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Say I have a random variable, and its mean or variance is changing over time, how do I detect this, given back-data? One idea is just to look at the recent values vs the less recent values and detect changes that way? Is there a standardized way to do this? A name for the method?

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  • $\begingroup$ In addition to dglm mentioned by @GordonSmyth, in glmmTMB you can model variation in the dispersion parameter of the response via a separate linear predictor. $\endgroup$ Commented Nov 17, 2022 at 10:40
  • $\begingroup$ nice thank you that helps for sure $\endgroup$ Commented Nov 24, 2022 at 9:23

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You could consider the dglm package from CRAN, which will do log-linear modelling for the variance at the same time as linear model modelling of the mean.

Here are some references:

References

Aitkin, M. (1987). Modelling variance heterogeneity in normal regression using GLIM. Journal of the Royal Statistical Society: Series C (Applied Statistics), 36(3), 332-339.

Smyth, G. K. (1989). Generalized linear models with varying dispersion. Journal of the Royal Statistical Society B 51(1), 47-60.

Rigby, R. A., & Stasinopoulos, M. D. (1995). Mean and dispersion additive models: applications and diagnostics. In Statistical Modelling (pp. 249-256). Springer, New York, NY.

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