Skip to main content Accessibility help
×
Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-17T17:07:17.099Z Has data issue: false hasContentIssue false

9 - The robustness of maximum likelihood estimation in structural equation models

Published online by Cambridge University Press:  12 January 2010

Get access

Summary

Introduction

General methods for the analysis of covariance structures were introduced by Joreskog (1970, 1973). Within the general theoretical framework it is possible to estimate parameters and their corresponding standard errors and to test the goodness-of-fit of a linear structural equation system by means of maximum likelihood methods. Although other methods of estimating such models (least squares procedures, instrumental variable methods) are available, we do not discuss them here.

For an introduction to the general model the reader is referred to Chapter 2 and for more detailed statistical discussions to Jöreskog (1978, 1982a, b). The LISREL model considers a data matrix Z(N × k) of N observations on k random vaŕiables. It is assumed that the rows of Z are independently distributed, each having a multivariate normal distribution with the same mean vector μ and the same covariance matrix ∑; that is, each case in the data is independently sampled from the same population. In a specified model there are s independent model parameters co, to be estimated. For large samples the sampling distribution of the estimated parameters ŵi and the sampling distribution of the likelihood ratio estimate for goodness-of-fit are approximately known, provided that the preceding assumptions hold. Under the same conditions the standard errors of the estimated parameters seŵi are also known asymptotically. In the following, standardized parameter estimates are defined by ŵ*i = (ŵi − ωi)/seŵi. For large samples the sampling distribution of ŵ*i is approximately standard normal, and the goodness-of-fit estimate has an approximate chi-square distribution with k(k + 1)/2 – s degrees of freedom.

Type
Chapter
Information
Structural Modeling by Example
Applications in Educational, Sociological, and Behavioral Research
, pp. 160 - 188
Publisher: Cambridge University Press
Print publication year: 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×