Conclusions

Phase One of the study yielded ambiguous results. There was evidence of chaotic dynamics but that evidence was not robust, principally due to sample size. However, the presence of irregularity and random components interspersed with periodicities pointed to nonlinear, if not chaotic dynamics.

Phase Two results are much more promising. RD and RA are robust to nonstationarity (indeed they are designed to deal with nonstationarity) and are appropriate for use with relatively short time series. The results of RD indicate the data reflect a fractal random process when examined across geographic regions. The differences in the Hurst exponent, the scaling index and the fractal dimensions across public health regions point to sociodemographic factors that influence memory across time scales and may be linked to varying degrees of persistence in the time series.

Recurrence analysis also holds out promise of a means of identifying shifts in the underlying dynamics of the process. These shifts, then, may be precursors to more obvious changes in overall mean and variance. Also, such shifts may reveal periods in the process that are more sensitive to perturbations in the form of interventions.

Despite the success of the study outlined there remain challenging questions to be answered.

1. How can the values associated with nonlinear dynamics (recurrence, Hurst exponent, Lyapunov exponent, scaling index, fractal dimension and the like) be exploited as sensitive, early measures of shifts in a process?
2. How can the values associated with nonlinear dynamics be linked to sociodemographic factors in the environment of teen mothers?
3. Are traditional linear measures such as correlation and regression valid for identifying the relationships of sociodemographic factors with nonlinear parameters?
4. Can two groups with different nonlinear properties validly be compared using linear statistics?
5. Are nonlinear techniques more useful than linear ones for policy evaluation and targeting of interventions?

This work was funded by grants from the National Institute for Nursing Research (1R15 NR 03733-01) and from the National Center for Child Health and Human Development (1 RO3 HD 37207-01).