By Terry E. Duncan
This booklet offers a accomplished creation to latent variable progress curve modeling (LGM) for studying repeated measures. It provides the statistical foundation for LGM and its quite a few methodological extensions, together with a few useful examples of its use. it's designed to use the reader’s familiarity with research of variance and structural equation modeling (SEM) in introducing LGM ideas. pattern information, syntax, enter and output, are supplied for EQS, Amos, LISREL, and Mplus at the book’s CD. in the course of the e-book, the authors current various LGM concepts which are priceless for lots of varied learn designs, and various figures offer useful diagrams of the examples.
Updated all through, the second one variation positive factors 3 new chapters—growth modeling with ordered express variables, progress blend modeling, and pooled interrupted time sequence LGM techniques. Following a brand new association, the e-book now covers the advance of the LGM, through chapters on multiple-group concerns (analyzing progress in a number of populations, speeded up designs, and multi-level longitudinal approaches), after which detailed subject matters similar to lacking information versions, LGM strength and Monte Carlo estimation, and latent progress interplay types. The version standards formerly incorporated 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 functional advisor is perfect for quite a lot of social and behavioral researchers attracted to the dimension of swap over the years, together with social, developmental, organizational, academic, purchaser, character and scientific psychologists, sociologists, and quantitative methodologists, in addition to for a textual content on latent variable progress curve modeling or as a complement for a path on multivariate data. A prerequisite of graduate point facts is recommended.
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Additional resources for An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, and Application, Second Edition
Where b1 is the intercept, b2 is the slope (amount of vertical increase per unit of horizontal run of the growth curve), ti is the ith value of time, ei represents the time-specific errors of prediction, and i is the value of time. 26 V2 = b1 + 1 b2 + e2 . 27 Relating these equations back to Fig. 2a, for any given individual, b1 corresponds to the intercept factor score (F1), b2 corresponds to the slope factor score (F2), and ei corresponds to the time-specific errors of prediction. 29 where L1 = 0 at Time 1 simply starts the curve at this point by rescaling the intercept factor to represent initial status, and L2 = 1 at Time 2 indicates that from Time 1 to Time 2 there is 1 unit of change.
E1 = E2 = 0). FIG. 1. Representation of a two-factor LGM for two time points. SPECIFICATION OF THE LGM 19 To identify this model, two slope loadings must be fixed to two different values. Fixing the regression coefficient relating F2 and V1 at zero and F2 and V2 at 1 has the effect of locating the intercept at the initial measurement, V1. Although the choice of loadings is somewhat arbitrary, the intercept factor is bound to the time scale. Shifting the loadings on the slope factor alters the scale of time, which affects the interpretation of the intercept factor mean and variance.
Because monotonic stability puts severe demands on the structure of the means, variances, and covariances of the observed variables, the model should be adopted only when it makes sense theoretically and the data warrant it. Such would be the case when the rank ordering of individuals does not vary across time despite mean level changes. SUMMARY It is crucial to recognize the limitations of trying to build an adequate model of social behavior with just two points in time. Many important assumptions must be made that can fundamentally affect the conclusions drawn about the nature of change over time on the constructs of interest.
An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, and Application, Second Edition by Terry E. Duncan