Estimation of a cluster-level regression model under nonresponse within clusters
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Estimation of a cluster-level regression model under nonresponse within clusters Nuanpan Lawson1 · Chris Skinner2
Received: 28 March 2017 / Accepted: 22 August 2017 / Published online: 9 September 2017 © The Author(s) 2017. This article is an open access publication
Abstract When sample surveys are clustered and subject to non-response, it is possible to study cluster-level association between response rates and cluster-level quantities derived from survey variables. The existence of association may suggest informative nonresponse with possible biasing effects. In this paper, this problem is studied for the case where the aim is to fit a cluster-level regression model. Two possible underlying models for nonresponse with potential biasing effects are considered. Alternative estimators of regression coefficients under these models are proposed. The properties of these estimators are studied in two simulation studies and with real data from a survey of employees, where the clusters consist of workplaces. Keywords Cluster specific nonignorable nonresponse · Cluster sample · Informative nonresponse · Regression model · Selection
1 Introduction A feature of nonresponse in clustered survey data is that it is possible to study cluster-level association between response rates and aggregate statistics, such as means or proportions, for survey variables of interest. Thus, if pi denotes the response rate among elementary sample units in cluster i and y¯ri denotes the mean of a variable Y among responding units within cluster i then it is possible to study the association between these two quantities across clusters, perhaps conditional on some other cluster-level factors. In contrast, no equivalent association can be observed at the elementary unit level (in unclustered data) since Y is missing for nonresponding units.
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Chris Skinner [email protected]
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Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
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Department of Statistics, London School of Economics and Political Science, London, UK
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N. Lawson, C. Skinner
The occurrence of such cluster-level association between pi and y¯ri may be suggestive of some kind of informative nonresponse. In this paper, we consider this issue when the objective is to fit a regression model at the cluster level, as may be of scientific relevance when the clusters are of analytic interest. As a motivating example in Sect. 3, we consider a survey of employees, where the clusters consist of workplaces and there is analytic interest in how the well-being of employees at a workplace depends upon different kinds of innovations at the workplace. Another example is a survey of hospital patients about the quality of care received, where there may be interest in analysis at the hospital level but nonresponse may arise at the individual patient level [9]. We shall be interested in the case where testing for inclusion of pi or some function of it as a covariate in the model may be used as some kind of diagnostic for informative
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