The models of the previous chapters assume observed responses are independent. However many studies yield correlated observations. Correlation results from the sampling design or the way data are collected. Here are some practical situations leading to correlated responses.

• Claims experience is often studied on the same policy over successive time periods. For example claims on a given policy may be studied for each of five years. Claims for a given policyholder in successive years are correlated. A particularly bad driver will have higher than average claims in successive years, and conversely for a good driver. Here the average is calculated given the other rating variables. Responses on the same individual or policy at different points in time will tend to be more alike than responses on different individuals or policies with the same characteristics.

• When writing crop insurance policies in a given state, the state may be divided into geographical regions. Each region is likely to experience roughly the same weather conditions and hence different policies in the same region are likely to have a similar claims experience.

• Industries and companies are often classified into groups with a hierarchical structure. For example, a supermarket is a subdivision of “Supermarket and Grocery Stores” which in turn is a subdivision of “Food Retailing.” Companies in the same industry group are more similar than a group of randomly selected companies.

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