By Kenneth A. Bollen
An efficient strategy for facts research within the social sciencesThe contemporary explosion in longitudinal info within the social sciences highlights the necessity for this well timed booklet. Latent Curve types: A Structural Equation point of view presents an efficient strategy to learn latent curve types (LCMs). this sort of facts positive aspects random intercepts and slopes that allow every one case in a pattern to have a unique trajectory through the years. in addition, researchers can comprise variables to foretell the parameters governing those trajectories.The authors synthesize an enormous volume of study and findings and, while, offer unique effects. The ebook analyzes LCMs from the viewpoint of structural equation types (SEMs) with latent variables. whereas the authors talk about basic regression-based systems which are valuable within the early levels of LCMs, many of the presentation makes use of SEMs as a using software. This state-of-the-art paintings contains a few of the authors' contemporary paintings at the autoregressive latent trajectory version, indicates new versions for technique components in a number of symptoms, discusses repeated latent variable versions, and establishes the identity of various LCMs.This textual content has been completely class-tested and makes vast use of pedagogical instruments to assist readers in learning and utilising LCMs quick and simply to their very own information units. Key gains include:Chapter introductions and summaries that supply a brief evaluate of highlightsEmpirical examples supplied all through that let readers to check their newly stumbled on wisdom and become aware of functional applicationsConclusions on the finish of every bankruptcy that rigidity the fundamental issues that readers have to comprehend for development to extra refined topicsExtensive footnoting that issues how you can the first literature for additional information on specific topicsWith its emphasis on modeling and using various examples, this is often an outstanding booklet for graduate classes in latent trajectory types in addition to a supplemental textual content for classes in structural modeling. This e-book is a superb relief and reference for researchers in quantitative social and behavioral sciences who have to study longitudinal facts.
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Additional resources for Latent Curve Models: A Structural Equation Perspective (Wiley Series in Probability and Statistics)
Example text
Under these two assumptions, there are now T + 5 unknowns for the linear model. The necessary condition for identification will not be satisfied with only two waves of data because there will be seven unknown parameters and only five known parameters with which to work. 3 Instead, we use an algebraic approach to investigate identification. , E(y1 ) instead 1 Moments are characteristics of the distribution of random variables. Depending on the distribution from which the observed variable is drawn and the model structure, it is sometimes theoretically possible to use higher-order moments of the observed variables to aid in parameter identification.
The ML θ is consistent, asymptotically unbiased, asymptotically normal, and asymptotically efficient. 8 The maximum likelihood function here that is typical of SEM is formulated so that this function is minimized. 58) Thus, tests of statistical significance are available when we substitute the estimated values of θ into the asymptotic covariance matrix. Robustness to Nonnormality The ML estimator maintains its desirable asymptotic properties when the observed variables have the same multivariate kurtosis as a multivariate normal distribution (Browne, 1984), a condition referred to as no excess multivariate kurtosis.
The 12 T (T + 3) formula is general and provides the number of means, variances, and covariances available no matter the number of waves of data. There will be N T parameters for VAR( it ), T parameters for λt , and 12 K(K + 3) parameters for µα , µβ , ψ α , ψ ββ , and ψ αβ , where K equals the total number of latent variables to describe the trajectory. For instance, K = 1 if there only is a random intercept, K = 2 if there is a random intercept and random slope, K = 3 when a random quadratic term is added, and so on.