In previous work the investigator had developed the Disturbed Highest Derivative Polynomial (DHDP) as a model-free time curve and had published the theoretical development for its use as the overall time curve in a linear Gaussian model for longitudinal data with fixed covariate effects and autocorrelated errors but without subject effects. For the logistic model, the DHDP would replace the constant which appeared in the log odds in the non-longitudinal case. The first-order DHDP was a straight line whose slope received random disturbances over time. As such, it was capable of fitting a rich variety of arbitrarily changing time curves. The second-order DHDP would generally provide a fit with smaller high frequency variation. There are a number of longitudinal data analysis methods currently available for Gaussian and binary-logistic data. They all have in common the requirement to explicitly model the overall time curve--usually by a low order deterministic polynomial. The main significance of this proposal was to represent the overall time curve by a DHDP, thereby allowing the possibility for fitting arbitrarily changing time curves without explicitly modeling the form of the change over time. The order of the DHDP can be selected by a modification of the Akaike Information Criterion. The Poisson model should be useful in fitting the periodic reported incidence of a rare disease. The relationship of the DHDP to the Smoothing Polynomial Spline (SPS) was shown and methods were developed for using a SPS instead of a DHDP in analysis. Robustness of the methods were examined by computer simulation studies which evaluated and compared the ability of the DHDP and SPS models to estimate covariate effects and time curves when the time curves were generated by processes other than DHDP.