We start with some simple repeated measures data and we shall use them to illustrate models of increasing complexity. The data set consists of nine measurements made on 26 boys between the ages of 11 and 13.5 years, approximately 3 months apart [16].

A Equations y patient, clinic

y patient, clinic patient, clinic^ 0 clinic^ 1 patient, clinic

/?0patient clinic 0.012i 0.040 } + U Q eiMff + e Qpatient clmc

0 clinic

0 patient, clinic

-2*loglikelikood(IGLS) = 9316.870(4059 of4059 cases in use)

Fonts Su<i■ 'J iiii: + - Add Teii> iitinwileii Nunllrttai Cleai

Figure 3. Equation screen with estimates.

Figure 4, produced by MLwiN, shows the mean heights by the mean age at each measurement occasion. We assume that growth can be represented by a polynomial function, whose coefficients vary from individual to individual. Other functions are possible, including fractional polynomials or non-linear functions, but for simplicity we confine ourselves to examining a fourth-order polynomial in age (t) centred at an origin of 12.25 years. In some applications of growth curve modelling transformations of the time scale may be useful, often to orthogonal polynomials. In the present case the use of ordinary polynomials provides an accessible interpretation and does not lead to computational problems, for example due to near-collinearities. The model we fit can be written as follows:

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