By Terry E. Duncan
This publication offers a accomplished advent to latent variable development curve modeling (LGM) for examining repeated measures. It provides the statistical foundation for LGM and its quite a few methodological extensions, together with a few sensible examples of its use. it really is designed to use the reader’s familiarity with research of variance and structural equation modeling (SEM) in introducing LGM ideas. pattern info, syntax, enter and output, are supplied for EQS, Amos, LISREL, and Mplus at the book’s CD. through the booklet, the authors current various LGM options which are worthwhile for lots of diverse examine designs, and various figures supply beneficial diagrams of the examples.
Updated all through, the second one version positive factors 3 new chapters—growth modeling with ordered express variables, development combination modeling, and pooled interrupted time sequence LGM techniques. Following a brand new association, the publication now covers the advance of the LGM, through chapters on multiple-group concerns (analyzing progress in a number of populations, sped up designs, and multi-level longitudinal approaches), after which distinctive issues akin to lacking information types, LGM strength and Monte Carlo estimation, and latent development interplay versions. The version requisites formerly integrated within the appendices at the moment are on hand 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 dimension of switch over the years, together with social, developmental, organizational, academic, shopper, character and medical psychologists, sociologists, and quantitative methodologists, in addition to for a textual content on latent variable development curve modeling or as a complement for a path on multivariate data. A prerequisite of graduate point information is recommended.
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Extra info for An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, and Application, Second Edition
To illustrate, let B0(t) = [1, 1, 1] and B1(t) = [0, 1, 2] represent the function for the data at Time 1 through Time 3, respectively. In addition, let mean intercept = 2 and mean slope = 1. 32 Y(3) = Mi + 2Ms + E(3). 36 SPECIFICATION OF THE LGM 33 where B(t) = 2 indicates that from Time 1 to the third time point there are 2 units of change. Therefore, B(t) describes change in terms of linear differences from initial status at Time 1. Given that B(t) represents the same relation for all individuals, it is likely that individual differences will not only exist in level, Mi(n), but also in the estimated developmental trajectories, Ms(n) (McArdle & Hamagami, 1991).
FIG. 4. Representation of a two-factor unspecified LGM. 32 CHAPTER 2 The mathematical model for the LGM depicted in Fig. 30 where Y(t, n) = observed score at Time t, Mi(n) = unobserved score for the intercept, Ms(n) = unobserved score for the shape, E(t, n) = unobserved error, and B(t) = basis coefficient for Time t. Observed scores are specified to be a weighted sum of two individual latent variables: Mi(n) is a variable representing individual differences in level of some attribute and is a constant for any individual across time; Ms(n) is a shape variable representing individual differences in the rate of change over time.
Standard deviations are presented on the diagonal. ror). LGM, however, allows variations and extensions of the general repeated measures ANOVA and MLM approaches. For example, LGM has the advantage of allowing for a test of the adequacy of the hypothesized growth form and measurement error distributions of either a homoscedastic or heteroscedastic nature. INCLUDING PREDICTORS AND SEQUELAE OF CHANGE IN GROWTH CURVE MODELS As noted earlier, growth curve methodology consists of two stages. First, a regression curve, not necessarily linear, is fit to the repeated measures of each individual in the sample.
An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, and Application, Second Edition by Terry E. Duncan