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Stata Technical Bulletin

STB-4

smv2 Analyzing repeated measurements—some practical alternatives

William H. Rogers, CRC, FAX 310-393-7551

Longitudinal studies (also known as panels or cross-sectional time-series) are some of the most potentially informative
yet complicated studies to analyze. A typical longitudinal study follows individuals over time to monitor the effects of some
experimental treatment. For example, two baseline measures might be taken and then a drug administered to half the sample.
The patients are assessed one, two, and three months later.

One technique for analyzing such data is repeated measures ANOVA, a powerful statistical technique with a well-deserved
reputation for flexibility in addressing the complex relationships found in longitudinal studies. As a result, the technique is often
recommended by well-intentioned theoreticians and authors of texts when, in practice, it is not usable in certain situations because
the data are too messy. The most troublesome aspect of this messiness, from a repeated measures ANOVA standpoint, is missing
data. One might set out to assess patients one, two, and three months later, but some patients may skip the first assessment,
others the second, and so on.

Longitudinal studies can be successfully analyzed without resorting to repeated measures ANOVA and without discarding
potentially informative incomplete observations. Moreover, the analytic alternatives throw the assumptions into sharper focus,
are more descriptive, and offer more possibilities to connect intuition to analysis.

To demonstrate this, I will present some data that pose interesting substantive questions and reveal some of the complexities
caused by missing data. We will then examine simple cross-sectional regressions and the behavior of changes over time and
finally, we will compute individual “slopes” for each observation and analyze those slopes. When we are through, we will have
a better understanding of this data than if we had been able to apply repeated measures ANOVA to this data. The message is
that, even had the data been clean enough to apply repeated measures ANOVA, we might still wish to pursue these alternative,
less exotic techniques.

The data are drawn from a real study (Tarlov et al. 1989). The underlying data consist of thousands of variables including
variables recording marital status and gender, age, race (coded 1 for nonwhites and 0 for whites), and mental health measured at
5 points in time for patients suffering from chronic diseases (either mental or physical). The goal of our analysis is to model the
relationship between the demographic information and mental health. The five time periods are unequally spaced. There are two
measurements at the beginning, 3 months apart. The last three measurements follow 1, 2, and 4 years later. Our data contains

As a way of getting to know this sample, I begin by presenting a series of marital status tabulations summarizing the mental
health index:

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