Abstract
Recall that in Chapter 6, a class of correlation models was discussed for the analysis of longitudinal count data collected from a large number of independent individuals, whereas in Chapter 4, we discussed the analysis of count data collected from the members of a large number of independent families. Thus, in Chapter 4, familial correlations among the responses of the members of a given family were assumed to be caused by the influence of the same family effect on the members of the family, whereas in Chapter 6, longitudinal correlations were assumed to be generated through a dynamic relationship among the repeated counts collected from the same individual. A comparison between the models in these two chapters (4 and 6) clearly indicates that modelling the longitudinal correlations for count data through a common individual random effect would be inappropriate. If it is, however, thought that the longitudinal count responses may also be influenced by an invisible random effect due to the individual, this will naturally create a complex correlation structure where repeated responses will satisfy a longitudinal correlation structure but conditional on the individual random effect.
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Sutradhar, B.C. (2011). Longitudinal Mixed Models for Count Data. In: Dynamic Mixed Models for Familial Longitudinal Data. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8342-8_8
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