By Ams Special Session on Algebraic Methods in Statistics, Marlos A. G. Viana, Donald St. P. Richards (ed.)

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ISBN-13: 9780821826874

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Algebraic tools and arguments in facts and chance are renowned, from Gauss' least squares precept via Fisher's approach to variance decomposition. The relevance of group-theoretic arguments, for instance, grew to become obtrusive within the Eighties. Such recommendations stay of curiosity at the present time, besides different advancements, resembling using graph thought in modelling complicated stochastic systems.This quantity relies on lectures provided on the AMS specific consultation on Algebraic equipment and data held on the college of Notre Dame (Indiana) and on contributed articles solicited for this quantity. The articles are meant to foster communique among representatives of the various medical components within which those features are applied and to additional the fad of using algebraic tools within the components of records and chance. this is often certainly one of few volumes dedicated to the topic of algebraic tools in information and likelihood. the wide variety of themes coated during this quantity demonstrates the energetic point of analysis and possibilities ongoing in those components

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**Extra resources for Algebraic Methods in Statistics and Probability**

**Sample text**

Instead of scaling the latent variable as a function of a manifest indicator, we could also fix the variance of the latent construct at some value, typically 1. This would result in just a small change to the model specifications, as follows. This suggests that a one standard deviation increase in the latent variable is associated with a change in the manifest indicators equivalent to the ele‑ ments of lambda‑y. In regression terms, the first situation where scaling is done in lambda‑y is analogous to the unstandardized (b) regression coef‑ ficient.

This very general statistical model encom‑ passes a variety of statistical methods such as regression, factor analysis, and path analysis. In this book, we assume that the reader has familiarity with this general class of models, along with at least one software pack‑ age for their estimation. Several excellent introductory volumes are avail‑ able for learning structural equation modeling, including Arbuckle (2006), Bollen (1989b), Byrne (1998), Hayduk (1987), Hoyle (1995), Kaplan (2009), Kelloway (1998), Raykov and Marcoulides (2006), and Schumacker and Lomax (2004), as well as several others.

Software programs vary considerably in terms of the default values they impose upon a model, so being explicit can help ensure that the model you specified is the one you intended to estimate. This is particularly true with the MPlus software, where the default initial values vary from one type of model to another. In structural equation modeling, there are three different types of model parameters. A parameter may be fixed (FI) to a specific value (VA), typi‑ cally 0 or 1. It may also be freely (FR) estimated.

### Algebraic Methods in Statistics and Probability by Ams Special Session on Algebraic Methods in Statistics, Marlos A. G. Viana, Donald St. P. Richards (ed.)

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