[R-sig-ME] Testing assumption multilevel analysis

[Fox, John]

Hi Ben et al.,

Chiming in a bit late, there's some discussion of various diagnostics (nonlinearity, unusual data, collinearity) for mixed-effects models in Ch. 8 of Fox and Weisberg, An R Companion to Applied Regression, 3rd Ed. (Sage, 2019).

Best,
 John

--------------------------------------
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
Web: socialsciences.mcmaster.ca/jfox/



> -----Original Message-----
> From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces using r-project.org]
> On Behalf Of Ben Bolker
> Sent: Monday, August 26, 2019 12:23 PM
> To: r-sig-mixed-models using r-project.org
> Subject: Re: [R-sig-ME] Testing assumption multilevel analysis
> 
> 
>   Carrying on (in case it's useful to future readers):
> 
>   - I'll go a little bit further than Phillip and point out that
> independence of errors is difficult to test *at all* without further
> information (e.g. spatial and temporal structure).  If you do have
> spatial/temporal structure you can try computing autocorrelation functions
> (e.g. using lme() and ACF())
>   - lack of multicollinearity is *not* an assumption of multilevel
> analysis.  It is a potential problem (in that it makes inference and
> prediction harder), but not a violation of the assumptions.  I like this
> paper:
> 
> Graham, Michael H. “Confronting Multicollinearity in Ecological Multiple
> Regression.” Ecology 84, no. 11 (2003): 2809–15.
> https://doi.org/10.1890/02-3114.
> 
> 
> 
> On 2019-08-26 11:35 a.m., Phillip Alday wrote:
> > Please keep the list in CC.
> >
> > As Ben Bolker mentioned in his reply: for most things, the assumptions
> > carry over from the non-mixed case and the graphical diagnostics are
> > done the same way. I would in general avoid explicit statistical tests
> > of model assumptions (e.g. various tests of normality) because, like
> > all tests, they have failure modes (especially related to sensitivity
> > and
> > specificity) and don't actually tell you what any potential violation
> > of assumptions is doing to your statistical procedure.
> >
> > For multicollinearity, there is one additional diagnostic that lme4
> > gives you in its summary output, namely the correlation of fixed
> > effects. The exact meaning of this is perhaps a little technical
> > (https://stat.ethz.ch/pipermail/r-sig-mixed-models/2009q1/001941.html)
> > , but in practical terms a high correlation suggests that there may be
> > multicollinearity. Multicollinearity also tends to show itself in
> > inflated standard errors (in the fixed effects), much as it does for
> > standard linear regression.
> >
> > Regarding independence of errors: I find that to be an assumption that
> > is often best checked by knowing something about your data generating
> > process. For example, there may be some autocorrelation in the errors
> > between observations due to the way data are collected.
> >
> > Best,
> > Phillip
> >
> > On 26/8/19 2:23 pm, Katharina Tostmann wrote:
> >> Hello Phillip,
> >>
> >> Yes, I know it is a very big question about the assumptions in general.
> >> At this time I got a little information about linearity, normal
> >> distibution and variance homogenity. But what ist about
> >> mulitcollinearity and independency? Do you have any idea to check
> >> this in a multilevel context?
> >>
> >> Thank you in advance.
> >>
> >>
> >> best regards from Germany
> >>
> >> Katharina
> >>
> >> Am Mo., 26. Aug. 2019 um 14:14 Uhr schrieb Phillip Alday
> >> <phillip.alday using mpi.nl <mailto:phillip.alday using mpi.nl>>:
> >>
> >>     This is a rather open-ended request -- you're more likely to get
> helpful
> >>     advice if you're a bit more specific. For example, which model
> >>     assumptions do you want to test in particular? What do your data
> look
> >>     like? Which assumptions do you think your data might violate? Why
> do you
> >>     want to explicitly test assumptions? (e.g. Are you worried about
> >>     inflated Type-I error? Often it's better to worry less about
> assumptions
> >>     per se and instead focus on "does my model capture the relevant
> aspects
> >>     of my data?")
> >>
> >>     Phillip
> >>
> >>     On 24/8/19 11:08 am, Katharina Tostmann wrote:
> >>     > Hello together,
> >>     >
> >>     > I'm calculating a multi-level analysis in R. However, I do not
> >>     understand
> >>     > how to test the model assumptions. In my second hypothesis I also
> >>     have a
> >>     > mediation with, whereby I also have no idea how to test the model
> >>     > assumptions.
> >>     > Can anyone help here? Thank you and best regards
> >>     >
> >>     > Katharina
> >>     >
> >>     >       [[alternative HTML version deleted]]
> >>     >
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> >>
> >
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