An Introduction to the Use of Linear Models with Correlated Data

Benoît Laplante, Benoît-Paul Hébert


Correlated data originate when observations are not selected independently
because of sampling design, study design (especially panel studies), or spatial
distribution of the population. In these situations, conventional methods for
estimating the parameters of linear models are inappropriate, and the
conventional methods for estimating the variances of these estimates may yield biased results. These two problems are different, but they are related. This paper provides an introduction to the problems caused by correlated data and to possible solutions to these problems. First, we present the two problems and try to specify the relations between the two as clearly as possible. Second, we provide a critical presentation of random effects, mixed effects and hierarchical models that would help researchers to see their relevance in other kinds of linear models, particularly the so-called measurement models.

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