lme4 and PIRLS

Grace, Justin <justin.grace at ...> writes:

Dear group,

I have been advised that I need to use penalised iteratively
reweighted least squares (PIRLS) to improve some of my lmer models,
rather than my current REML approach.

I have spent a fair bit of time using mixed models but this is new
to me, I was wondering if someone could explain whether this can be
implemented in or on top of lme4, if there is a package to do so, or
if I need to code manually.  Also, why and how this is an
improvement.

The purpose of our models is to build patient-specific growth curves
and then use these models to predict a new patient's growth and then
improve this model after some observations have been made.

PIRLS is the algorithm that glmer uses; it allows the variance of
the residuals to be a specified function of the mean rather than being
constant as in the standard linear mixed model.  Typically, you would
use PIRLS (automatically) when you decided to use a generalized mixed
model because your data represented (e.g.) counts or proportions.

  I don't feel I have quite enough context to answer your other
questions. If someone has advised you that you should use PIRLS, can
you go back and ask *them* why it's an improvement?

  Just to clarify, "REML" and "ML" are _criteria_ for fitting,
wherease "PIRLS" is an _algorithm_ (it is generally used to fit
a ML criterion).

  Ben Bolker

Hi Ben,

Thanks for your response.

I think I rushed my question - I am aware of the distinction between PIRLS as a penalisation method and REML as an assessment of fit. Is there an equivalent penalisation routine run in lmer?

I am using lmer, not glmer (the outcome is pseudo-continuous - a 20 item score, but with some count-like properties over time and a ceiling effect: see graph, BI is the outcome)

When we include individual and temporal random effects the residuals appear normal. There is a lot of noise however, and since the model is to be used as a prognostic tool in new populations I want to make sure the predictions are robust and not over fitting.

I have validated in external data sets in addition to using cross-validation procedures internally.



Thanks,
Justin



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-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Ben Bolker
Sent: 25 July 2013 13:56
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] lme4 and PIRLS

Grace, Justin <justin.grace at ...> writes:

Dear group,

I have been advised that I need to use penalised iteratively 
reweighted least squares (PIRLS) to improve some of my lmer models, 
rather than my current REML approach.

I have spent a fair bit of time using mixed models but this is new to 
me, I was wondering if someone could explain whether this can be 
implemented in or on top of lme4, if there is a package to do so, or 
if I need to code manually.  Also, why and how this is an improvement.

The purpose of our models is to build patient-specific growth curves 
and then use these models to predict a new patient's growth and then 
improve this model after some observations have been made.

PIRLS is the algorithm that glmer uses; it allows the variance of the residuals to be a specified function of the mean rather than being constant as in the standard linear mixed model.  Typically, you would use PIRLS (automatically) when you decided to use a generalized mixed model because your data represented (e.g.) counts or proportions.

  I don't feel I have quite enough context to answer your other questions. If someone has advised you that you should use PIRLS, can you go back and ask *them* why it's an improvement?

  Just to clarify, "REML" and "ML" are _criteria_ for fitting, wherease "PIRLS" is an _algorithm_ (it is generally used to fit a ML criterion).

  Ben Bolker

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Grace, Justin <justin.grace at ...> writes:

I think I rushed my question - I am aware of the distinction between
PIRLS as a penalisation method and REML as an assessment of fit. Is
there an equivalent penalisation routine run in lmer?

We're still failing to communicate ... in my world, PIRLS is
an algorithm, not a 'penalisation method'.  The meaning of
'penalisation' in the term is that the conditional deviance
(the deviance of the data conditional on a particular set of
conditional mode estimates) is penalised by the variation of
the conditional modes around zero.

I am using lmer, not glmer (the outcome is pseudo-continuous - a 20
item score, but with some count-like properties over time and a
ceiling effect: see graph, BI is the outcome)

lmer is already using penali[sz]ed least squares (where 'penalised'
is used in the same sense as above), but uses a more specialized
algorithm that works to calculate the profile likelihood of the
theta (RE variance-covariance) parameters.  PIRLS would just be a less
efficient but more general way to arrive at the same answers.

When we include individual and temporal random effects the residuals
appear normal. There is a lot of noise however, and since the model
is to be used as a prognostic tool in new populations I want to make
sure the predictions are robust and not over fitting.

There is a 'robustlmm' package on CRAN ... or you could use
the 'ordinal' package to treat your data as ordinal rather than
approximately (conditionally) Normal ...