Global Warming and the Weights of Rats: Uses of the Variogram in the Analysis of Longitudinal Data

Abstract

Monthly data have been assembled on the temperature of the Earth for the last 140 years. Time series analysis of such data have indicated that — under the ‘business as usual’ scenario — the world is warming. This is however somewhat sensitive to the choice of model for the covariance structure and the estimation procedure used.

Repeated measurements are common in laboratory and other experiments. One such involves monitoring the weights of different sets of rats over a period. Exactly the same time techniques as above may be used and are now being recommended in classical statistical analyses of such data.

The variogram can provide a basis for satisfactory modelling in both cases. Two estimating procedures are considered. The first is a variant on the classic ‘method-of-moments’ procedures, adapted for estimating in the presence of trend. The second is the use of maximum likelihood procedures. The paper will thus illustrate methods that have been recently proposed in classical statistical literature.