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Random: level 1(SE in brackets) ffe2 0.24(0.05) a 6.59(1.90)

Random: level 1(SE in brackets) ffe2 0.24(0.05) a 6.59(1.90)

accomplished within the GLS step for the random parameters by modifying (5) to

w w so that the parameter S is the common level-1 covariance (between occasions). Goldstein et al. [16] show how to model quite general non-linear covariance functions and in particular those of the form cov(eíeí-s) = o;2 exp(-g(a,s)), where s is the time difference between occasions. This allows the correlation between occasions to vary smoothly as a function of their (continuous) time difference. A simple example is where g = as, which, in discrete time, produces an AR(1) model. The GLS step now involves non-linear estimation that is accomplished in a standard fashion using a Taylor series approximation within the overall iterative scheme. Pourahmadi [21,22] considers similar models but restricted to a fixed set of discrete occasions.

Table II shows the results of fitting the model with g = as together with a seasonal component. If this component has amplitude, say, a we can write it in the form a cos(t*+y), where t* is measured from the start of the calendar year. Rewriting this in the form aj cos(t*)-a2 sin(t*) we can incorporate the cos(t*), sin(t*) as two further predictor variables in the fixed part of the model. In the present case a2 is small and non-significant and is omitted. The results

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