[R-sig-ME] Testing assumption multilevel analysis

[Ben Bolker]

  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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