[R-sig-ME] [EXTERNAL] Fwd: What "pseudoreplication" or "degrees of freedom inflation" is in multilevel models?

[Philippi, Tom]

Hurlbert 1984 is the core citation for "pseudoreplication":
Hurlbert, S.H., 1984. Pseudoreplication and the design of ecological field experiments. Ecological monographs, 54(2), pp.187-211.

My take is that for split plots, blocked experiments, repeated measures, etc., Hurlbert's pseudoreplication is simply ecologists testing one experimental treatment against the wrong error term: treating subplots as independent for treatments applied to the whole plot, etc.  The same thing in the temporal form would be treatments applied to subjects, but then subjects remeasured repeatedly over time, and testing as if those repeated measures were independent.

1980s-era calculations for split plot or repeated measures designs required tests for sphericity (equal covariance across all and various adjustments to degrees of freedom).  Modern mixed models approaches allow explicitly specifying the statistical model to match the experimental (or sampling) design.  One way of setting up a model testing a treatment applied to whole plots is have whole plots be the "subject", and the subplots be some form of repeated measures within subjects.  It is even possible to fit spatially-structured covariance for subplots in a field, or AR structure for repeated measures over time.

Even though he is more of a SAS guy than R guru, I find Stroup's book with his "What Would Fisher Do?" a good explanation of the issues and approaches of matching the analysis structure to the experimental structure, but that may be because I appreciate his sense of humor:
Stroup, W.W., 2012. Generalized linear mixed models: modern concepts, methods and applications. CRC press.
The StroupGLMM package has datasets and R code for that book.

There are several very good R books on mixed models: Bates, Bolker, Faraway, Woods, Zuur, and others.

Tom
 

-----Original Message-----
From: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> On Behalf Of Michele Scandola
Sent: Friday, October 2, 2020 1:54 AM
To: r-sig-mixed-models using r-project.org
Subject: [EXTERNAL] [R-sig-ME] Fwd: What "pseudoreplication" or "degrees of freedom inflation" is in multilevel models?



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Dear all,

probably I am asking something very naive.
In that case, I am sorry, it is not my intention to bother you.
Recently I have found online some references concerning a "pseudoreplication" or "degrees of freedom inflation" that I understood may happen when you do not add in the random effects a factor that is a within-subjects factor.
From the "degrees of freedom inflation" point-of-view, this is more connected with p-value estimation, leading to an increased first-type error. From the "pseudoreplication" point-of-view, it is as we are declaring that data that are dependent, as they were independent.

Is it right? Do you have any specific bibliographic reference about that?

Thanks a lot for your time, best regards,

Michele Scandola

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