Poster #24 - Analyzing Longitudinal Data Using Natural Cubic Smoothing Splines

• In Event: 2-001 - Poster Session 1 during Breakfast

Abstract

Analyzing longitudinal data holds a prominent role in developmental science having been the focus of considerable research for many years. Almost a century ago Merrell (1931) made it clear that individually fitted growth curves were necessary for the accurate analysis of longitudinal data. When fitting individual curves to longitudinal data, there are two broad challenges. The first concerns the estimation of a useful summary of growth and the second involves making comparisons between observed individuals. This paper focuses mainly on the first challenge, the estimation of a useful summary of individual growth. If the change over time is unquestionably linear parameter estimates of the model can be easily computed. With nonlinearity, however, this is not always a straightforward process. For example, consider the plots in Figures 1 and 2 displaying California First-Year Mental Scale cognitive scores (a test administered in the Berkeley Growth Study from 1 to 12 months of age). Numerous approaches have been proposed to model such nonlinear data patterns, however, because many of these either impose overly restrictive assumptions or are computationally demanding, their effectiveness and level of precision is not always assured.

This paper introduces an alternative approach using a natural cubic smoothing spline model. In keeping with the recommendation provided by Wood, Steinley, and Jackson (2015) that there is really no right model but one can at least determine which models are informative, the approach is shown to provide excellent summarizations of change consistent with the examined data. It is particularly appropriate in research situations where the absence of assumptions about the form of growth is a reasonable conjecture. Given recent interest in analyzing secondary and open source data (especially with electronic devices involving repeatedly reported behaviors or symptoms), there is also a need for robust approaches related to functional form, data set size, number and interval time between measurement occasions. Natural cubic smoothing splines address such issues.

The perspective taken is that building and using the proposed modeling approach is part of an iterative process during which a model is formulated and tested against observed data. This process also fits nicely within the exploratory data mining framework where interest is on developing and applying algorithms to find patterns and structures in data. To execute the numerical analyses needed and generate the necessary trajectory plots, a simple computerized implementation via programmed macros and spreadsheet templates in Microsoft Excel is also illustrated.

Author

• Katerina M. Marcoulides, University of Florida
  Presenting Author