An overview is given of modeling of longitudinal and multilevel data using a latent variable framework. Particular emphasis is placed on growth modeling. A latent variable model is presented for three-level data, where the modeling of the longitudinal part of the data imposes both a covariance and a mean structure. Examples are discussed where repeated observations are made on students sampled within classrooms and schools.
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References
1.
BockR. Darrell. 1989. Multilevel Analysis of Educational Data. San Diego: Academic Press.
2.
BollenKen A.1989. Structural Equations with Latent Variables. New York: Wiley.
3.
BrykAnthony S.RaudenbushStephen W.. 1992. Hierarchical Linear Models: Applications and Data Analysis Methods. Newbury Park, CA: Sage.
GoldsteinHarvey I.1987. Multilevel Models in Educational and Social Research. London: Oxford University Press.
6.
JöreskogKarl G.SörbomDag1977. “Statistical Models and Methods for Analysis of Longitudinal Data.” In Latent Variables in Socio-Economic Models, edited by AignerD. J.GoldbergerA. S., 285–325. Amsterdam: North-Holland.
7.
LairdNan M.WareJames H.. 1982. “Random-Effects Models for Longitudinal Data.”Biometrics38:963–74.
8.
LordFrederic M.NovickMelvin R.. 1968. Statistical Theories of Mental Test Scores. Reading, MA: Addison-Wesley.
McDonaldRodGoldsteinHarvey. 1989. “Balanced Versus Unbalanced Designs for Linear Structural Relations in Two-Level Data.”British Journal of Mathematical and Statistical Psychology42:215–32.
11.
MeredithWilliamTisakJohn. 1984. “Tuckerizing Curves.” Paper presented at the Psychometric Society annual meetings, Santa Barbara, CA.
12.
MeredithWilliamTisakJohn. 1989. “Latent Variable Modeling in Heterogeneous Populations.”Psychometrika54:557–85.
13.
MuthénBengt. 1983. “Latent Variable Structural Equation Modeling with Categorical Data.”Journal of Econometrics22:43–65.
MuthénBengt. 1990. “Mean and Covariance Structure Analysis of Hierarchical Data.” Paper presented at the Psychometric Society meeting in Princeton, New Jersey. UCLA Statistics Series #62, August 1990.
16.
MuthénBengt. 1991a. “Analysis of Longitudinal Data Using Latent Variable Models with Varying Parameters.” In Best Methods for the Analysis of Change. Recent Advances, Unanswered Questions, Future Directions, edited by CollinsL.HornJ., 1–17. Washington: American Psychological Association.
17.
MuthénBengt. 1991b. “Multilevel Factor Analysis of Class and Student Achievement Components.”Journal of Educational Measurement28:338–54.
18.
MuthénBengt. 1993. “Latent Variable Modeling of Growth with Missing Data and Multilevel Data.” In Multivariate Analysis: Future Directions 2, edited by RaoC. R.CuadrasC. M., 199–210. Amsterdam: North-Holland.
19.
MuthénBengt. 1994a. “Multilevel Covariance Structure Analysis.”Sociological Methods and Research22:376–98.
20.
MuthénBengt. 1994b. “Latent Variable Growth Modeling with Multilevel Data.” Paper presented at the UCLA conference Latent Variable Modeling with Applications to Causality. March, 1994. To appear in Latent Variable Modeling with Applications to Causality, edited by BerkaneMaia. Cambridge, MA: Springer-Verlag.
21.
MuthénBengtSatorraAlbert. 1995. “Complex Sample Data in Structural Equation Modeling.” In Sociological Methodology 1995, edited by MarsdenPeter V., 267–316. Cambridge, MA: Blackwell.
22.
RafteryAdrian E.1993. “Bayesian Model Selection in Structural Equation Models.” In Testing Structural Equation Models, edited by BollenKennethScottLong J., 163–80. Newbury Park, CA: Sage.
23.
RafteryAdrian E.1995. “Bayesian Model Selection in Social Research.” In Sociological Methodology 1995, edited by MarsdenPeter V., 111–63. Cambridge, MA: Blackwell.
24.
SchmidtW.WolfeR. G.KiferE.. (in press). “The Identification and Description of Student Growth in Mathematics Achievement.” In L. Burstein (Ed.), The IEA Study of Mathematics III: Student Growth and Classroom Processes. Edited by BursteinL.. London: Pergamon.
25.
SkinnerC. J.HoltD.SmithT. M. F.. 1989. Analysis of Complex Surveys. Chichester, England: Wiley.
26.
WheatonBlairMuthénBengtDuaneAlwinSummersGene. 1977. “Assessing Reliability and Stability in Panel Models.” In Sociological Methodology 1977, edited by HeiseD. R., 84–136. San Francisco: Jossey-Bass.
27.
WillettJohn B.SayerAlice G.. 1993. “Using Covariance Structure Analysis to Detect Correlates and Predictors of Individual Change over Time.”Psychological Bulletin116:368–81.