Relating Factor Models for Longitudinal Data to Quasi-Simplex and NARMA Models

In this article we show the one-factor model can be rewritten as a quasi-simplex model. Using this result along with addition theorems from time series analysis, we describe a common general model, the nonstationary autoregressive moving average (NARMA) model, that includes as a special case, any latent variable model with continuous indicators and continuous latent variables. As an example, we show the NARMA representations of the linear growth curve model and the growth curve model with estimated basis vector coefficients. In certain instances rewriting competing models may help the investigator to compare different models. Here we compare the "hybrid" behavior genetics model of Eaves and Hewitt to the quasi-simplex model of Boomsma and Molenaar and show that both have equivalent NARMA representations which differ only in order.

[1]  Peter C. M. Molenaar,et al.  State Space Techniques in Structural Equation Modeling Transformation of latent variables in and out of latent variable models , 2003 .

[2]  Clive W. J. Granger,et al.  Time series modeling and interpretation , 2001 .

[3]  Kenneth A. Bollen,et al.  The best of both worlds: Combining autoregressive and latent curve models. , 2001 .

[4]  Peter C. M. Molenaar,et al.  Comment on fitting MA time series by structural equation models , 1999 .

[5]  T. Raykov.  Satisfying a Simplex Structure is Simpler Than it Should Be: A Latent Curve Analysis Revisit. , 1998, Multivariate behavioral research.

[6]  Peter C. M. Molenaar,et al.  The covariance between level and shape in the latent growth curve model with estimated basis vector coefficients , 1998 .

[7]  Stef van Buuren,et al.  Fitting arma time series by structural equation models , 1997 .

[8]  Peter C. M. Molenaar,et al.  Dynamic factor analysis of nonstationary multivariate time series , 1992 .

[9]  J J McArdle,et al.  Modeling incomplete longitudinal and cross-sectional data using latent growth structural models. , 1992, Experimental aging research.

[10]  R. Steyer,et al.  States and traits in psychological assessment. , 1992 .

[11]  William Meredith,et al.  Latent curve analysis , 1990 .

[12]  J. Mcardle,et al.  Patterns of Change within Latent Variable Structural Equation Models , 1990 .

[13]  J K Hewitt,et al.  Resolving causes of developmental continuity or “tracking.” I. Longitudinal twin studies during growth , 1988, Behavior genetics.

[14]  D I Boomsma,et al.  The genetic analysis of repeated measures. I. Simplex models , 1987, Behavior genetics.

[15]  J J McArdle,et al.  Latent growth curves within developmental structural equation models. , 1987, Child development.

[16]  R. MacCallum.  Relationships between linear systems theory and covariance structure modeling , 1986 .

[17]  A C Heath,et al.  A theory of developmental change in quantitative phenotypes applied to cognitive development , 1986, Behavior genetics.

[18]  D. Rindskopf.  Using phantom and imaginary latent variables to parameterize constraints in linear structural models , 1984 .

[19]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[20]  Sik-Yum Lee.  Estimation of covariance structure models with parameters subject to functional restraints , 1980 .

[21]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[22]  Michael D. Geurts,et al.  Time Series Analysis: Forecasting and Control , 1977 .

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

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

[25]  Louis Guttman,et al.  A generalized simplex for factor analysis , 1955 .