This article gives an introduction to some new techniques for multilevel covariance structure modeling with latent variables. Although these techniques only incorporate a subset of models that are relevant to multilevel data, the techniques do provide a large set of new analysis possibilities and have the advantage that they only require conventional structural equation modeling software. The presentation draws on methodology presented in earlier works by the author.
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References
1.
Battese, G. E.
, R. M. Harter, and W. A. Fuller. 1988. “An Error-Components Model for Prediction of County Crop Areas Using Survey Satellite Data.”Journal of the American Statistical Association83:23-36.
2.
Bock, R. D.
1989. Multilevel Analysis of Educational Data. San Diego, CA: Academic Press.
3.
Cochran, W. G.
1977. Sampling Techniques. 3rd ed.Toronto: Wiley.
4.
Cronbach, L. J. 1976. “Research on Classrooms and Schools: Formulation of Questions, Design, and Analysis.” Unpublished manuscript, Stanford University, Stanford Evaluation Consortium, School of Education.
5.
Crosswhite, F. J.
, J. A. Dossey, J. O. Swafford, C. C. McKnight, and T. J. Cooney. 1985. Second International Mathematics Study: Summary Report for the United States. Champaign, IL: Stipes.
6.
Fuller, W. A.
and G. E. Battese. 1973. “Transformations for Estimation of Linear Models With Nested-Error Structure.”Journal of the American Statistical Association68:626-632.
7.
Gold, K.
, and B. Muthén, B. Forthcoming. “Extensions of Covariance Structure Analysis: Hierarchical Modeling of Multidimensional Achievement Data.”Journal of Educational Measurement.
8.
Harnqvist, K.1978. “Primary Mental Abilities of Collective and Individual Levels.”Journal of Educational Psychology70:706-716.
9.
Harnqvist, K.
, J.-E. Gustafsson, B. Muthén, and G. Nelson. Forthcoming. “Hierarchical Models of Ability at Individual and Class Levels.”Intelligence.
10.
Keesling, J. W.
and D. E. Wiley. 1974. “Regression Models of Hierarchical Data.” Paper presented at the Annual Meeting of the Psychometric Society, Palo Alto, CA, March.
11.
Kish, L.
1965. Survey Sampling. New York: Wiley.
12.
Koch, G. G.1983. “Intraclass Correlation Coefficient.”Encyclopedia of Statistical Sciences4:212-217.
13.
Laird, N. M.
and J. H. Ware. 1982. “Random-Effects Models for Longitudinal Data.”Biometrics65:581-590.
14.
Longford, N. T.
and B. Muthén. 1992. “Factor Analysis for Clustered Observations.”Psychometrika5:581-597.
15.
Malec, D.
and J. Sedransk. 1985. “Bayesian Inference for Finite Population Parameters in Multistage Cluster Sampling.”Journal of the American Statistical Association80:897-840.
16.
McDonald, R. P.
and H. Goldstein. 1989. “Balanced Versus Unbalanced Designs for Linear Structural Relations in Two-Level Data.”British Journal of Mathematical and Statistical Psychology42:215-232.
17.
Muthén, B.1989. “Latent Variable Modeling in Heterogeneous Populations. Presidential Address to the Psychometric Society, July 1989.”Psychometrika54:557-585.
18.
Muthén, B.
1990. “Mean and Covariance Structure Analysis of Hierarchical Data.” Paper presented at the Psychometric Society meeting in Princeton, New Jersey, June.
19.
Muthén, B.1991. “Multilevel Factor Analysis of Class and Student Achievement Components.”Journal of Educational Measurement28:338-354.
20.
Muthén, B.
and A. Satorra. 1989. Multilevel aspects of varying parameters in structural models. Pp. 87-99 in Multilevel Analysis of Educational Data, edited by R. D. Bock. San Diego: Academic Press.
21.
Muthén, B.
and A. Satorra. 1991. Complex Sample Data in Structural Equation Modeling. Manuscript submitted for publication.
22.
Nelson, G.
and B. Muthén. 1991. Analysis Preparation Steps for Multilevel Analysis Using LISCOMP (Technical Report). Los Angeles, University of California.
23.
Schmidt, W.
and J. Wisenbaker. 1986. Hierarchical Data Analysis: An Approach Based on Structural Equations. CEPSE, No. 4., Research Series. East Lansing, MI: Department of Counseling Educational Psychology and Special Education.
24.
Scott, A.
and T.M.F. Smith. 1969. “Estimation in Multi-Stage Surveys.”Journal of the American Statistical Association64:830-840.
25.
Skinner, C. J.
, D. Holt, and T.M.F. Smith. 1989. Analysis of Complex Surveys. Chichester: Wiley.
26.
Swamy, P.A.V.B.1970. “Efficient Inference in a Random Coefficient Regression Model.”Econometrica38:311-323.
27.
Winer, B. J.
, D. R. Brown, and K. M. Michels. 1991. Statistical Principles in Experimental Design. New York: McGraw-Hill.
