An Application of the Growth Curve Model to a Spatial Temporal data

Abstract

For the case when the longitudinal measurement data is observed in an individual with spatial information, we attempt to apply a growth curve model with interaction terms in time and space.　Considering basis functions of time and space, simultaneous confidence intervals for predicted curves on the time axis or predicted surfaces in space are given for each fixed condition.　We also consider the application of a local growth curve model to reduce the number of bases for the interaction terms, especially in space.　The proposed method is applied to the temperature data observed at 35 stations in Canada for six periods from March to August, and the applicability of the model is verified.　The fit of the proposed model is good in terms of multiple correlation coefficients between observation and fitted values, although the observed temperature data show various changes over time such in different stations.