Familial models for count data are also known as Poisson mixed models for count data. In this setup, count responses along with a set of multidimensional covariates are collected from the members of a large number of independent families. Let yij denote the count response for the jth (j =1, …,ni) member on the ith (i=1, …, K) family/cluster. Also, let xij = (xij1, …,xijp)′ denote the p covariates associated with the count response yij. For example, in a health economics study, a state government may be interested to know the effects of certain socioeconomic and epidemiological covariates such as gender, education level, and age on the number of visits by a family member to the house physician in a particular year. Note that in this problem it is also likely that the count responses of the members of a family are influenced by a common random family effect, say γi. This makes the count responses of any two members of the same family correlated, and this correlation is usually referred to as the familial correlation. It is of scientific interest to find the effects of the covariates on the count responses of an individual member after taking the familial correlations into account.
Generalize Linear Mixed Model Relative Bias Count Response Familial Correlation Approximate Likelihood
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