I searched regarding change in variance over time, but everything I saw was about relatively long time series. I have a series of 5 time points, equally spaced, but with different people missing at each time point. There are about 15 variables I am interested in, all medical things like levels of glucose and blood pressure and so on.

For modeling, I am using a multilevel model; but plotting the data shows that for some variables, the variance declines. Medically, this is a good thing. Several of the variables are bad if they are too low or too high. But how can I test this change in variance? And might this lead to a way of distinguishing the amount of change I am seeing from regression to the mean?

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    $\begingroup$ A simple graphical way is to calculate the coefficient of variation and graph it for the 15 variables over the 5 time points. Testing for regression to the mean is meaningless (pun not intended!), it is mathematical property. Economists have a literature on "convergence" that may be a more meaningful way to look at the series over time. $\endgroup$ – Andy W Jun 11 '13 at 13:20

You can model that heteroscedasticity using a multilevel model and see if the model fit improves with something like a likelihood ratio test. This can be done in the nlme package in R using the weights argument.


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