[R-sig-ME] Exponent random effect in nlmer

Cole, Tim tim.cole at ucl.ac.uk
Tue Oct 11 12:30:47 CEST 2016

Dear Thierry,

Thanks very much for your speedy response.

I agree my model looks odd, but it has a theoretical basis which I'd prefer not to spell out at this stage. Suffice to say that
* -Inf < y < Inf
* 0 < E(y) < 1
* there is a subject random effect.

For these reasons the usual models and/or transformations won't work, whereas my proposed exponent random effect ought to. I just need to fit it, to see if I'm right!

Best wishes,
Tim.cole at ucl.ac.uk<mailto:Tim.cole at ucl.ac.uk> Phone +44(0)20 7905 2666 Fax +44(0)20 7905 2381
Population, Policy and Practice Programme
UCL Great Ormond Street Institute of Child Health, London WC1N 1EH, UK

From: Thierry Onkelinx <thierry.onkelinx at inbo.be<mailto:thierry.onkelinx at inbo.be>>
Date: Tuesday, 11 October 2016 11:06
To: Tim Cole <tim.cole at ucl.ac.uk<mailto:tim.cole at ucl.ac.uk>>
Cc: "r-sig-mixed-models at r-project.org<mailto:r-sig-mixed-models at r-project.org>" <r-sig-mixed-models at r-project.org<mailto:r-sig-mixed-models at r-project.org>>
Subject: Re: [R-sig-ME] Exponent random effect in nlmer

Dear Tim,

y centred on 0 and a valid range (0, 1) seems to be conflicting statements.

Here a some solutions depending on y

- y stems from a binomial process
     - use a binomial glmm.
- y is continuous and you are willing to transform y
    - 0 < y <  1
        - apply a logit transformation on y. lmer(plogis(y) ~ f + (1 | id) )
    - 0 <= y < 1
        - apply a log transformation on y. lmer(log(y) ~ f + (1 | id) )
    - 0 < y <= 1
        - apply a log transformation on 1 - y. lmer(log(1 - y) ~ f + (1 | id) )
- y is continuous are not willing to transform y
   - use a beta regression with 0 and/or 1 inflation in case you have 0 or 1 in the data. Have a look at the gamlss package to fit this model.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht

To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. ~ John Tukey

2016-10-11 11:29 GMT+02:00 Cole, Tim <tim.cole at ucl.ac.uk<mailto:tim.cole at ucl.ac.uk>>:
I have a model of the form
  m1 <- lmer(y ~ f + (1 | id) )
where y is a continuous variable centred on zero, f is a unordered factor with coefficients b such 0 < b < 1, and there is a signficant random subject intercept.

The random intercept can lead to predicted values outside the valid range (0, 1). For this reason I'd like to reformulate the model as
m2 <- nlmer(y ~ (f - 1) ^ exp(1 | id) )   (using a invalid but I hope obvious notation), where the random effect is now a power centred on 1. This would constrain the fitted values to be within c(0, 1).

My question is: can this be done in nlmer, and if so how? Please can someone point me in the right direction?

Tim Cole
Tim.cole at ucl.ac.uk<mailto:Tim.cole at ucl.ac.uk><mailto:Tim.cole at ucl.ac.uk<mailto:Tim.cole at ucl.ac.uk>> Phone +44(0)20 7905 2666<tel:%2B44%280%2920%207905%202666> Fax +44(0)20 7905 2381<tel:%2B44%280%2920%207905%202381>
Population, Policy and Practice Programme
UCL Great Ormond Street Institute of Child Health, London WC1N 1EH, UK

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