[R-sig-ME] Fwd: Continuous variable as random slope and the minimum number of levels for a categorical variable to be treated as random

Conor Michael Goold conor.goold at nmbu.no
Fri Apr 14 12:50:00 CEST 2017


The post you link to is to treating "random effect" solely as the blocking factor or hierarchical grouping factor in the model, when one wants to estimate different intercept parameters for each of the grouping factors. For instance, when observations are nested within individuals as in the sleep study, then individuals are the grouping factor or the "random effect" and will have their own intercept. Actually, in one of the comments (second one), the author admits he doesn't include the topic of random slopes for brevity. But even with random slope terms, the slope is varying with respect to the same blocking factor as the intercept. 

However, continuous variables that respect order (e.g. different ages) can also be treated as random effects or grouping variables through Gaussian process models. 

When you say you have seen GLMMs with only 2 levels, do you mean random slopes or random intercepts? I'm guessing the former based on your first question. 

The minimum size for a discrete grouping factor is dependent on the exact context (e.g. how many parameters are being estimated), but many recommend 5 as a minimum (although, this would only stand for the simplest of models) and more is always better. For instance, Stegmueller 2013 (http://onlinelibrary.wiley.com/doi/10.1111/ajps.12001/abstract) says that having at least 15-20 levels of the grouping factor in ML estimation is best, whereas Bayesian methods are more robust at lower number of levels per grouping factor. 

Also, as another commenter discussed, the random/fixed effect terms can be confusing and perhaps a better way to think about these sorts of models is simply whether parameters vary by some grouping factor or not. Thus, you could have intercepts or slopes varying with respect to a grouping factor. I prefer to write "Intercepts and the slope of predictor X varied by each individual" rather than "Random intercepts and slopes were included" because I think it's ultimately clearer about what is being done and what readers can expect from the analysis.

Best regards
Conor Goold
PhD Student
Phone:        +47 67 23 27 24

Norwegian University of Life Sciences
Campus Ås. www.nmbu.no

From: R-sig-mixed-models <r-sig-mixed-models-bounces at r-project.org> on behalf of Michele Scandola <michele.scandola at gmail.com>
Sent: Friday, April 14, 2017 12:05 PM
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] Fwd: Continuous variable as random slope and the minimum number of levels for a categorical variable to be treated as random

Dear all,

I've recently read in this page (https://dynamicecology.
wordpress.com/2015/11/04/is-it-a-fixed-or-random-effect/) the following
text "First you CANNOT treat a continuous variable as a random effect. So
if you are putting area or temperature or body size is in they may be a
nuisance/control variable but they are a fixed effect. Of course you are
only estimating one parameter (the slope) so there is no degree of freedom
cost to treating it as random. And it makes no sense to ask what is the
variance across a continuous variable."
Actually I don't know why it doesn't make any sense ask what is the
variance across a continuous variable.
I've seen the classical example on sleepstudy data which treats a cntinuous
variable as random slope:
fm1 <- lmer (Reaction~Days+(Days|Subject), sleepstudy)
with sleepstudy$Days being a continuous variable, and lmer estimates the
variance of the Days slope.

So... is it OK to use a continuous variable as random slope or not?

Furthermore the post says: "[...] you should not treat a categorical
variable with only two levels (e.g. two sites), also known as a binary
variable, as a random effect. You wouldn’t take two measures and then try
to estimate variance, but that is what you’re asking R to do if you treat
it as random. Beyond that there is a lot of debate. But many people think
should have at least 5 levels (e.g. 5 sites) before you treat something as

Actually I've seen a lot of GLMMs done with random factors with just 2
levels. Is it acceptable or not?

Thanks in advance,


Research Associate @ NPSY-Lab.VR - University of Verona
Research Associate @ AgliotiLab - University of Rome "La Sapienza"
Iscrizione all'albo A dell'Ordine degli Psicologi del Veneto n.7733

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