StATS: Longitudinal data analysis (no date)
[This is a very early draft]
Longitudinal data are data where each patient is observed on multiple
occasions over time. Analysis of longitudinal data are challenging because
measurements on the same subject are correlated. Another way to think about
this is that two measurements on the same subject will have less variation
than two measurements on different subjects.
A closely related concept is the cluster design. A cluster design is one
where the researcher selects clusters of patients rather than selects
patients individually. For example, a researcher might randomly select
several families and evaluate all children in that family. As another
example, a researcher might randomly select several clinical practices and
then evaluate a random group of patients at each practice. In a cluster
design, two measurements on patients within the same cluster will have less
variations than measurements of two patients in differing clusters. . In
genetics, this correlation is of great interest, and can help you understand
concepts like heritability.
Many of the methods described below for longitudinal designs would also be
useful for cluster designs. For simplicity, I will discuss these methods
solely from the perspective of a longitudinal design.
If your data are continuous, then there are several "classical" approaches
such as multivariate analysis of variance and repeated measures analysis of
variance. These approaches work well for simple well structured longitudinal
An alternative is to use mixed linear models. These models handle missing
data well and can handle situations where the times of measurement vary from
one patient to another.
In a mixed linear model, you specify a particular structure for the
correlations. For example, an autoregressive structure is commonly used to
represent structure where correlations are strongest for measurements close
in time and which become weaker for measurements that are further separated
In many situations, the correlations are not of direct interest, but we
only account for them because failure to do so will lead to incorrect
When you are examining the correlation structure, a statistic called the
Akaike Information Criteria (AIC). This statistic measures how closely the
model fits the data, but it includes a penalty for overly complex models.
Unfortunately, there are two different formulas for AIC. For one formula, a
large value of AIC is good, and for the other formula, a small value is good.
AIC values should only be compared for models where the only change is in
the correlation structure. It would not make sense to compare an AIC from a
model with linear relationships to a model with quadratic relationships.
What if your data is not continuous? L. Fang discussed some of the
approaches commonly used when the data represents binomial counts.
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This page was written by
Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more
information? I have a page with general help
resources. You can also browse for pages similar to this one at Category: Mixed models.