# [R-sig-ME] glmer syntax for model with "common" random effects

ONKELINX, Thierry Thierry.ONKELINX at inbo.be
Fri May 16 10:24:24 CEST 2014

```Dear Steven,

Please keep the mailing list in cc. Others might chime in and you might get a faster reply.

You need to create a variable the combines both norms. That is what Norm_Combined <- interaction(Norm_XY, Norm_21) does. Then you could do glmer(Sex ~ 1 + Norm_XY + Norm_21 + (Norm_Combined|Pat_ID/Proc_ID), data =  PGD_21.df,family = binomial). Note that this would be equivalent to glmer(Sex ~ 1 + Norm_XY + Norm_21 + (Norm_XY * Norm_21|Pat_ID/Proc_ID), data =  PGD_21.df,family = binomial). So even more complex than your original model.

Note that (1|A/B) is equivalent to (1|A + 1|A:B) Therefor my suggestion to use (1|Pat_ID) + (1|PatID:Proc_ID) + (1|Pat_ID:Norm_Combined) + (1|PatID: Proc_ID:Norm_Combined) which is the verbatim of (1|PatID/Proc_ID/Norm_Combined) + (1|PatID/ /Norm_Combined). This model allows the same fit as (Norm_Combined|Pat_ID/Proc_ID) but assumes that all levels of Norm_Combined come from a univariate iid normal distribution (same variance and uncorrelated). (Norm_Combined|Pat_ID/Proc_ID)
assumes that the levels of Norm_Combined come from a multivariate normal distribution. And hence requires a lot more parameters.

If this is not what you want, then give us the mathematical equation of the model that you need.

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
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx op inbo.be
www.inbo.be

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-----Oorspronkelijk bericht-----
Van: orzack [mailto:orzack op freshpond.org]
Verzonden: woensdag 14 mei 2014 15:20
Aan: ONKELINX, Thierry
Onderwerp: RE: [R-sig-ME] glmer syntax for model with "common" random effects

Dear Thierry,
many thanks for your suggestion. I think we are talking past each other, which is likely mostly due to my not being clear and/or my not understanding your suggestion. Perhaps this would help clarify:

in my first email, I presented this model

>model <- glmer(Sex ~ 1 + Norm_XY + Norm_21 + ((Norm_XY +
>Norm_21)|Pat_ID/Proc_ID), data =  PGD_21.df,family = binomial))

this generates a "common" or "overall" estimate of the intercept, i.e., one that estimates the random effects for both predictors combined. What I would like is a model that provides a similar "combined" estimate for the slope. it would be something like

>model <- glmer(Sex ~ 1 + Norm_XY + Norm_21 +
>((COMBINEDNORM)|Pat_ID/Proc_ID), data =  PGD_21.df,family =
>binomial))

so that the fixed effects are calculated separately but norm-specific estimates of the random effects for the slope were not provided.

When I use the interaction approach you mention, glmer returns estimates for each combination of the levels

>
>I think you want something like this (if I understand you question correctly).
>
>PGD_21.df\$Norm_Inter <- interaction(PGD_21.df\$NormXY,
>PGD_21.df\$Norm_21) model <- glmer(Sex ~ 1 + Norm_XY + Norm_21 + (1|Pat_ID) + (1|PatID:
>Proc_ID) + (1|Pat_ID:Norm_Inter) + (1|PatID: Proc_ID:Norm_Inter), data
>=  PGD_21.df,family = binomial)
>

I want to reduce the AIC penalty. This increases it unless I misunderstand your syntax. Speaking of which, what does this syntax mean

1|PatID: Proc_ID:Norm_Inter?

In my problem, only  PatID and Proc_ID provide estimates of random effects.

I look forward to hearing from you.

S.
--
Steven Orzack

The Fresh Pond Research Institute
173 Harvey Street
Cambridge, MA. 02140
617 864-4307

www.freshpond.org
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