Power of the likelihood ratio test in covariance structure analysis

A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.

[1]  G. Hardy.  A Course of Pure Mathematics , 1910 .

[2]  A. Wald.  Tests of statistical hypotheses concerning several parameters when the number of observations is large , 1943 .

[3]  M. G. Kendall,et al.  The advanced theory of statistics. Vols. 2. , 1969 .

[4]  T. Apostol.  Mathematical Analysis , 1957 .

[5]  E. L. Lehmann,et al.  Significance Level and Power , 1958 .

[6]  S. D. Silvey,et al.  The Lagrangian Multiplier Test , 1959 .

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

[8]  W. E. Lever,et al.  THE LIMITING DISTRIBUTION OF THE LIKELIHOOD RATIO STATISTIC UNDER A CLASS OF LOCAL ALTERNATIVES. , 1967 .

[9]  T. Hayton.  The Advanced Theory of Statistics, Vol. 3 , 1968 .

[10]  Paul I. Feder,et al.  On the Distribution of the Log Likelihood Ratio Test Statistic When the True Parameter is "Near" the Boundaries of the Hypothesis Regions , 1968 .

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

[12]  T. W. F. Stroud,et al.  Fixed Alternatives and Wald's Formulation of the Noncentral Asymptotic Behavior of the Likelihood Ratio Statistic , 1972 .

[13]  L. Tucker,et al.  A reliability coefficient for maximum likelihood factor analysis , 1973 .

[14]  Robert V. Foutz,et al.  The Performance of the Likelihood Ratio Test When the Model is Incorrect , 1977 .

[15]  Willem E. Saris,et al.  Detection of Specification Errors in Linear Structural Equation Models , 1979 .

[16]  Robert I. Jennrich,et al.  A study of algorithms for covariance structure analysis with specific comparisons using factor analysis , 1979 .

[17]  A. Ronald Gallant,et al.  Statistical Inference in an Implicit, Nonlinear, Simultaneous Equation Model in the Context of Maximum Likelihood Estimation , 1980 .

[18]  P. Bentler.  MULTIVARIATE ANALYSIS WITH LATENT VARIABLES: CAUSAL MODELING , 1980 .

[19]  P. Bentler,et al.  Significance Tests and Goodness of Fit in the Analysis of Covariance Structures , 1980 .

[20]  Stephen Barnett,et al.  Matrix Methods for Engineers and Scientists , 1982 .

[21]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[22]  A. Ronald Gallant,et al.  On unification of the asymptotic theory of nonlinear econometric models , 1982 .

[23]  Michael W. Browne,et al.  Topics in Applied Multivariate Analysis: COVARIANCE STRUCTURES , 1982 .

[24]  K. Jöreskog,et al.  Analysis of linear structural relationships by maximum likelihood and least squares methods , 1983 .

[25]  A. Boomsma.  On the robustness of LISREL (maximum likelihood estimation) against small sample size and non-normality. , 1984 .