By Terry E. Duncan
This publication offers a complete creation to latent variable development curve modeling (LGM) for examining repeated measures. It offers the statistical foundation for LGM and its quite a few methodological extensions, together with a couple of sensible examples of its use. it truly is designed to use the reader’s familiarity with research of variance and structural equation modeling (SEM) in introducing LGM options. pattern information, syntax, enter and output, are supplied for EQS, Amos, LISREL, and Mplus at the book’s CD. during the ebook, the authors current numerous LGM concepts which are worthy for plenty of diversified study designs, and diverse figures offer precious diagrams of the examples.
Updated all through, the second one version positive factors 3 new chapters—growth modeling with ordered specific variables, progress combination modeling, and pooled interrupted time sequence LGM ways. Following a brand new association, the ebook now covers the improvement of the LGM, through chapters on multiple-group concerns (analyzing development in a number of populations, speeded up designs, and multi-level longitudinal approaches), after which distinctive themes similar to lacking information types, LGM energy and Monte Carlo estimation, and latent progress interplay versions. The version requirements formerly incorporated within the appendices are actually to be had at the CD so the reader can extra simply adapt the versions to their very own research.
This sensible consultant is perfect for a variety of social and behavioral researchers drawn to the size of switch over the years, together with social, developmental, organizational, academic, client, character and medical psychologists, sociologists, and quantitative methodologists, in addition to for a textual content on latent variable progress curve modeling or as a complement for a direction on multivariate information. A prerequisite of graduate point information is recommended.
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Additional resources for An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, and Application, Second Edition
The basic idea of identification is to impose sufficient constraints on model parameters to ensure a unique solution. For a more complete discussion of mean and covariance structure analysis, see Bentler and Wu (2005). Tests for overall model fit suggest a perfect fit of the model to the data, given the saturated nature of the hypothesized model. With three repeated measures, there are 3 variances, 3 covariances, and 3 observed means, or 9 pieces of information, to use in model estimation. The model estimates 3 variances, 3 covariances, and 3 means for the constant, linear, and quadratic latent factors, resulting in zero degrees of freedom.
Like the Mi(n) score, Ms(n) is a constant for any individual across time. The contribution of Ms(n) to Y(t, n), however, changes as a function of the basis coefficient, B(t). E(n) is an error variable representing an unobserved random score, with a mean of zero and no correlation with any other variable over time. Such errors are expected to change randomly over time for any individual. The basis term, B(t), is a mathematical function relating variable Y to variable t, specified in terms of linear departures from an origin, and may be of linear or nonlinear form.
Although the correlations give some idea as to the relative magnitude of these effects, the analysis does not indicate their level of significance. f. 000 The Latent Growth Curve Model. The diagrammatic representation of the three-factor saturated latent growth curve model is presented in Fig. 1. Specific restrictions must be placed on this model to correspond with the assumptions from the general linear modeling procedure (MANOVA) previously presented. First, the orthogonal polynomial transformation matrix generated from the MANOVA procedure is used to represent the regression coefficients relating the latent factors to the observed variables, rather than the coefficients presented in chapter 2.