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Goldstein, Harvey; McDonald, Roderick P. – Psychometrika, 1988
A general model is developed for the analysis of multivariate multilevel data structures. Special cases of this model include: repeated measures designs; multiple matrix samples; multilevel latent variable models; multiple time series and variance and covariance component models. (Author)
Descriptors: Equations (Mathematics), Mathematical Models, Matrices, Multivariate Analysis
Peer reviewed Peer reviewed
McDonald, Roderick P. – Psychometrika, 1993
A general model for two-level multivariate data, with responses possibly missing at random, is described. The model combines regressions on fixed explanatory variables with structured residual covariance matrices. The likelihood function is reduced to a form enabling computational methods for estimating the model to be devised. (Author)
Descriptors: Computation, Estimation (Mathematics), Mathematical Models, Models
Peer reviewed Peer reviewed
McDonald, Roderick P. – Psychometrika, 1981
An expression is given for weighted least squares estimators of oblique common factors of factor analyses, constrained to have the same covariance matrix as the factors they estimate. A proof of the uniqueness of the solution is given. (Author/JKS)
Descriptors: Analysis of Covariance, Factor Analysis, Least Squares Statistics, Mathematical Models
Peer reviewed Peer reviewed
McDonald, Roderick P.; Hartmann, Wolfgang M. – Multivariate Behavioral Research, 1992
An algorithm for obtaining initial values for the minimization process in covariance structure analysis is developed that is more generally applicable for computing parameters connected to latent variables than the currently existing ones. The algorithm is formulated in terms of the RAM model but can be extended. (SLD)
Descriptors: Algorithms, Correlation, Equations (Mathematics), Estimation (Mathematics)
Peer reviewed Peer reviewed
Velicer, Wayne F.; McDonald, Roderick P. – Multivariate Behavioral Research, 1991
The general transformation approach to time series analysis is extended to the analysis of multiple unit data by the development of a patterned transformation matrix. The procedure includes alternatives for special cases and requires only minor revisions in existing computer software. (SLD)
Descriptors: Cross Sectional Studies, Data Analysis, Generalizability Theory, Mathematical Models
Peer reviewed Peer reviewed
McDonald, Roderick P.; And Others – Psychometrika, 1993
A reparameterization is formulated that yields estimates of scale-invariant parameters in recursive path models with latent variables, and (asymptotically) correct standard errors, without the use of constrained optimization. The method is based on the logical structure of the reticular action model. (Author)
Descriptors: Correlation, Equations (Mathematics), Error of Measurement, Estimation (Mathematics)