Latent growth curves within developmental structural equation models.

This report uses structural equation modeling to combine traditional ideas from repeated-measures ANOVA with some traditional ideas from longitudinal factor analysis. A longitudinal model that includes correlations, variances, and means is described as a latent growth curve model (LGM). When merged with repeated-measures data, this technique permits the estimation of parameters representing both individual and group dynamics. The statistical basis of this model allows hypothesis testing of various developmental ideas, including models of alternative dynamic functions and models of the sources of individual differences in these functions. Aspects of these latent growth models are illustrated with a set of longitudinal WISC data from young children and by using the LISREL V computer program.

[1]  J. Connell,et al.  A Structural Modeling Approach to the Study of Attachment and Strange Situation Behaviors , 1982 .

[2]  R T Osborne,et al.  A longitudinal investigation of change in the factorial composition of intelligence with age in young school children. , 1967, The Journal of genetic psychology.

[3]  R. P. McDonald,et al.  A simple comprehensive model for the analysis of covariance structures: Some remarks on applications , 1980 .

[4]  C. Harris.  Problems in measuring change , 1965 .

[5]  M. Appelbaum,et al.  Developmental changes in mental performance. , 1973, Monographs of the Society for Research in Child Development.

[6]  R. Q. Bell,et al.  An experimental test of the accelerated longitudinal approach. , 1954, Child development.

[7]  John R. Nesselroade,et al.  Beyond autoregressive models: some implications of the trait-state distinction for the structural modeling of developmental change. , 1987, Child development.

[8]  David Rogosa,et al.  A growth curve approach to the measurement of change. , 1982 .

[9]  J. Horn,et al.  Cattell's Scree Test In Relation To Bartlett's Chi-Square Test And Other Observations On The Number Of Factors Problem. , 1979, Multivariate behavioral research.

[10]  R. P. McDonald,et al.  Some algebraic properties of the Reticular Action Model for moment structures. , 1984, The British journal of mathematical and statistical psychology.

[11]  N. Bayley,et al.  Individual patterns of development. , 1956, Child development.

[12]  Mark Appelbaum,et al.  Bias in the Analysis of Repeated-Measures Designs: Some Alternative Approaches. , 1973 .

[13]  C. Hertzog,et al.  Repeated-measures analysis of variance in developmental research: selected issues. , 1985, Child development.

[14]  John J. McArdle,et al.  Perspectives on Mathematical/Statistical Model Building (MASMOB) in research on aging. , 1980 .

[15]  J. Mcardle,et al.  Latent variable growth within behavior genetic models , 1986, Behavior genetics.

[16]  D. Baumrind.  Specious causal attributions in the social sciences: the reformulated stepping-stone theory of heroin use as exemplar. , 1983, Journal of personality and social psychology.

[17]  Ledyard R. Tucker,et al.  Determination of parameters of a functional relation by factor analysis : a technical report , 1955 .

[18]  J. S. Tanaka,et al.  A fit index for covariance structure models under arbitrary GLS estimation , 1985 .

[19]  Hubert M. Blalock,et al.  Causal models in panel and experimental designs , 1985 .

[20]  John B. Willett,et al.  Understanding correlates of change by modeling individual differences in growth , 1985 .

[21]  R. Mccall.  Transitions in Early Mental Development. , 1977 .

[22]  Karl G. Jöreskog,et al.  Statistical estimation of structural models in longitudinal-developmental investigations , 1979 .

[23]  J. Jack McArdle,et al.  Causal modeling applied to psychonomic systems simulation , 1980 .

[24]  L R Bergman,et al.  A Longitudinal Factor Model For Studying Change In Ability Structure. , 1977, Multivariate behavioral research.

[25]  Jay Magidson,et al.  Advances in factor analysis and structural equation models , 1979 .

[26]  Albert N. Link,et al.  The changing composition of R & D , 1985 .

[27]  John J. McArdle,et al.  Mathematical-Statistical Model Building in Analysis of Developmental Data , 1984 .

[28]  O. D. Duncan,et al.  Introduction to Structural Equation Models. , 1977 .

[29]  M. Browne,et al.  Cross-Validation Of Covariance Structures. , 1983, Multivariate behavioral research.

[30]  P. Hofstaetter.  The changing composition of intelligence: a study in T-technique. , 1954, The Journal of genetic psychology.

[31]  C. Schriesheim.  Causal Analysis: Assumptions, Models, and Data , 1982 .

[32]  R. Q. Bell,et al.  Convergence: an accelerated longitudinal approach. , 1953, Child development.

[33]  Lawrence R. James,et al.  Causal Analysis: Assumptions, Models, and , 1983 .

[34]  S. G. Vandenberg,et al.  Hereditary factors in human growth. , 1965, Human biology.

[35]  Ronald G. Stansfield,et al.  Sociological Methodology 1982 , 1983 .

[36]  S. Mulaik.  Exploratory Statistics and Empiricism , 1985, Philosophy of Science.

[37]  H. F. Gollob,et al.  Taking account of time lags in causal models. , 1987, Child development.

[38]  L. Cronbach.  Year-to-year correlations of mental tests: a review of the Hofstaetter analysis. , 1967, Child development.

[39]  John R. Nesselroade,et al.  Longitudinal Research in the Study of Behavior and Development , 1979 .

[40]  J. Connell,et al.  The Study of Transitions , 1984 .

[41]  Michael Lane,et al.  Introduction to structuralism , 1970 .

[42]  S Karlin,et al.  On "Path analysis in genetic epidemiology: a critique". , 1983, American journal of human genetics.

[43]  John B. Willett,et al.  Satisfying a Simplex Structure is Simpler than it should be , 1985 .

[44]  David Rindskopf,et al.  Parameterizing inequality constraints on unique variances in linear structural models , 1983 .

[45]  Robert L. Linn,et al.  A Simplex Model for Analyzing Academic Growth , 1977 .

[46]  Roderick P. McDonald,et al.  Factor Analysis and Related Methods , 1985 .

[47]  G. Bronson,et al.  On the distinction between fear and wariness. , 1977, Child development.

[48]  Raymond B. Cattell,et al.  Handbook of multivariate experimental psychology , 1968 .

[49]  M. Browne.  Asymptotically distribution-free methods for the analysis of covariance structures. , 1984, The British journal of mathematical and statistical psychology.

[50]  Lisa L. Harlow,et al.  Robust Structural Equation Models: Implications for Developmental Psychology. , 1987 .

[51]  Karl G. Jöreskog,et al.  ESTIMATION AND TESTING OF SIMPLEX MODELS , 1970 .

[52]  C. R. Rao,et al.  Some statistical methods for comparison of growth curves. , 1958 .

[53]  Robert J. Sternberg,et al.  Mechanisms of cognitive development , 1984 .

[54]  George W. Bohrnstedt,et al.  Use of Null Models in Evaluating the Fit of Covariance Structure Models , 1985 .

[55]  R. T. Osborne,et al.  A Longitudinal Investigation of the Intellectual Differentiation Hypothesis. , 1972 .

[56]  R. Wilson,et al.  The Louisville Twin Study: developmental synchronies in behavior. , 1983, Child Development.

[57]  D. Hultsch,et al.  Learning-ability relations in adulthood. , 1976, Human development.

[58]  T. Cook,et al.  Quasi-experimentation: Design & analysis issues for field settings , 1979 .

[59]  A. Satorra,et al.  Power of the likelihood ratio test in covariance structure analysis , 1985 .

[60]  L G Humphreys,et al.  Longitudinal correlation analysis of standing height and intelligence. , 1985, Child development.

[61]  S. Wright.  On "Path analysis in genetic epidemiology: a critique". , 1983, American journal of human genetics.

[62]  J. S. Tanaka.  "How Big Is Big Enough?": Sample Size and Goodness of Fit in Structural Equation Models with Latent Variables. , 1987 .

[63]  H. Goldsmith.  Genetic influences on personality from infancy to adulthood. , 1983, Child development.