timepath97


This site contains background information and guides for using the Timepath97 program.
The major divisions of the site (navigable through the TABS at the top of the page) are:


Short Description

Timepath97 is a program (using the SAS system) for longitudinal data analysis based on statistical models for collections of growth curves. The program carries out useful descriptive analyses along with parameter estimation and inference procedures for common longitudinal data structures.
The program is composed of:
a SAS macro  timepath97.sas   (along with  jackboot.sas )
*plus* a graphical frontend for program input  timepath97.exe   for Win95/NT (see Tp Startup TAB).
All these components are available from the Download TAB.


Program Overview and History
Approach to Longitudinal Data Analysis
Data analysis strategies and methods in Timepath97 follow directly from the modeling approach that has been the basis for my writings (1980 onward) and computational programs (1981 onward) for longitudinal data analysis. The unifying theme is that longitudinal research questions can be addressed by models and methods that start with the individual unit trajectories-- useful methods for the analysis of longitudinal data take as the starting point a model for the individual history. The simplest instance of this type of model for a quantitative outcome is a straight-line growth curve for each individual. Fitting such a model to the individual's data points can be thought of as using the model to smooth the data in order to derive an attribute for the individual, such as the rate of improvement or decline in that measure. The power of this approach is the straightforward way in which such analyses can be built up for complex settings (e.g. comparing groups, assessments of stability, and so forth) without losing firm contact with the data, and extensions to more complex growth models or settings retain the basic approach, only the technical details increase.

Examples of descriptive and inferential analyses using past versions of the computational programs, along with basic discussion of measurement of change issues, can be found in

Rogosa, D. R., and Saner, H. M. (1995). Longitudinal data analysis examples with random coefficient models. Journal of Educational and Behavioral Statistics, 20, 149-170.
Also: Reply to Discussants, 234-238.
Data Examples from Rogosa-Saner are available from this page.

Rogosa, D. R. (1995). Myths and methods: "Myths about longitudinal research," plus supplemental questions. In The analysis of change, J. M. Gottman, Ed. Hillsdale, New Jersey: Lawrence Erlbaum Associates, 3-65.
Selected Data and Analysis Examples from the Myths chapter are available from this page.

For a reminder of measurement of change history

Timepath Program History
Since 1981, I have used various versions of a program we call Timepath for the analysis of quantitative longitudinal panel data: program originally developed with the assistance of John Willett and Gary Williamson (see Williamson et al. 1991), with later versions written with Ghassan Ghandour. In this program, ordinary least-squares regression is used to estimate the growth curve model from the longitudinal data for each individual. As the empirical rate of change can be treated as an attribute of an individual, the obtained slopes for each individual regression can be profitably used for various descriptive analyses. Such descriptive analyses may, in many situations, be more important and informative than the formal parameter estimation.

In the original Timepath , maximum likelihood estimates derived from the results in Blomqvist (1977) were used to estimate many of the parameters and variance components for the population of individual growth curves. In the case of complete data for Y and W and the same observation times for all individuals (call that "synchronous" data), it is straightforward to implement computation of the closed-form maximum-likelihood estimates of parameters. Starting with the Rogosa & Ghandour, 1987 version, standard errors for these parameter estimates and confidence intervals for the parameters are obtained by bootstrap resampling methods in which rows (individual units) are resampled (reported standard errors are just the standard deviations over 4000 bootstrap replications, and the endpoints of the reported 90% confidence intervals are just the 5% and 95% values of the empirical distributions from the resampling ). More sophisticated and more accurate confidence intervals (BCa method) are used in Timepath97.

Prior versions of Timepath treated situations with missing longitudinal observations (deliberately) in a very simple manner--the individual growth curves are fit to the data that are present, and the overall SSE from the individual fits is just weighted according to the observations present. In Rogosa and Saner (1995), comparisons with newer computational programs based on Hierarchical Linear Model methodology (especially the HLM program of Bryk & Raudenbush) showed that simple-minded use of Ordinary Least-Squares and minor adaptations of the closed-form mle produced (even for situations were individuals were measured at different times and missing observations) quite satisfactory point estimates--besides providing the information on uncertainty of estimation these programs lacked.

Why a New Program?
The advent of advanced and widely available mixed-model estimation procedures (PROC MIXED in SAS or lme in S-plus), better computing equipment (to make practical the resampling procedures used with mixed-model estimation), and in SAS, the ability to manipulate output from procedures via ODS capabilities, all combine to make it attractive to extend the Timepath approach to more complex data structures (see Data Structures TAB). And that's what Timepath97 does (at present).