keeping both numerically and factor coded factors

Dear Elisa,

Yes, one of the possible steps is to force correlations to zero, but then
you are imposing (possibly unreasonable) constraints at the cost of trying
to make the model converge. It is a highly questionable procedure to remove
something or impose constraints purely to cause a model to converge. Random
variables that arise in nature as part of the same data generating process
are rarely uncorrelated. It may be that the correlations are small and
/can/ reasonably be set to zero, but you should investigate whether this is
reasonable first.

Removing random slopes is usually a good way to proceed.

If you can't make progress this way you could try the rstanarm package
which provides a drop in replacement for lmer and will fit the model using
a Bayesian approach. Then, the convergence diagnostics should provide a
better way to solve the problem. It may be that one or more of the variance
components and/or correlations between them are close to zero, in which
case you can remove them from the random structure.


On Wed, 31 Jul 2019, 09:14 MONACO Elisa, <elisa.monaco at unifr.ch> wrote:

Thank you,

Robert Long, I think we are claiming the same idea: the maximal model is
too complex (overparameterized and with a degenerate/singular solution) and
I want to reduce the random structure, following the steps suggested by
Bates et al.. Am I correct?
However one of these steps it's indeed "forcing to zero the correlation
parameters" and check the good fit of the consequent model. Therefore my
question on how to arrange my D factor in the random structure.

I still don't know how to handle CS model suggested by Bolker ((1|g/f))
and how to integrate more factors in that structure ((f1*f2|g/f3)?) ... any
suggestions would be much appreciated!

Elisa Monaco


-----Message d'origine-----
De : R-sig-mixed-models <r-sig-mixed-models-bounces at r-project.org> De la
part de Robert Long
Envoy? : mercredi, 24 juillet 2019 10:33
? : R-mixed models mailing list <r-sig-mixed-models at r-project.org>
Objet : Re: [R-sig-ME] keeping both numerically and factor coded factors

It is quite possible that such a complex random structure will not be
supported by the data.

In your initial email you mentioned correlations between random effects.
However, since the model did not converge, there is no point in
intetpreting them. Moreover, to force them to be uncorrelated is possibly
making unrealistic constraints on the model.

Why do seek such a complex random structure ? If you are following the
advice by Barr et al (2013) to "keep it maximal", this is often very poor
advice, as noted by Bates et al (2015), Bates being the primary author of
the lme4 package:

https://arxiv.org/pdf/1506.04967








On Wed, 24 Jul 2019, 09:01 MONACO Elisa, <elisa.monaco at unifr.ch> wrote:

Dear all,
many thanks for your answers and sorry for not providing the details.

My experiment is a 2X2X4 within subject design, with all three factors
being categorical: L=Language of the stimuli (2 levels), V= type of
the stimuli (2 levels), D= delay of brain stimulation (4 levels). My
dependent variable is the amplitude of a physiological measure.

I thought to build my maximal mixed model in which all the factors are
crossed within subjects and only D is crossed within items (items are
the same, repeated at different delays of stimulation):

lmer(MEPzed ~ L * V * D  + (D|items), data=mydata,
control=lmerControl(optCtrl=list(maxfun=1e6)))

So, to answer @Robert Long: my factor D I was referring to is a random
slope, with4 levels

to answer at Ben Bolker:
indeed I don't think that my factor D falls in the 2 cases you
mentioned,
because:
 a) the differences between each level is not the same for each level
(150ms-75ms-75ms-150ms) and we don't expect en effect ordered in time,
we expect the effect to be present at one or more latencies depending
on L;
b) the factor has more than two levels.

According to all of this, I should go for a CS model, right?
I'm a newbie in this field, so can you please give me some indications
of what can I read about it or some indications to understand how to
handle this (especially if I want to reduce gradually the random
structure of the subjects part, see modelreduced2)/?

modelreduced1: lmer(MEPzed ~ L * V * D + (L*V*D|subjects) +
(1|items/D), data=mydata,
control=lmerControl(optCtrl=list(maxfun=1e6)))

modelreduced2: lmer(MEPzed ~ L * V * D + (L*V|subjects/D) +
(1|items/D), data=mydata,
control=lmerControl(optCtrl=list(maxfun=1e6)))


Another point: is this semplification indipendent of which type of
contrast I set for D (I'll set sum contrast for V and L, but I'm still
reasoning on what is the best for D)?

Thank you in advance for this big help and please tell me if you need
further clarifications or code.

 Elisa Monaco | PhD student

parameterized.

My questions are:
a)    is it true that I can use my factor as it is when read by R,

i.e.

"int"?
b)    if yes, does it make sense to keep in the model both the factor

in

the nominal form as fixed effect and the factor in the numerical
form as random effect?

Many thanks for your help,

Elisa Monaco | PhD student

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  I generally agree with Robert's point of view - I don't *necessarily*
object to removing correlations, but you have to think carefully about
what it means.

  As to the question of "how should I put more than one factor into a
compound symmetric model"?: suppose you want to make (L*V*D|subjects)
compound symmetric.  You (unfortunately) have a variety of choices.  If
you really want all CS interactions represented, I think you need the
equivalent of (1|subjects/(L+V+D)^2) (which probably won't work as
written, i.e.

 (1|subjects) +
 (1|subjects:L) + (1|subjects:V) + (1|subjects:D) +
 (1|subjects:L:V) + (1|subjects:V:D) + (1|subjects:D:L)

(if you included the (1|subjects:L:V:D) term it would be redundant with
the residual error term).  This is getting complex again -- 7 parameters
(still much better than (L*V*D|subjects), which gives you (16*17)/2 =
136 parameters to estimate) ...

  I'm not sure rstanarm will solve your problems.  That is, I don't see
how the convergence diagnostics that rstanarm gives you are going to be
much more useful than lme4's in deciding how to simplify the problem.
On the other hand, rstanarm offers a big advantage in allowing you to
set priors to keep the solutions to the fitted problem more realistic -
it also integrates over the uncertainty in a useful way.

  [Robert: sorry if I missed or misconstrued something in your answer.
Could you be a little more specific in how you would use rstanarm's
output & diagnostics to help solve this kind of problem?]

 Ben Bolker



On 2019-08-01 10:02 a.m., Robert Long wrote:

Dear Elisa,

Yes, one of the possible steps is to force correlations to zero, but then
you are imposing (possibly unreasonable) constraints at the cost of trying
to make the model converge. It is a highly questionable procedure to remove
something or impose constraints purely to cause a model to converge. Random
variables that arise in nature as part of the same data generating process
are rarely uncorrelated. It may be that the correlations are small and
/can/ reasonably be set to zero, but you should investigate whether this is
reasonable first.

Removing random slopes is usually a good way to proceed.

If you can't make progress this way you could try the rstanarm package
which provides a drop in replacement for lmer and will fit the model using
a Bayesian approach. Then, the convergence diagnostics should provide a
better way to solve the problem. It may be that one or more of the variance
components and/or correlations between them are close to zero, in which
case you can remove them from the random structure.


On Wed, 31 Jul 2019, 09:14 MONACO Elisa, <elisa.monaco at unifr.ch> wrote:

Thank you,

Robert Long, I think we are claiming the same idea: the maximal model is
too complex (overparameterized and with a degenerate/singular solution) and
I want to reduce the random structure, following the steps suggested by
Bates et al.. Am I correct?
However one of these steps it's indeed "forcing to zero the correlation
parameters" and check the good fit of the consequent model. Therefore my
question on how to arrange my D factor in the random structure.

I still don't know how to handle CS model suggested by Bolker ((1|g/f))
and how to integrate more factors in that structure ((f1*f2|g/f3)?) ... any
suggestions would be much appreciated!

Elisa Monaco


-----Message d'origine-----
De : R-sig-mixed-models <r-sig-mixed-models-bounces at r-project.org> De la
part de Robert Long
Envoy? : mercredi, 24 juillet 2019 10:33
? : R-mixed models mailing list <r-sig-mixed-models at r-project.org>
Objet : Re: [R-sig-ME] keeping both numerically and factor coded factors

It is quite possible that such a complex random structure will not be
supported by the data.

In your initial email you mentioned correlations between random effects.
However, since the model did not converge, there is no point in
intetpreting them. Moreover, to force them to be uncorrelated is possibly
making unrealistic constraints on the model.

Why do seek such a complex random structure ? If you are following the
advice by Barr et al (2013) to "keep it maximal", this is often very poor
advice, as noted by Bates et al (2015), Bates being the primary author of
the lme4 package:

https://arxiv.org/pdf/1506.04967








On Wed, 24 Jul 2019, 09:01 MONACO Elisa, <elisa.monaco at unifr.ch> wrote:

Dear all,
many thanks for your answers and sorry for not providing the details.

My experiment is a 2X2X4 within subject design, with all three factors
being categorical: L=Language of the stimuli (2 levels), V= type of
the stimuli (2 levels), D= delay of brain stimulation (4 levels). My
dependent variable is the amplitude of a physiological measure.

I thought to build my maximal mixed model in which all the factors are
crossed within subjects and only D is crossed within items (items are
the same, repeated at different delays of stimulation):

lmer(MEPzed ~ L * V * D  + (D|items), data=mydata,
control=lmerControl(optCtrl=list(maxfun=1e6)))

So, to answer @Robert Long: my factor D I was referring to is a random
slope, with4 levels

to answer at Ben Bolker:
indeed I don't think that my factor D falls in the 2 cases you
mentioned,
because:
 a) the differences between each level is not the same for each level
(150ms-75ms-75ms-150ms) and we don't expect en effect ordered in time,
we expect the effect to be present at one or more latencies depending
on L;
b) the factor has more than two levels.

According to all of this, I should go for a CS model, right?
I'm a newbie in this field, so can you please give me some indications
of what can I read about it or some indications to understand how to
handle this (especially if I want to reduce gradually the random
structure of the subjects part, see modelreduced2)/?

modelreduced1: lmer(MEPzed ~ L * V * D + (L*V*D|subjects) +
(1|items/D), data=mydata,
control=lmerControl(optCtrl=list(maxfun=1e6)))

modelreduced2: lmer(MEPzed ~ L * V * D + (L*V|subjects/D) +
(1|items/D), data=mydata,
control=lmerControl(optCtrl=list(maxfun=1e6)))


Another point: is this semplification indipendent of which type of
contrast I set for D (I'll set sum contrast for V and L, but I'm still
reasoning on what is the best for D)?

Thank you in advance for this big help and please tell me if you need
further clarifications or code.

 Elisa Monaco | PhD student

parameterized.

My questions are:
a)    is it true that I can use my factor as it is when read by R,

i.e.

"int"?
b)    if yes, does it make sense to keep in the model both the factor

in

the nominal form as fixed effect and the factor in the numerical
form as random effect?

Many thanks for your help,

Elisa Monaco | PhD student

        [[alternative HTML version deleted]]

      [[alternative HTML version deleted]]

        [[alternative HTML version deleted]]

	[[alternative HTML version deleted]]