[R-sig-ME] Collinearity diagnostics for (mixed) multinomial models
Juho Kristian Ruohonen
juho@kr|@t|@n@ruohonen @end|ng |rom gm@||@com
Thu Feb 2 22:08:24 CET 2023
Many thanks to John and Philip (and Georges behind the scenes). I'll keep
an eye on this thread. If there's a solution before my thesis goes to
print, I'll certainly adopt it posthaste.
Otherwise, I might just end up reporting all C-1 GVIF^(1/(2*DF)) statistics
for each binary subregression for each predictor, as calculated by
car::vif(). It's a bit messy, but then multinomial models themselves are
messy with their C-1 sets of coefficients, and this would be no different.
At least it's maximally transparent.
That said, I hope our experts reach a breakthrough.
Best,
Juho
ke 1. helmik. 2023 klo 18.19 John Fox (jfox using mcmaster.ca) kirjoitti:
> Dear Phillip (and Juho),
>
> You raise a reasonable point but, unfortunately, one that isn't really
> relevant to the problem at hand.
>
> Applied to a linear model, which is the context in which generalized
> variance inflation was originally defined in the paper by me and Georges
> Monette cited in ?car::vif, the GVIF *is* invariant with respect to
> inessential changes to the model such as centering regressors or any
> change in the bases for the regressor subspaces of terms in the model.
> The GVIF compares the size of the joint confidence region for the set of
> coefficients for a term in the model to its size in a utopian situation
> in which the subspace for the term is orthogonal to the subspaces of the
> other terms, and reduces to the usual VIF when the term in one-dimensional.
>
> Generalized variance inflation has subsequently been extended to some
> other regression models, such as generalized linear models, and it
> retains these essential invariances (although interpretation isn't as
> straightforward).
>
> In response to Juho's original question, I conjectured an extension to
> multinomial logit models, tested some of its invariance properties, but
> unfortunately didn't test sufficiently extensively. (I did suggest
> additional tests that I didn't perform.) It's clear from Juho's example
> that my conjecture was wrong.
>
> The reason that I hadn't yet responded to Juho's recent question is that
> Georges and I are still trying to understand why my proposed definition
> fails for multinomial logit models. It appears to work, for example, for
> multivariate linear models. Neither of us, at this point, has a solution
> to Juho's problem, and it's possible that there isn't one. We're
> continuing to discuss the problem, and one of us will post an update to
> the list if we come up with either a solution or a clear explanation of
> why my proposal failed.
>
> Thank you for prompting me to reply, if only in a preliminary manner.
>
> Best,
> John
>
> --
> John Fox, Professor Emeritus
> McMaster University
> Hamilton, Ontario, Canada
> web: https://socialsciences.mcmaster.ca/jfox/
>
> On 2023-02-01 12:19 a.m., Phillip Alday wrote:
> > I haven't seen an answer go by yet, but here's a breadcrumb:
> >
> > Iacobucci, D., Schneider, M.J., Popovich, D.L. et al. Mean centering
> > helps alleviate “micro” but not “macro” multicollinearity. Behav Res 48,
> > 1308–1317 (2016). https://doi.org/10.3758/s13428-015-0624-x
> >
> >
> >
> > On 26/1/23 8:56 am, Juho Kristian Ruohonen wrote:
> >> Dear all,
> >>
> >> I'm resurrecting this thread because a problem has come up which might
> need
> >> fixing once someone gets around to writing a relevant R package.
> >>
> >> In this same thread last March, John Fox showed me how to compute GVIFs
> for
> >> a *nnet* multinomial model. I then wrote a simple function that loops
> >> through all predictors in such a model and applies John's code to them,
> >> returning the GVIF, DF, and GVIF^(1/(2*Df)) statistic for each
> predictor.
> >> Available here
> >> <https://github.com/jkruohon/StatsMisc/blob/main/gvif_multinom.R>, the
> >> function seems to work just fine, reproducing John's results exactly on
> the
> >> carData examples. Likewise, applying this function to my own research
> data
> >> yielded entirely plausible results.
> >>
> >> But to my horror, I now discover that *when I refit my multinomial model
> >> with two quantitative predictors centered, the GVIF statistics change
> >> considerably** -- *even though the model has the same fit and virtually
> >> identical coefficients (except for the intercepts) as the original one.
> How
> >> can this be? The only thing that changes between the two models is the
> set
> >> of intercepts which, moreover, are specifically excluded from the GVIF
> >> calculations.
> >>
> >> Below is a minimal example. The anonymized datafile is downloadable here
> >> <https://github.com/jkruohon/StatsMisc/raw/main/d_anon.RData>.
> >>
> >>> mod1 <- multinom(y ~., data = d.anon, maxit = 999)
> >>> gvif.multinom(mod1) # x6 and x26 top the collinearity list
> >> GVIF DF GVIF^(1/(2df))
> >> x6 3.463522e+03 3 3.889732
> >> x26 2.988396e+03 3 3.795244
> >> x27 1.390830e+03 3 3.341019
> >> x2 3.889656e+02 3 2.701792
> >> x13 2.930026e+02 3 2.577183
> >> x19 2.051250e+04 6 2.287362
> >> x25 7.043339e+03 6 2.092417
> >> x24 1.078212e+07 12 1.963493
> >> x9 2.357662e+01 3 1.693351
> >> x17 1.991744e+01 3 1.646413
> >> x5 3.869759e+02 6 1.643010
> >> x12 1.787075e+01 3 1.616927
> >> x18 2.943991e+02 6 1.605997
> >> x1 2.700175e+03 9 1.551075
> >> x16 2.576739e+04 12 1.526844
> >> x7 1.483341e+02 6 1.516829
> >> x20 1.159374e+01 3 1.504425
> >> x3 1.612637e+04 12 1.497318
> >> x28 1.081693e+01 3 1.487136
> >> x10 9.706880e+00 3 1.460539
> >> x22 9.459035e+00 3 1.454257
> >> x15 9.124519e+00 3 1.445556
> >> x14 7.017242e+00 3 1.383655
> >> x21 6.404687e+00 3 1.362750
> >> x8 6.072614e+00 3 1.350712
> >> x11 4.797251e+00 3 1.298670
> >> x4 3.665742e+03 18 1.256043
> >> x23 3.557201e+00 3 1.235525
> >>
> >> Now we refit the model with the quantitative predictors x6 and x26
> centered:
> >>
> >>> d.anon$x6 <- d.anon$x6 - mean(d.anon$x6)
> >>> d.anon$x26 <- d.anon$x26 - mean(d.anon$x26)
> >>> mod2 <- update(mod1, data = d.anon, maxit = 999)
> >>> c(logLik(mod1), logLik(mod2)) # same fit to the data
> >> [1] -2074.133 -2074.134
> >>
> >>> gvif.multinom(mod2)
> >> GVIF DF GVIF^(1/(2df))
> >> x2 6.196959e+04 3 6.290663
> >> x13 3.031115e+04 3 5.583850
> >> x27 2.552811e+04 3 5.426291
> >> x14 1.642231e+04 3 5.041646
> >> x6 1.573721e+04 3 5.005967
> >> x26 1.464437e+04 3 4.946277
> >> x9 1.262667e+04 3 4.825564
> >> x10 5.714321e+03 3 4.228251
> >> x19 2.255013e+07 6 4.099798
> >> x25 1.227033e+07 6 3.897068
> >> x12 3.394139e+03 3 3.876635
> >> x15 1.938364e+03 3 3.531067
> >> x11 1.685265e+03 3 3.449674
> >> x21 8.429450e+02 3 3.073500
> >> x23 7.639755e+02 3 3.023523
> >> x22 6.887451e+02 3 2.971733
> >> x17 5.640312e+02 3 2.874422
> >> x20 3.855848e+02 3 2.697864
> >> x24 1.444083e+10 12 2.650430
> >> x7 7.148911e+04 6 2.538166
> >> x18 1.674603e+04 6 2.249017
> >> x5 9.662266e+03 6 2.148275
> >> x16 6.264044e+07 12 2.112851
> >> x1 6.634544e+05 9 2.105882
> >> x3 1.558132e+07 12 1.993847
> >> x8 6.168472e+01 3 1.987755
> >> x4 4.256459e+06 18 1.528059
> >> x28 9.783234e+00 3 1.462448
> >>
> >> And so I'm at my wits' end. The models are virtually identical, yet the
> >> GVIF statistics are very different. I don't know which ones to trust.
> >> Worse, the discrepancy makes me disinclined to trust either of them --
> >> which is a return to Square One, i.e. the situation where GVIF
> statistics
> >> for multinomial models did not exist. And I don't know which
> >> multicollinearity metric I can present in my thesis, if any.
> >>
> >> I hope someone can help.
> >>
> >> Best,
> >>
> >> Juho
> >>
> >>
> >>
> >>
> >>
> >> ke 2. maalisk. 2022 klo 16.35 John Fox (jfox using mcmaster.ca) kirjoitti:
> >>
> >>> Dear Juho,
> >>>
> >>> On 2022-03-02 6:23 a.m., Juho Kristian Ruohonen wrote:
> >>>> One last comment, John: Sorry if I seemed to be implying that you (or
> >>>> anyone else) should debug my code for me. That wasn't the idea. I do
> >>>> believe that the function locates the intended rows/columns
> >>>> successfully. I just wasn't entirely positive what those intended
> >>>> rows/columns should be when dealing with a multicategory factor.
> >>>> Presently, it locates every row/column involving the multicategory
> >>>> factor in question, so the number of rows/columns identified is the
> >>>> number of factor levels minus one, times the number of response
> >>>> categories minus one. I hope that's correct.
> >>>
> >>> OK, that's a fair remark. Yes, what you describe is correct.
> >>>
> >>> You can also reassure yourself that your function is working properly
> by:
> >>>
> >>> (1) If you haven't already done so, show that you get the same GVIFs
> >>> from your function as from the one I sent you used directly.
> >>>
> >>> (2) Vary the baseline level of the response variable and confirm that
> >>> you get the same GVIFs.
> >>>
> >>> (3) Vary the basis for the regressor subspace for a factor, e.g.,
> either
> >>> by using contr.sum() in place of the default contr.treatment() or by
> >>> changing the baseline level of the factor for contr.treatment(), and
> >>> again confirm that the GVIFs are unchanged.
> >>>
> >>> Best,
> >>> John
> >>>
> >>>>
> >>>> My current plan is to present the output of the new function in my
> >>>> thesis and credit you for the math. But if *vif()* gets a relevant
> >>>> update before my project is finished, then I'll use that and cite the
> >>>> /car /package instead.
> >>>>
> >>>> Thanks again for your help.
> >>>>
> >>>> Best,
> >>>>
> >>>> Juho
> >>>>
> >>>> ti 1. maalisk. 2022 klo 23.54 John Fox (jfox using mcmaster.ca
> >>>> <mailto:jfox using mcmaster.ca>) kirjoitti:
> >>>>
> >>>> Dear Juho,
> >>>>
> >>>> On 2022-03-01 3:13 p.m., Juho Kristian Ruohonen wrote:
> >>>> > Dear John,
> >>>> >
> >>>> > Yes, my function uses your code for the math. I was just
> hoping to
> >>>> > verify that it is handling multicategory factors correctly
> (your
> >>>> > examples didn't involve any).
> >>>>
> >>>> That's not really my point. Your code sets up computations for
> the
> >>>> various terms in the model automatically, while the function I
> sent
> >>>> requires that you locate the rows/columns for the intercepts and
> each
> >>>> focal term manually. If you haven't already done so, you could
> check
> >>>> that your function is identifying the correct columns and
> getting the
> >>>> corresponding GVIFs.
> >>>>
> >>>> >
> >>>> > I guess interactions aren't that important after all, given
> that
> >>> the
> >>>> > chief concern is usually collinearity among main effects.
> >>>>
> >>>> I wouldn't say that, but it's not clear what collinearity means
> in
> >>>> models with interactions, and if you compute VIFs or GVIFs for
> "main
> >>>> effects" in models with interactions, you'll probably get
> nonsense.
> >>>>
> >>>> As I said, I think that this might be a solvable problem, but one
> >>> that
> >>>> requires thought about what needs to remain invariant.
> >>>>
> >>>> I think that we've probably come to end for now.
> >>>>
> >>>> John
> >>>>
> >>>> >
> >>>> > Many thanks for all your help.
> >>>> >
> >>>> > Best,
> >>>> >
> >>>> > Juho
> >>>> >
> >>>> > ti 1. maalisk. 2022 klo 18.01 John Fox (jfox using mcmaster.ca
> >>>> <mailto:jfox using mcmaster.ca>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>)
> kirjoitti:
> >>>> >
> >>>> > Dear Juho,
> >>>> >
> >>>> > On 2022-03-01 8:24 a.m., Juho Kristian Ruohonen wrote:
> >>>> > > Dear John (Fox, as well as other list members),
> >>>> > >
> >>>> > > I've now written a simple function to try and calculate
> >>>> GVIFS for
> >>>> > all
> >>>> > > predictors in a nnet::multinom() object based on John's
> >>>> example
> >>>> > code. If
> >>>> > > its results are correct (see below), I will proceed to
> >>> write a
> >>>> > version
> >>>> > > that also works with mixed-effects multinomial models
> fit
> >>> by
> >>>> > > brms::brm(). Here's the code:
> >>>> > >
> >>>> > > gvif.multinom <- function(model){
> >>>> > > (classes <- model$lev)
> >>>> > > (V.all <- vcov(model))
> >>>> > > (V.noIntercepts <-
> V.all[!grepl("\\(Intercept\\)$",
> >>>> > > rownames(V.all), perl = T),
> >>>> > >
> !grepl("\\(Intercept\\)$",
> >>>> > > colnames(V.all), perl = T)])
> >>>> > > (R <- cov2cor(V.noIntercepts))
> >>>> > > (terms <- attr(model$terms, "term.labels"))
> >>>> > > (gvif <- numeric(length = length(terms)))
> >>>> > > (names(gvif) <- terms)
> >>>> > > (SE.multiplier <- numeric(length =
> length(terms)))
> >>>> > > (names(SE.multiplier) <- terms)
> >>>> > > #The line below tries to capture all factor
> levels
> >>>> into a
> >>>> > regex
> >>>> > > for coef name matching.
> >>>> > > (LevelsRegex <- paste0("(",
> >>>> paste(unlist(model$xlevels),
> >>>> > collapse
> >>>> > > = "|"),")?"))
> >>>> > >
> >>>> > > for(i in terms){
> >>>> > > #The regex stuff below tries to ensure all
> >>>> interaction
> >>>> > > coefficients are matched, including those involving
> >>>> factors.
> >>>> > > if(grepl(":", i)){
> >>>> > > (termname <- gsub(":", paste0(LevelsRegex,
> >>> ":"), i,
> >>>> > perl = T))
> >>>> > > }else{termname <- i}
> >>>> > > (RegexToMatch <- paste0("^(",
> >>>> > paste(classes[2:length(classes)],
> >>>> > > collapse = "|") ,"):", termname, LevelsRegex, "$"))
> >>>> > >
> >>>> > > #Now the actual calculation:
> >>>> > > (indices <- grep(RegexToMatch, rownames(R),
> perl
> >>>> = T))
> >>>> > > (gvif[i] <- det(R[indices, indices]) *
> >>>> det(R[-indices,
> >>>> > > -indices]) / det(R))
> >>>> > > (SE.multiplier[i] <-
> >>> gvif[i]^(1/(2*length(indices))))
> >>>> > > }
> >>>> > > #Put the results together and order them by
> degree
> >>>> of SE
> >>>> > inflation:
> >>>> > > (result <- cbind(GVIF = gvif, `GVIF^(1/(2df))` =
> >>>> > SE.multiplier))
> >>>> > > return(result[order(result[,"GVIF^(1/(2df))"],
> >>>> decreasing
> >>>> > = T),])}
> >>>> > >
> >>>> > >
> >>>> > > The results seem correct to me when applied to John's
> >>> example
> >>>> > model fit
> >>>> > > to the BEPS data. However, that dataset contains no
> >>> multi-df
> >>>> > factors, of
> >>>> > > which my own models have many. Below is a maximally
> simple
> >>>> > example with
> >>>> > > one multi-df factor (/region/):
> >>>> > >
> >>>> > > mod1 <- multinom(partic ~., data =
> carData::Womenlf)
> >>>> > > gvif.multinom(mod1)
> >>>> > >
> >>>> > > GVIF GVIF^(1/(2df))
> >>>> > > children 1.298794 1.067542
> >>>> > > hincome 1.184215 1.043176
> >>>> > > region 1.381480 1.020403
> >>>> > >
> >>>> > >
> >>>> > > These results look plausible to me. Finally, below is
> an
> >>>> example
> >>>> > > involving both a multi-df factor and an interaction:
> >>>> > >
> >>>> > > mod2 <- update(mod1, ~. +children:region)
> >>>> > > gvif.multinom(mod2)
> >>>> > >
> >>>> > > GVIF GVIF^(1/(2df))
> >>>> > > children:region 4.965762e+16 11.053482
> >>>> > > region 1.420418e+16 10.221768
> >>>> > > children 1.471412e+03 6.193463
> >>>> > > hincome 6.462161e+00 1.594390
> >>>> > >
> >>>> > >
> >>>> > > These results look a bit more dubious. To be sure, it
> is
> >>> to be
> >>>> > expected
> >>>> > > that interaction terms will introduce a lot of
> >>>> collinearity. But an
> >>>> > > 11-fold increase in SE? I hope someone can tell me
> whether
> >>>> this is
> >>>> > > correct or not!
> >>>> >
> >>>> > You don't need someone else to check your work because you
> >>>> could just
> >>>> > apply the simple function that I sent you yesterday,
> which,
> >>>> though not
> >>>> > automatic, computes the GVIFs in a transparent manner.
> >>>> >
> >>>> > A brief comment on GVIFs for models with interactions
> (this
> >>>> isn't the
> >>>> > place to discuss the question in detail): The Fox and
> Monette
> >>>> JASA
> >>>> > paper
> >>>> > addresses the question briefly in the context of a two-way
> >>>> ANOVA, but I
> >>>> > don't think that the approach suggested there is easily
> >>>> generalized.
> >>>> >
> >>>> > The following simple approach pays attention to what's
> >>>> invariant under
> >>>> > different parametrizations of the RHS side of the model:
> >>>> Simultaneously
> >>>> > check the collinearity of all of the coefficients of an
> >>>> interaction
> >>>> > together with the main effects and, potentially,
> lower-order
> >>>> > interactions that are marginal to it. So, e.g., in the
> model
> >>>> y ~ a +
> >>>> > b +
> >>>> > a:b + c, you'd check all of the coefficients for a, b, and
> >>>> a:b together.
> >>>> >
> >>>> > Alternatively, one could focus in turn on each explanatory
> >>>> variable and
> >>>> > check the collinearity of all coefficients to which it is
> >>>> marginal. So
> >>>> > in y ~ a + b + c + a:b + a:c + d, when you focus on a,
> you'd
> >>>> look at
> >>>> > all
> >>>> > of the coefficients for a, b, c, a:b, and a:c.
> >>>> >
> >>>> > John
> >>>> >
> >>>> > >
> >>>> > > Best,
> >>>> > >
> >>>> > > Juho
> >>>> > >
> >>>> > >
> >>>> > >
> >>>> > >
> >>>> > >
> >>>> > >
> >>>> > >
> >>>> > >
> >>>> > >
> >>>> > >
> >>>> > >
> >>>> > > ti 1. maalisk. 2022 klo 0.05 John Fox (
> jfox using mcmaster.ca
> >>>> <mailto:jfox using mcmaster.ca>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>
> >>>> > > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>) kirjoitti:
> >>>> > >
> >>>> > > Dear Juha,
> >>>> > >
> >>>> > > On 2022-02-28 5:00 p.m., Juho Kristian Ruohonen
> wrote:
> >>>> > > > Apologies for my misreading, John, and many
> thanks
> >>>> for showing
> >>>> > > how the
> >>>> > > > calculation is done for a single term.
> >>>> > > >
> >>>> > > > Do you think *vif()* might be updated in the
> near
> >>>> future
> >>>> > with the
> >>>> > > > capability of auto-detecting a multinomial model
> >>>> and returning
> >>>> > > > mathematically correct GVIF statistics?
> >>>> > >
> >>>> > > The thought crossed my mind, but I'd want to do it
> in a
> >>>> > general way,
> >>>> > > not
> >>>> > > just for the multinom() function, and in a way that
> >>> avoids
> >>>> > incorrect
> >>>> > > results such as those currently produced for
> "multinom"
> >>>> > models, albeit
> >>>> > > with a warning. I can't guarantee whether or when
> I'll
> >>> be
> >>>> > able to do
> >>>> > > that.
> >>>> > >
> >>>> > > John
> >>>> > >
> >>>> > > >
> >>>> > > > If not, I'll proceed to writing my own function
> >>>> based on your
> >>>> > > example.
> >>>> > > > However, /car/ is such an excellent and widely
> used
> >>>> > package that the
> >>>> > > > greatest benefit to mankind would probably
> accrue
> >>>> if /car /was
> >>>> > > upgraded
> >>>> > > > with this feature sooner rather than later.
> >>>> > > >
> >>>> > > > Best,
> >>>> > > >
> >>>> > > > Juho
> >>>> > > >
> >>>> > > >
> >>>> > > >
> >>>> > > >
> >>>> > > >
> >>>> > > >
> >>>> > > >
> >>>> > > >
> >>>> > > >
> >>>> > > > ma 28. helmik. 2022 klo 17.08 John Fox
> >>>> (jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>
> >>>> > > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>
> >>>> > > > <mailto:jfox using mcmaster.ca <mailto:
> jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>>)
> kirjoitti:
> >>>> > > >
> >>>> > > > Dear Juho,
> >>>> > > >
> >>>> > > > On 2022-02-28 2:06 a.m., Juho Kristian
> Ruohonen
> >>>> wrote:
> >>>> > > > > Dear Professor Fox and other list
> members,
> >>>> > > > >
> >>>> > > > > Profuse thanks for doing that detective
> work
> >>> for
> >>>> > me! I myself
> >>>> > > > thought
> >>>> > > > > the inflation factors reported by
> >>>> > check_collinearity() were
> >>>> > > > suspiciously
> >>>> > > > > high, but unlike you I lacked the
> expertise
> >>>> to identify
> >>>> > > what was
> >>>> > > > going on.
> >>>> > > > >
> >>>> > > > > As for your suggested approach, have I
> >>>> understood this
> >>>> > > correctly:
> >>>> > > > >
> >>>> > > > > Since there doesn't yet exist an R
> function
> >>>> that will
> >>>> > > calculate the
> >>>> > > > > (G)VIFS of multinomial models correctly,
> my
> >>> best
> >>>> > bet for
> >>>> > > now is
> >>>> > > > just to
> >>>> > > > > ignore the fact that such models
> partition
> >>>> the data
> >>>> > into C-1
> >>>> > > > subsets,
> >>>> > > > > and to calculate approximate GVIFs from
> the
> >>>> entire
> >>>> > dataset at
> >>>> > > > once as if
> >>>> > > > > the response were continuous? And a
> simple
> >>>> way to
> >>>> > do this
> >>>> > > is to
> >>>> > > > > construct a fake continuous response,
> call
> >>>> > > *lm(fakeresponse ~.)*,
> >>>> > > > and
> >>>> > > > > apply *car::vif()* on the result?
> >>>> > > >
> >>>> > > > No, you misunderstand my suggestion, which
> >>>> perhaps isn't
> >>>> > > surprising
> >>>> > > > given the length of my message. What you
> >>>> propose is what I
> >>>> > > suggested as
> >>>> > > > a rough approximation *before* I confirmed
> that
> >>> my
> >>>> > guess of the
> >>>> > > > solution
> >>>> > > > was correct.
> >>>> > > >
> >>>> > > > The R code that I sent yesterday showed how
> to
> >>>> compute the
> >>>> > > GVIF for a
> >>>> > > > multinomial regression model, and I
> suggested
> >>>> that you
> >>>> > write
> >>>> > > either a
> >>>> > > > script or a simple function to do that.
> Here's
> >>>> a function
> >>>> > > that will
> >>>> > > > work
> >>>> > > > for a model object that responds to vcov():
> >>>> > > >
> >>>> > > > GVIF <- function(model, intercepts, term){
> >>>> > > > # model: regression model object
> >>>> > > > # intercepts: row/column positions of
> >>>> intercepts
> >>>> > in the
> >>>> > > coefficient
> >>>> > > > covariance matrix
> >>>> > > > # term: row/column positions of the
> >>>> coefficients
> >>>> > for the
> >>>> > > focal term
> >>>> > > > V <- vcov(model)
> >>>> > > > term <- colnames(V)[term]
> >>>> > > > V <- V[-intercepts, -intercepts]
> >>>> > > > V <- cov2cor(V)
> >>>> > > > term <- which(colnames(V) %in% term)
> >>>> > > > gvif <- det(V[term, term])*det(V[-term,
> >>>> -term])/det(V)
> >>>> > > > c(GVIF=gvif,
> >>>> > "GVIF^(1/(2*p))"=gvif^(1/(2*length(term))))
> >>>> > > > }
> >>>> > > >
> >>>> > > > and here's an application to the multinom()
> >>>> example that I
> >>>> > > showed you
> >>>> > > > yesterday:
> >>>> > > >
> >>>> > > > > colnames(vcov(m)) # to get coefficient
> >>>> positions
> >>>> > > > [1] "Labour:(Intercept)"
> >>>> > "Labour:age"
> >>>> > > >
> >>>> > > > [3] "Labour:economic.cond.national"
> >>>> > > > "Labour:economic.cond.household"
> >>>> > > > [5] "Labour:Blair"
> >>>> > "Labour:Hague"
> >>>> > > >
> >>>> > > > [7] "Labour:Kennedy"
> >>>> > "Labour:Europe"
> >>>> > > >
> >>>> > > > [9] "Labour:political.knowledge"
> >>>> > > "Labour:gendermale"
> >>>> > > >
> >>>> > > > [11] "Liberal Democrat:(Intercept)"
> >>>> "Liberal
> >>>> > > Democrat:age"
> >>>> > > >
> >>>> > > > [13] "Liberal
> Democrat:economic.cond.national"
> >>>> "Liberal
> >>>> > > > Democrat:economic.cond.household"
> >>>> > > > [15] "Liberal Democrat:Blair"
> >>>> "Liberal
> >>>> > > > Democrat:Hague"
> >>>> > > >
> >>>> > > > [17] "Liberal Democrat:Kennedy"
> >>>> "Liberal
> >>>> > > > Democrat:Europe"
> >>>> > > > [19] "Liberal Democrat:political.knowledge"
> >>>> "Liberal
> >>>> > > > Democrat:gendermale"
> >>>> > > >
> >>>> > > > > GVIF(m, intercepts=c(1, 11), term=c(2,
> 12))
> >>>> # GVIF
> >>>> > for age
> >>>> > > > GVIF GVIF^(1/(2*p))
> >>>> > > > 1.046232 1.011363
> >>>> > > >
> >>>> > > >
> >>>> > > > Finally, here's what you get for a linear
> model
> >>>> with
> >>>> > the same RHS
> >>>> > > > (where
> >>>> > > > the sqrt(VIF) should be a rough
> approximation to
> >>>> > GVIF^(1/4)
> >>>> > > reported by
> >>>> > > > my GVIF() function):
> >>>> > > >
> >>>> > > > > m.lm <- lm(as.numeric(vote) ~ . - vote1,
> >>>> data=BEPS)
> >>>> > > > > sqrt(car::vif(m.lm))
> >>>> > > > age
> >>> economic.cond.national
> >>>> > > > economic.cond.household
> >>>> > > > Blair
> >>>> > > > 1.006508
> >>> 1.124132
> >>>> > > > 1.075656
> >>>> > > > 1.118441
> >>>> > > > Hague
> >>> Kennedy
> >>>> > > > Europe
> >>>> > > > political.knowledge
> >>>> > > > 1.066799
> >>> 1.015532
> >>>> > > > 1.101741
> >>>> > > > 1.028546
> >>>> > > > gender
> >>>> > > > 1.017386
> >>>> > > >
> >>>> > > >
> >>>> > > > John
> >>>> > > >
> >>>> > > > >
> >>>> > > > > Best,
> >>>> > > > >
> >>>> > > > > Juho
> >>>> > > > >
> >>>> > > > > ma 28. helmik. 2022 klo 2.23 John Fox
> >>>> > (jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>
> >>>> > > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>
> >>>> > > > <mailto:jfox using mcmaster.ca
> >>>> <mailto:jfox using mcmaster.ca> <mailto:jfox using mcmaster.ca
> >>>> <mailto:jfox using mcmaster.ca>>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>>
> >>>> > > > > <mailto:jfox using mcmaster.ca
> >>>> <mailto:jfox using mcmaster.ca> <mailto:jfox using mcmaster.ca
> >>>> <mailto:jfox using mcmaster.ca>>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>
> >>>> > > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>>>)
> kirjoitti:
> >>>> > > > >
> >>>> > > > > Dear Juho,
> >>>> > > > >
> >>>> > > > > I've now had a chance to think about
> this
> >>>> > problem some
> >>>> > > more,
> >>>> > > > and I
> >>>> > > > > believe that the approach I
> suggested is
> >>>> correct. I
> >>>> > > also had an
> >>>> > > > > opportunity to talk the problem over
> a
> >>>> bit with
> >>>> > Georges
> >>>> > > > Monette, who
> >>>> > > > > coauthored the paper that introduced
> >>>> > generalized variance
> >>>> > > > inflation
> >>>> > > > > factors (GVIFs). On the other hand,
> the
> >>>> results
> >>>> > > produced by
> >>>> > > > > performance::check_collinearity() for
> >>>> > multinomial logit
> >>>> > > > models don't
> >>>> > > > > seem to be correct (see below).
> >>>> > > > >
> >>>> > > > > Here's an example, using the
> >>>> nnet::multinom()
> >>>> > function
> >>>> > > to fit a
> >>>> > > > > multinomial logit model, with
> alternative
> >>>> > > parametrizations of the
> >>>> > > > > LHS of
> >>>> > > > > the model:
> >>>> > > > >
> >>>> > > > > --------- snip -----------
> >>>> > > > >
> >>>> > > > > > library(nnet) # for multinom()
> >>>> > > > > > library(carData) # for BEPS data
> set
> >>>> > > > >
> >>>> > > > > > # alternative ordering of the
> >>>> response levels:
> >>>> > > > > > BEPS$vote1 <- factor(BEPS$vote,
> >>>> > levels=c("Labour",
> >>>> > > "Liberal
> >>>> > > > > Democrat", "Conservative"))
> >>>> > > > > > levels(BEPS$vote)
> >>>> > > > > [1] "Conservative" "Labour"
> >>>> "Liberal
> >>>> > > Democrat"
> >>>> > > > > > levels(BEPS$vote1)
> >>>> > > > > [1] "Labour" "Liberal
> Democrat"
> >>>> > "Conservative"
> >>>> > > > >
> >>>> > > > > > m <- multinom(vote ~ . - vote1,
> >>>> data=BEPS)
> >>>> > > > > # weights: 33 (20 variable)
> >>>> > > > > initial value 1675.383740
> >>>> > > > > iter 10 value 1345.935273
> >>>> > > > > iter 20 value 1150.956807
> >>>> > > > > iter 30 value 1141.921662
> >>>> > > > > iter 30 value 1141.921661
> >>>> > > > > iter 30 value 1141.921661
> >>>> > > > > final value 1141.921661
> >>>> > > > > converged
> >>>> > > > > > m1 <- multinom(vote1 ~ . - vote,
> >>>> data=BEPS)
> >>>> > > > > # weights: 33 (20 variable)
> >>>> > > > > initial value 1675.383740
> >>>> > > > > iter 10 value 1280.439304
> >>>> > > > > iter 20 value 1165.513772
> >>>> > > > > final value 1141.921662
> >>>> > > > > converged
> >>>> > > > >
> >>>> > > > > > rbind(coef(m), coef(m1)) #
> compare
> >>>> coefficients
> >>>> > > > > (Intercept)
> >>> age
> >>>> > > > economic.cond.national
> >>>> > > > > economic.cond.household
> >>>> > > > > Labour 0.9515214
> -0.021913989
> >>>> > > 0.5575707
> >>>> > > > > 0.15839096
> >>>> > > > > Liberal Democrat 1.4119306
> -0.016810735
> >>>> > > 0.1810761
> >>>> > > > > -0.01196664
> >>>> > > > > Liberal Democrat 0.4604567
> 0.005102666
> >>>> > > -0.3764928
> >>>> > > > > -0.17036682
> >>>> > > > > Conservative -0.9514466
> 0.021912305
> >>>> > > -0.5575644
> >>>> > > > > -0.15838744
> >>>> > > > > Blair
> Hague
> >>>> > Kennedy
> >>>> > > Europe
> >>>> > > > > political.knowledge
> >>>> > > > > Labour 0.8371764
> -0.90775585
> >>>> 0.2513436
> >>>> > > -0.22781308
> >>>> > > > > -0.5370612
> >>>> > > > > Liberal Democrat 0.2937331
> -0.82217625
> >>>> 0.6710567
> >>>> > > -0.20004624
> >>>> > > > > -0.2034605
> >>>> > > > > Liberal Democrat -0.5434408
> 0.08559455
> >>>> 0.4197027
> >>>> > > 0.02776465
> >>>> > > > > 0.3336068
> >>>> > > > > Conservative -0.8371670
> 0.90778068
> >>>> -0.2513735
> >>>> > > 0.22781092
> >>>> > > > > 0.5370545
> >>>> > > > > gendermale
> >>>> > > > > Labour 0.13765774
> >>>> > > > > Liberal Democrat 0.12640823
> >>>> > > > > Liberal Democrat -0.01125898
> >>>> > > > > Conservative -0.13764849
> >>>> > > > >
> >>>> > > > > > c(logLik(m), logLik(m1)) # same
> fit
> >>>> to the data
> >>>> > > > > [1] -1141.922 -1141.922
> >>>> > > > >
> >>>> > > > > > # covariance matrices for
> >>> coefficients:
> >>>> > > > > > V <- vcov(m)
> >>>> > > > > > V1 <- vcov(m1)
> >>>> > > > > > cbind(colnames(V), colnames(V1))
> #
> >>>> compare
> >>>> > > > > [,1]
> >>>> > [,2]
> >>>> > > > >
> >>>> > > > > [1,] "Labour:(Intercept)"
> >>>> > > "Liberal
> >>>> > > > > Democrat:(Intercept)"
> >>>> > > > > [2,] "Labour:age"
> >>>> > > "Liberal
> >>>> > > > > Democrat:age"
> >>>> > > > >
> >>>> > > > > [3,]
> "Labour:economic.cond.national"
> >>>> > > "Liberal
> >>>> > > > > Democrat:economic.cond.national"
> >>>> > > > > [4,]
> "Labour:economic.cond.household"
> >>>> > > "Liberal
> >>>> > > > > Democrat:economic.cond.household"
> >>>> > > > > [5,] "Labour:Blair"
> >>>> > > "Liberal
> >>>> > > > > Democrat:Blair"
> >>>> > > > > [6,] "Labour:Hague"
> >>>> > > "Liberal
> >>>> > > > > Democrat:Hague"
> >>>> > > > > [7,] "Labour:Kennedy"
> >>>> > > "Liberal
> >>>> > > > > Democrat:Kennedy"
> >>>> > > > > [8,] "Labour:Europe"
> >>>> > > "Liberal
> >>>> > > > > Democrat:Europe"
> >>>> > > > > [9,] "Labour:political.knowledge"
> >>>> > > "Liberal
> >>>> > > > > Democrat:political.knowledge"
> >>>> > > > > [10,] "Labour:gendermale"
> >>>> > "Liberal
> >>>> > > > > Democrat:gendermale"
> >>>> > > > > [11,] "Liberal Democrat:(Intercept)"
> >>>> > > > > "Conservative:(Intercept)"
> >>>> > > > > [12,] "Liberal Democrat:age"
> >>>> > > > "Conservative:age"
> >>>> > > > >
> >>>> > > > > [13,] "Liberal
> >>>> Democrat:economic.cond.national"
> >>>> > > > > "Conservative:economic.cond.national"
> >>>> > > > > [14,] "Liberal
> >>>> Democrat:economic.cond.household"
> >>>> > > > >
> "Conservative:economic.cond.household"
> >>>> > > > > [15,] "Liberal Democrat:Blair"
> >>>> > > > "Conservative:Blair"
> >>>> > > > >
> >>>> > > > > [16,] "Liberal Democrat:Hague"
> >>>> > > > "Conservative:Hague"
> >>>> > > > >
> >>>> > > > > [17,] "Liberal Democrat:Kennedy"
> >>>> > > > "Conservative:Kennedy"
> >>>> > > > >
> >>>> > > > > [18,] "Liberal Democrat:Europe"
> >>>> > > > "Conservative:Europe"
> >>>> > > > >
> >>>> > > > > [19,] "Liberal
> >>> Democrat:political.knowledge"
> >>>> > > > > "Conservative:political.knowledge"
> >>>> > > > > [20,] "Liberal Democrat:gendermale"
> >>>> > > > > "Conservative:gendermale"
> >>>> > > > >
> >>>> > > > > > int <- c(1, 11) # remove
> intercepts
> >>>> > > > > > colnames(V)[int]
> >>>> > > > > [1] "Labour:(Intercept)"
> >>> "Liberal
> >>>> > > Democrat:(Intercept)"
> >>>> > > > >
> >>>> > > > > > colnames(V1)[int]
> >>>> > > > > [1] "Liberal Democrat:(Intercept)"
> >>>> > > "Conservative:(Intercept)"
> >>>> > > > > > V <- V[-int, -int]
> >>>> > > > > > V1 <- V1[-int, -int]
> >>>> > > > >
> >>>> > > > > > age <- c(1, 10) # locate age
> >>>> coefficients
> >>>> > > > > > colnames(V)[age]
> >>>> > > > > [1] "Labour:age" "Liberal
> >>>> Democrat:age"
> >>>> > > > > > colnames(V1)[age]
> >>>> > > > > [1] "Liberal Democrat:age"
> >>>> "Conservative:age"
> >>>> > > > >
> >>>> > > > > > V <- cov2cor(V) # compute
> coefficient
> >>>> > correlations
> >>>> > > > > > V1 <- cov2cor(V1)
> >>>> > > > >
> >>>> > > > > > # compare GVIFs:
> >>>> > > > > > c(det(V[age, age])*det(V[-age,
> >>>> -age])/det(V),
> >>>> > > > > + det(V1[age, age])*det(V1[-age,
> >>>> -age])/det(V1))
> >>>> > > > > [1] 1.046232 1.046229
> >>>> > > > >
> >>>> > > > > --------- snip -----------
> >>>> > > > >
> >>>> > > > > For curiosity, I applied car::vif()
> and
> >>>> > > > > performance::check_collinearity() to
> >>> these
> >>>> > models to
> >>>> > > see what
> >>>> > > > they
> >>>> > > > > would
> >>>> > > > > do. Both returned the wrong answer.
> vif()
> >>>> > produced a
> >>>> > > warning, but
> >>>> > > > > check_collinearity() didn't:
> >>>> > > > >
> >>>> > > > > --------- snip -----------
> >>>> > > > >
> >>>> > > > > > car::vif(m1)
> >>>> > > > > age
> >>>> economic.cond.national
> >>>> > > > > economic.cond.household
> >>>> > > > > 15.461045
> >>>> 22.137772
> >>>> > > > > 16.693877
> >>>> > > > > Blair
> >>>> Hague
> >>>> > > > > Kennedy
> >>>> > > > > 14.681562
> >>>> 7.483039
> >>>> > > > > 15.812067
> >>>> > > > > Europe
> >>>> political.knowledge
> >>>> > > > > gender
> >>>> > > > > 6.502119
> >>>> 4.219507
> >>>> > > > > 2.313885
> >>>> > > > > Warning message:
> >>>> > > > > In vif.default(m1) : No intercept:
> vifs
> >>>> may not be
> >>>> > > sensible.
> >>>> > > > >
> >>>> > > > > >
> performance::check_collinearity(m)
> >>>> > > > > # Check for Multicollinearity
> >>>> > > > >
> >>>> > > > > Low Correlation
> >>>> > > > >
> >>>> > > > > Term VIF
> >>> Increased SE
> >>>> > Tolerance
> >>>> > > > > age 1.72
> >>>> 1.31
> >>>> > 0.58
> >>>> > > > > economic.cond.national 1.85
> >>>> 1.36
> >>>> > 0.54
> >>>> > > > > economic.cond.household 1.86
> >>>> 1.37
> >>>> > 0.54
> >>>> > > > > Blair 1.63
> >>>> 1.28
> >>>> > 0.61
> >>>> > > > > Hague 1.94
> >>>> 1.39
> >>>> > 0.52
> >>>> > > > > Kennedy 1.70
> >>>> 1.30
> >>>> > 0.59
> >>>> > > > > Europe 2.01
> >>>> 1.42
> >>>> > 0.50
> >>>> > > > > political.knowledge 1.94
> >>>> 1.39
> >>>> > 0.52
> >>>> > > > > gender 1.78
> >>>> 1.33
> >>>> > 0.56
> >>>> > > > > >
> performance::check_collinearity(m1)
> >>>> > > > > # Check for Multicollinearity
> >>>> > > > >
> >>>> > > > > Low Correlation
> >>>> > > > >
> >>>> > > > > Term VIF
> >>> Increased SE
> >>>> > Tolerance
> >>>> > > > > age 1.19
> >>>> 1.09
> >>>> > 0.84
> >>>> > > > > economic.cond.national 1.42
> >>>> 1.19
> >>>> > 0.70
> >>>> > > > > economic.cond.household 1.32
> >>>> 1.15
> >>>> > 0.76
> >>>> > > > > Blair 1.50
> >>>> 1.22
> >>>> > 0.67
> >>>> > > > > Hague 1.30
> >>>> 1.14
> >>>> > 0.77
> >>>> > > > > Kennedy 1.19
> >>>> 1.09
> >>>> > 0.84
> >>>> > > > > Europe 1.34
> >>>> 1.16
> >>>> > 0.75
> >>>> > > > > political.knowledge 1.30
> >>>> 1.14
> >>>> > 0.77
> >>>> > > > > gender 1.23
> >>>> 1.11
> >>>> > 0.81
> >>>> > > > >
> >>>> > > > > --------- snip -----------
> >>>> > > > >
> >>>> > > > > I looked at the code for vif() and
> >>>> > check_collinearity() to
> >>>> > > > see where
> >>>> > > > > they went wrong. Both failed to
> handle
> >>>> the two
> >>>> > > intercepts in
> >>>> > > > the model
> >>>> > > > > correctly -- vif() thought there was
> no
> >>>> > intercept and
> >>>> > > > > check_collinearity() just removed the
> >>> first
> >>>> > intercept
> >>>> > > but not the
> >>>> > > > > second.
> >>>> > > > >
> >>>> > > > > In examining the code for
> >>>> check_collinearity(), I
> >>>> > > discovered a
> >>>> > > > > couple of
> >>>> > > > > additional disconcerting facts.
> First,
> >>>> part of the
> >>>> > > code seems
> >>>> > > > to be
> >>>> > > > > copied from vif.default(). Second,
> as a
> >>>> > consequence,
> >>>> > > > > check_collinearity() actually
> computes
> >>>> GVIFs rather
> >>>> > > than VIFs
> >>>> > > > (and
> >>>> > > > > doesn't reference either the Fox and
> >>>> Monette paper
> >>>> > > > introducing GVIFs or
> >>>> > > > > the car package) but doesn't seem to
> >>>> understand
> >>>> > that, and,
> >>>> > > > for example,
> >>>> > > > > takes the squareroot of the GVIF
> >>>> (reported in the
> >>>> > > column marked
> >>>> > > > > "Increased SE") rather than the 2p
> root
> >>>> (when there
> >>>> > > are p > 1
> >>>> > > > > coefficients in a term).
> >>>> > > > >
> >>>> > > > > Here's the relevant code from the two
> >>>> functions
> >>>> > (where
> >>>> > > . . .
> >>>> > > > denotes
> >>>> > > > > elided lines) -- the default method
> for
> >>>> vif() and
> >>>> > > > > .check_collinearity(),
> >>>> > > > > which is called by
> >>>> check_collinearity.default():
> >>>> > > > >
> >>>> > > > > --------- snip -----------
> >>>> > > > >
> >>>> > > > > > car:::vif.default
> >>>> > > > > function (mod, ...)
> >>>> > > > > {
> >>>> > > > > . . .
> >>>> > > > > v <- vcov(mod)
> >>>> > > > > assign <-
> attr(model.matrix(mod),
> >>>> "assign")
> >>>> > > > > if
> (names(coefficients(mod)[1]) ==
> >>>> > "(Intercept)") {
> >>>> > > > > v <- v[-1, -1]
> >>>> > > > > assign <- assign[-1]
> >>>> > > > > }
> >>>> > > > > else warning("No intercept:
> vifs
> >>>> may not be
> >>>> > > sensible.")
> >>>> > > > > terms <- labels(terms(mod))
> >>>> > > > > n.terms <- length(terms)
> >>>> > > > > if (n.terms < 2)
> >>>> > > > > stop("model contains fewer
> >>>> than 2 terms")
> >>>> > > > > R <- cov2cor(v)
> >>>> > > > > detR <- det(R)
> >>>> > > > > . . .
> >>>> > > > > for (term in 1:n.terms) {
> >>>> > > > > subs <- which(assign ==
> term)
> >>>> > > > > result[term, 1] <-
> >>>> det(as.matrix(R[subs,
> >>>> > > subs])) *
> >>>> > > > > det(as.matrix(R[-subs,
> >>>> > > > > -subs]))/detR
> >>>> > > > > result[term, 2] <-
> length(subs)
> >>>> > > > > }
> >>>> > > > > . . .
> >>>> > > > > }
> >>>> > > > >
> >>>> > > > > > performance:::.check_collinearity
> >>>> > > > > function (x, component, verbose =
> TRUE)
> >>>> > > > > {
> >>>> > > > > v <- insight::get_varcov(x,
> >>>> component =
> >>>> > component,
> >>>> > > > verbose =
> >>>> > > > > FALSE)
> >>>> > > > > assign <- .term_assignments(x,
> >>>> component,
> >>>> > verbose =
> >>>> > > > verbose)
> >>>> > > > > . . .
> >>>> > > > > if (insight::has_intercept(x))
> {
> >>>> > > > > v <- v[-1, -1]
> >>>> > > > > assign <- assign[-1]
> >>>> > > > > }
> >>>> > > > > else {
> >>>> > > > > if (isTRUE(verbose)) {
> >>>> > > > > warning("Model has no
> >>>> intercept. VIFs
> >>>> > > may not be
> >>>> > > > > sensible.",
> >>>> > > > > call. = FALSE)
> >>>> > > > > }
> >>>> > > > > }
> >>>> > > > > . . .
> >>>> > > > > terms <-
> >>>> > labels(stats::terms(f[[component]]))
> >>>> > > > > . . .
> >>>> > > > > n.terms <- length(terms)
> >>>> > > > > if (n.terms < 2) {
> >>>> > > > > if (isTRUE(verbose)) {
> >>>> > > > >
> >>>> > warning(insight::format_message(sprintf("Not
> >>>> > > > enough model
> >>>> > > > > terms in the %s part of the model to
> >>>> check for
> >>>> > > > multicollinearity.",
> >>>> > > > > component)), call.
> =
> >>>> FALSE)
> >>>> > > > > }
> >>>> > > > > return(NULL)
> >>>> > > > > }
> >>>> > > > > R <- stats::cov2cor(v)
> >>>> > > > > detR <- det(R)
> >>>> > > > > . . .
> >>>> > > > > for (term in 1:n.terms) {
> >>>> > > > > subs <- which(assign ==
> term)
> >>>> > > > > . . .
> >>>> > > > > result <- c(result,
> >>>> > > det(as.matrix(R[subs, subs])) *
> >>>> > > > >
> det(as.matrix(R[-subs,
> >>>> > -subs]))/detR)
> >>>> > > > > . . .
> >>>> > > > > }
> >>>> > > > > . . .
> >>>> > > > > }
> >>>> > > > >
> >>>> > > > > --------- snip -----------
> >>>> > > > >
> >>>> > > > > So, the upshot of all this is that
> you
> >>>> should
> >>>> > be able
> >>>> > > to do
> >>>> > > > what you
> >>>> > > > > want, but not with either car::vif()
> or
> >>>> > > > > performance::check_collinearity().
> >>>> Instead, either
> >>>> > > write your own
> >>>> > > > > function or do the computations in a
> >>> script.
> >>>> > > > >
> >>>> > > > > There's also a lesson here about S3
> >>> default
> >>>> > methods:
> >>>> > > The fact
> >>>> > > > that a
> >>>> > > > > default method returns a result
> rather
> >>> than
> >>>> > throwing
> >>>> > > an error
> >>>> > > > or a
> >>>> > > > > warning doesn't mean that the result
> is
> >>> the
> >>>> > right answer.
> >>>> > > > >
> >>>> > > > > I hope this helps,
> >>>> > > > > John
> >>>> > > > >
> >>>> > > > >
> >>>> > > > > On 2022-02-26 3:45 p.m., Juho
> Kristian
> >>>> Ruohonen
> >>>> > wrote:
> >>>> > > > > > Dear John W,
> >>>> > > > > >
> >>>> > > > > > Thank you very much for the
> tip-off!
> >>>> > Apologies for not
> >>>> > > > responding
> >>>> > > > > earlier
> >>>> > > > > > (gmail apparently decided to
> direct
> >>>> your email
> >>>> > > right into the
> >>>> > > > > junk folder).
> >>>> > > > > > I am very pleased to note that the
> >>>> package you
> >>>> > > mention does
> >>>> > > > > indeed work
> >>>> > > > > > with *brms* multinomial models!
> >>>> Thanks again!
> >>>> > > > > >
> >>>> > > > > > Best,
> >>>> > > > > >
> >>>> > > > > > Juho
> >>>> > > > > >
> >>>> > > > > > pe 25. helmik. 2022 klo 19.23 John
> >>>> Willoughby
> >>>> > > > > (johnwillec using gmail.com
> >>>> <mailto:johnwillec using gmail.com>
> >>>> > <mailto:johnwillec using gmail.com <mailto:johnwillec using gmail.com
> >>
> >>>> <mailto:johnwillec using gmail.com <mailto:johnwillec using gmail.com>
> >>>> > <mailto:johnwillec using gmail.com <mailto:johnwillec using gmail.com
> >>>
> >>>> > > <mailto:johnwillec using gmail.com
> >>>> <mailto:johnwillec using gmail.com> <mailto:johnwillec using gmail.com
> >>>> <mailto:johnwillec using gmail.com>>
> >>>> > <mailto:johnwillec using gmail.com <mailto:johnwillec using gmail.com
> >
> >>>> <mailto:johnwillec using gmail.com <mailto:johnwillec using gmail.com>>>>
> >>>> > > > <mailto:johnwillec using gmail.com
> >>>> <mailto:johnwillec using gmail.com>
> >>>> > <mailto:johnwillec using gmail.com <mailto:johnwillec using gmail.com
> >>
> >>>> <mailto:johnwillec using gmail.com <mailto:johnwillec using gmail.com>
> >>>> > <mailto:johnwillec using gmail.com <mailto:johnwillec using gmail.com
> >>>
> >>>> > > <mailto:johnwillec using gmail.com
> >>>> <mailto:johnwillec using gmail.com> <mailto:johnwillec using gmail.com
> >>>> <mailto:johnwillec using gmail.com>>
> >>>> > <mailto:johnwillec using gmail.com <mailto:johnwillec using gmail.com
> >
> >>>> <mailto:johnwillec using gmail.com <mailto:johnwillec using gmail.com>>>>>)
> >>>> > > > > > kirjoitti:
> >>>> > > > > >
> >>>> > > > > >> Have you tried the
> >>> check_collinearity()
> >>>> > function
> >>>> > > in the
> >>>> > > > performance
> >>>> > > > > >> package? It's supposed to work on
> >>> brms
> >>>> > models, but
> >>>> > > whether it
> >>>> > > > > will work on
> >>>> > > > > >> a multinomial model I don't know.
> >>>> It works
> >>>> > well
> >>>> > > on mixed
> >>>> > > > models
> >>>> > > > > generated
> >>>> > > > > >> by glmmTMB().
> >>>> > > > > >>
> >>>> > > > > >> John Willoughby
> >>>> > > > > >>
> >>>> > > > > >>
> >>>> > > > > >> On Fri, Feb 25, 2022 at 3:01 AM
> >>>> > > > >
> >>>> <r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>>
> >>>> > > >
> >>>> <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>>>
> >>>> > > > >
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>>
> >>>> > > >
> >>>> <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>>>>>
> >>>> > > > > >> wrote:
> >>>> > > > > >>
> >>>> > > > > >>> Send R-sig-mixed-models mailing
> list
> >>>> > submissions to
> >>>> > > > > >>>
> r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
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> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>
> >>>> > > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>>
> >>>> > > > > <mailto:
> r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
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> >>>> > > <mailto:r-sig-mixed-models using r-project.org
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> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>
> >>>> > > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
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> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>>>
> >>>> > > > > >>>
> >>>> > > > > >>> To subscribe or unsubscribe via
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> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>>
> >>>> > > >
> >>>> <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>>>
> >>>> > > > >
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>>
> >>>> > > >
> >>>> <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-request using r-project.org
> >>>> <mailto:r-sig-mixed-models-request using r-project.org>>>>>
> >>>> > > > > >>>
> >>>> > > > > >>> You can reach the person
> managing
> >>>> the list at
> >>>> > > > > >>>
> >>>> r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>>>
> >>>> > > > <mailto:
> r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>>>>
> >>>> > > > >
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>>>
> >>>> > > > <mailto:
> r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>
> >>>> > <mailto:r-sig-mixed-models-owner using r-project.org
> >>>> <mailto:r-sig-mixed-models-owner using r-project.org>>>>>
> >>>> > > > > >>>
> >>>> > > > > >>> When replying, please edit your
> >>> Subject
> >>>> > line so it is
> >>>> > > > more specific
> >>>> > > > > >>> than "Re: Contents of
> >>>> R-sig-mixed-models
> >>>> > digest..."
> >>>> > > > > >>>
> >>>> > > > > >>>
> >>>> > > > > >>> Today's Topics:
> >>>> > > > > >>>
> >>>> > > > > >>> 1. Collinearity diagnostics
> for
> >>>> (mixed)
> >>>> > > multinomial
> >>>> > > > models
> >>>> > > > > >>> (Juho Kristian Ruohonen)
> >>>> > > > > >>>
> >>>> > > > > >>>
> >>>> > > > >
> >>>> > > >
> >>>> > >
> >>>> >
> >>>>
> >>>
> ----------------------------------------------------------------------
> >>>> > > > > >>>
> >>>> > > > > >>> Message: 1
> >>>> > > > > >>> Date: Fri, 25 Feb 2022 10:23:25
> >>> +0200
> >>>> > > > > >>> From: Juho Kristian Ruohonen
> >>>> > > > <juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>
> >>>> > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>>
> >>>> > > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>
> >>>> > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>>>
> >>>> > > > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>
> >>>> > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>>
> >>>> > > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>
> >>>> > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>>>>
> >>>> > > > > <mailto:
> juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>
> >>>> > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>>
> >>>> > > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>
> >>>> > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>>>
> >>>> > > > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>
> >>>> > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>>
> >>>> > > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>
> >>>> > <mailto:juho.kristian.ruohonen using gmail.com
> >>>> <mailto:juho.kristian.ruohonen using gmail.com>>>>>>
> >>>> > > > > >>> To: John Fox <jfox using mcmaster.ca
> >>>> <mailto:jfox using mcmaster.ca>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>
> >>>> > > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>
> >>>> > > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>>
> >>>> > > > <mailto:jfox using mcmaster.ca
> >>>> <mailto:jfox using mcmaster.ca> <mailto:jfox using mcmaster.ca
> >>>> <mailto:jfox using mcmaster.ca>>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>
> >>>> > > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>
> >>>> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>
> >>>> <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca>>>>>>
> >>>> > > > > >>> Cc:
> >>>> "r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>
> >>>> > > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>>
> >>>> > > > > <mailto:
> r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>
> >>>> > > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>>>"
> >>>> > > > > >>>
> >>>> <r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>
> >>>> > > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>>
> >>>> > > > > <mailto:
> r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>
> >>>> > > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>
> >>>> > <mailto:r-sig-mixed-models using r-project.org
> >>>> <mailto:r-sig-mixed-models using r-project.org>>>>>>
> >>>> > > > > >>> Subject: [R-sig-ME] Collinearity
> >>>> > diagnostics for
> >>>> > > (mixed)
> >>>> > > > > multinomial
> >>>> > > > > >>> models
> >>>> > > > > >>> Message-ID:
> >>>> > > > > >>> <
> >>>> > > > > >>>
> >>>> > > > >
> >>>> > > >
> >>>> > >
> >>>> >
> >>>>
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>>> <mailto:
> >>> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>
> >>>> >
> >>>> <mailto:
> >>> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>>>>
> >>>> > >
> >>>> >
> >>>> <mailto:
> >>> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>>>>>
> >>>> > > >
> >>>> > >
> >>>> >
> >>>> <mailto:
> >>> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>>>>>>
> >>>> > > > >
> >>>> > > >
> >>>> > >
> >>>> >
> >>>> <mailto:
> >>> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>>>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com>
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>> <mailto:
> CAG_dBVfZr1-P7Q3kbE8TGPm-_2sJixdGCHCtWM9Q9PEnd8ftZw using mail.gmail.com
> >>>>>>>>>
> >>>> > > > > >>> Content-Type: text/plain;
> >>>> charset="utf-8"
> >>>> > > > > >>>
> >>>> > > > > >>> Dear John (and anyone else
> >>> qualified to
> >>>> > comment),
> >>>> > > > > >>>
> >>>> > > > > >>> I fit lots of mixed-effects
> >>> multinomial
> >>>> > models in my
> >>>> > > > research,
> >>>> > > > > and I
> >>>> > > > > >> would
> >>>> > > > > >>> like to see some
> (multi)collinearity
> >>>> > diagnostics
> >>>> > > on the
> >>>> > > > fixed
> >>>> > > > > effects, of
> >>>> > > > > >>> which there are over 30. My
> models
> >>>> are fit
> >>>> > using the
> >>>> > > > Bayesian
> >>>> > > > > *brms*
> >>>> > > > > >>> package because I know of no
> >>>> frequentist
> >>>> > packages
> >>>> > > with
> >>>> > > > > multinomial GLMM
> >>>> > > > > >>> compatibility.
> >>>> > > > > >>>
> >>>> > > > > >>> With continuous or dichotomous
> >>>> outcomes,
> >>>> > my go-to
> >>>> > > > function for
> >>>> > > > > >> calculating
> >>>> > > > > >>> multicollinearity diagnostics
> is of
> >>>> course
> >>>> > > *vif()* from
> >>>> > > > the *car*
> >>>> > > > > >> package.
> >>>> > > > > >>> As expected, however, this
> function
> >>>> does not
> >>>> > > report sensible
> >>>> > > > > diagnostics
> >>>> > > > > >>> for multinomial models -- not
> even
> >>> for
> >>>> > standard
> >>>> > > ones fit
> >>>> > > > by the
> >>>> > > > > *nnet*
> >>>> > > > > >>> package's *multinom()* function.
> >>>> The reason, I
> >>>> > > presume, is
> >>>> > > > > because a
> >>>> > > > > >>> multinomial model is not really
> one
> >>>> but C-1
> >>>> > > regression
> >>>> > > > models
> >>>> > > > > (where C
> >>>> > > > > >> is
> >>>> > > > > >>> the number of response
> categories)
> >>>> and the
> >>>> > *vif()*
> >>>> > > > function is not
> >>>> > > > > >> designed
> >>>> > > > > >>> to deal with this scenario.
> >>>> > > > > >>>
> >>>> > > > > >>> Therefore, in order to obtain
> >>>> meaningful
> >>>> > collinearity
> >>>> > > > metrics,
> >>>> > > > > my present
> >>>> > > > > >>> plan is to write a simple helper
> >>>> function
> >>>> > that uses
> >>>> > > > *vif() *to
> >>>> > > > > calculate
> >>>> > > > > >>> and present (generalized)
> variance
> >>>> inflation
> >>>> > > metrics for
> >>>> > > > the C-1
> >>>> > > > > >>> sub-datasets to which the C-1
> >>> component
> >>>> > binomial
> >>>> > > models
> >>>> > > > of the
> >>>> > > > > overall
> >>>> > > > > >>> multinomial model are fit. In
> other
> >>>> words, it
> >>>> > > will partition
> >>>> > > > > the data
> >>>> > > > > >> into
> >>>> > > > > >>> those C-1 subsets, and then
> apply
> >>>> *vif()*
> >>>> > to as
> >>>> > > many linear
> >>>> > > > > regressions
> >>>> > > > > >>> using a made-up continuous
> response
> >>> and
> >>>> > the fixed
> >>>> > > effects of
> >>>> > > > > interest.
> >>>> > > > > >>>
> >>>> > > > > >>> Does this seem like a sensible
> >>>> approach?
> >>>> > > > > >>>
> >>>> > > > > >>> Best,
> >>>> > > > > >>>
> >>>> > > > > >>> Juho
> >>>> > > > > >>>
> >>>> > > > > >>>
> >>>> > > > > >>>
> >>>> > > > > >>
> >>>> > > > > >> [[alternative HTML
> version
> >>>> deleted]]
> >>>> > > > > >>
> >>>> > > > > >>
> >>>> _______________________________________________
> >>>> > > > > >> R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>>
> >>>> > > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>>>
> >>>> > > > > <mailto:
> R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>>
> >>>> > > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>>>> mailing list
> >>>> > > > > >>
> >>>> > >
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>
> >>>> > >
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>>
> >>>> > > >
> >>>> > <
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>
> >>>> > >
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>>>
> >>>> > > > >
> >>>> > >
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>
> >>>> > >
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>>
> >>>> > > >
> >>>> > <
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>
> >>>> > >
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>>>>
> >>>> > > > > >>
> >>>> > > > > >
> >>>> > > > > > [[alternative HTML version
> >>>> deleted]]
> >>>> > > > > >
> >>>> > > > > >
> >>>> _______________________________________________
> >>>> > > > > > R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>>
> >>>> > > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>>>
> >>>> > > > > <mailto:
> R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>>
> >>>> > > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>
> >>>> > > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>
> >>>> > <mailto:R-sig-mixed-models using r-project.org
> >>>> <mailto:R-sig-mixed-models using r-project.org>>>>> mailing list
> >>>> > > > > >
> >>>> > >
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>
> >>>> > >
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>>
> >>>> > > >
> >>>> > <
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>
> >>>> > >
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>>>
> >>>> > > > >
> >>>> > >
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>
> >>>> > >
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>>
> >>>> > > >
> >>>> > <
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>
> >>>> > >
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
> >>>> > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>> <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>>>>
> >>>> > > > > --
> >>>> > > > > John Fox, Professor Emeritus
> >>>> > > > > McMaster University
> >>>> > > > > Hamilton, Ontario, Canada
> >>>> > > > > web:
> >>>> https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>
> >>>> > > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>>
> >>>> > > > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>
> >>>> > > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>>>
> >>>> > > > >
> >>>> <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>
> >>>> > > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>>
> >>>> > > > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>
> >>>> > > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>>>>
> >>>> > > > >
> >>>> > > > --
> >>>> > > > John Fox, Professor Emeritus
> >>>> > > > McMaster University
> >>>> > > > Hamilton, Ontario, Canada
> >>>> > > > web:
> https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>
> >>>> > > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>>
> >>>> > > > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>
> >>>> > > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>>>
> >>>> > > >
> >>>> > > --
> >>>> > > John Fox, Professor Emeritus
> >>>> > > McMaster University
> >>>> > > Hamilton, Ontario, Canada
> >>>> > > web: https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>
> >>>> > > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>>
> >>>> > >
> >>>> >
> >>>>
> >>>
> ------------------------------------------------------------------------
> >>>> > --
> >>>> > John Fox, Professor Emeritus
> >>>> > McMaster University
> >>>> > Hamilton, Ontario, Canada
> >>>> > web: https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>> > <https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>>
> >>>> >
> >>>> --
> >>>> John Fox, Professor Emeritus
> >>>> McMaster University
> >>>> Hamilton, Ontario, Canada
> >>>> web: https://socialsciences.mcmaster.ca/jfox/
> >>>> <https://socialsciences.mcmaster.ca/jfox/>
> >>>>
> >>> --
> >>> John Fox, Professor Emeritus
> >>> McMaster University
> >>> Hamilton, Ontario, Canada
> >>> web: https://socialsciences.mcmaster.ca/jfox/
> >>>
> >>>
> >>
> >> [[alternative HTML version deleted]]
> >>
> >> _______________________________________________
> >> R-sig-mixed-models using r-project.org mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>
>
>
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