Determining the meaning of parameters in multilevel models for longitudinal data

This paper is concerned with parameter interpretation in longitudinal, multilevel models. Models are described that consider repeated observations nested within individuals. These models typically first estimate subject-specific parameters for growth curves that describe the development of some observed variable over time. Examples of such descriptors include polynomials. It is shown that interpretation of polynomial parameters can be facilitated by linear transformations. Examples of such transformations include centring (i.e. subtracting the mean from raw data). When parameters are specified such that they have no straightforward meaning at the first level of analysis, interpretation problems carry over to the second and higher levels. Therefore, proper specification of models at the first level is of utmost importance. Methods of transformation are introduced. Examples illustrate the method using data that describe children's vocabulary development in the second year of life.