variance increase over time: what analysis? I have some exposure data, where a number samples were exposed to a specific chemical over time.  The test was repeated at different concentrations.
At regular intervals a group of samples was tested for chemical accumulation -- the test is destructive, so the same sample cannot be tested across the whole exposure time.  At each testing time the same number of samples is analysed, but as I said the samples themselves are always different (though obviously they are all exposed together until they are randomly selected for the assay).
In addition, it is obvious that, while there is an obvious increase of the chemical in the samples over time, the variance of the concentration increases as the exposure time increases.
I am not really sure what is the best way to proceed here -- a simple transformation of the response does not seem to do the trick.
 A: If the data come from repeated measures where the units are measured at two or more points in time, increased variability in the outcome at later time points often results from growth or a time-exposure interaction. To assess this, you can measure growth one of two ways: by adjusting for time and its interaction with exposure in a model and testing the statistical significance of the interaction. Or you can fit a random slopes model and test the statistical significance of the random effect in a nested model.
If you have independent data, or yet another way to conceptualize growth, you can use a two-step model to fit a linear regression to the residuals as a function of time and measure the linear-heteroscedasticity (the LS slope) for statistical significance. In general a plot of residuals over time with a fitted curve is a variogram. Using smoothing splines can give a more robust way of measuring the tendency of growth or serial correlation in adjacent pairs of data.
A: Take a look at the (G)ARCH models: https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity. In those models, the variances of error terms in different time periods are allowed to have an "autoregressive" relations.
