On Joint Estimation of Regression and Overdispersion Parameters in Generalized Linear Models for Longitudinal Data
Liang and Zeger introduced a class of estimating equations that gives consistent estimates of regression parameters and of their variances in the class of generalized linear models for longitudinal data. When the response variable in such models is subject to overdispersion, the oerdispersion parameter does not only influence the marginal variance, it may also influence the mean of the response variable. In such cases, the overdispersion parameter plays a significant role in the estimation of the regression parameters. This raises the necessity for a joint estimation of the regression, as well as overdispersion parameters, in order to describe the marginal expectation of the outcome variable as a function of the covariates. To correct for the effect of overdispersion, we, therefore, exploit a general class of joint estimating equations for the regression and overdispersion parameters. This is done, first, under the working assumption that the observations for a subject are independent and then under the general condition that the observations are correlated. In the former case, both score and quasi-score estimating equations are developed. The score equations are obtained from the marginal likelihood of the data, and the quasi-score equations are derived by exploiting the first two moments of the marginal distribution. This quasi-score equations approach requires a weight matrix, usually referred to as the pseudo-covariance weight matrix, which we construct under the assumption that the observations for a subject (or in a cluster) are independent. In the later case when observations are correlated, quasi-score estimating equations are developed in the manner similar to that of the independence case but the pseudo-covariance weight matrix is constructed from a suitable working covariance matrix of the longitudinal observations, the joint distribution of the observations being unknown. Asymptotic theory is provided for the general class of joint estimators for the regression and overdispersion parameters. The asymptotic distributional results are also applied to develop suitable chi-square test for testing for the regression of the overdispersed data.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 56 (1996)
Issue (Month): 1 (January)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:56:y:1996:i:1:p:90-119. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.