK: 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.

  • Haller, A. O. and Butterworth, C. E. (1960), “Peer Influences on Levels of Occupational and Educational Aspiration,” Social Forces, 38, 289–295.

  • Harman, H. H. (1976), Modern Factor Analysis, 3rd 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.

  • Huber, P. J. (1981), Robust Statistics, New York: John Wiley & Sons.

  • Huynh, H. and Feldt, L. S. (1970), “Conditions Under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distributions,” Journal of the American Statistical Association, 65, 1582–1589.

  • James, L. R., Mulaik, S. A., and Brett, J. M. (1982), Causal Analysis, 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 A. S. Goldberger and O. D. Duncan, eds., Structural Equation Models in the Social Sciences, New York: Academic 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.

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

  • 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: Macmillan.

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

  • Loehlin, J. C. (1987), Latent Variable Models: An Introduction to Factor, Path, and Structural Analysis, Hillsdale, NJ: Lawrence Erlbaum Associates.

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

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

  • MacCallum, R. C. (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.

  • Mardia, K. V., Kent, J. T., and Bibby, J. M. (1979), Multivariate Analysis, London: Academic Press.

  • 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 and Instrumentation, 12, 193–209.

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

  • 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. and Hartmann, W. M. (1992), “A Procedure for Obtaining Initial Values of Parameters in the RAM Model,” Multivariate Behavioral Research, 27, 57–176.

  • McDonald, R. P. and Marsh, H. W. (1988), “Choosing a Multivariate Model: Noncentrality and Goodness of Fit,” Distributed paper.

  • Moré, J. J. (1978), “The Levenberg-Marquardt Algorithm: Implementation and Theory,” in G. A. Watson, ed., Lecture Notes in Mathematics, volume 30, 105–116, 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.

  • Morrison, D. F. (1990), Multivariate Statistical Methods, 3rd Edition, New York: McGraw-Hill.

  • 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.

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

  • Powell, M. J. D. (1978a), “Algorithms for Nonlinear Constraints That Use Lagrangian Functions,” Mathematical Programming, 14, 224–248.

  • Powell, M. J. D. (1978b), “A Fast Algorithm for Nonlinearly Constrained Optimization Calculations,” in G. A. Watson, ed., Lecture Notes in Mathematics, volume 630, 144–175, Berlin: Springer-Verlag.

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

  • Powell, M. J. D. (1982b), VMCWD: A Fortran Subroutine for Constrained Optimization, Technical Report DAMTP 1982/NA4, Cambridge University.

  • 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, S. L. (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, Technical Report LR-74-9, University of Massachusetts, Laboratory of Psychometric and Evaluative Research.

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

  • Wheaton, B., Muthén, B. O., Alwin, D. F., and Summers, G. F. (1977), “Assessing Reliability and Stability in Panel Models,” in D. R. Heise, ed., Sociological Methodology, San Francisco: Jossey-Bass.

  • Wiley, D. E. (1973), “The Identification Problem for Structural Equation Models with Unmeasured Variables,” in A. S. Goldberger and O. D. Duncan, eds., Structural Equation Models in the Social Sciences, New York: Academic Press.

  • Wilson, E. B. and Hilferty, M. M. (1931), “The Distribution of Chi-Square,” Proceedings of the National Academy of Sciences, 17, 684–688.

  • Yuan, K.-H. and Hayashi, K. (2010), “Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots,” Psychological Methods, 15, 335–351.

  • Yuan, K.-H. and Zhong, X. (2008), “Outliers, Leverage Observations, and Influential Cases in Factor Analysis: Using Robust Procedures to Minimize Their Effect,” Sociological Methodology, 38, 329–368.

  • 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.