[R-sig-ME] Question on random effect

Tue Jul 11 14:47:42 CEST 2017

Joaquín,

There are a very large number of R2 formulas for mixed models, but they are not all doing the same thing and do not always agree. Be prepared to defend any choice you make. Here are some references. 

Edwards, L. J., Muller, K. E., Wolfinger, R. D., Qaqish, B. F., & Schabenberger, O. (2008). An R2 statistic for fixed effects in the linear mixed model. Statistics in Medicine, 27(29), 6137-6157. doi:10.1002/sim.3429

Jaeger, B. C., Edwards, L. J., Das, K., & Sen, P. K. (2017). An R2 statistic for fixed effects in the generalized linear mixed model. Journal of Applied Statistics, 44(6), 1086-1105. doi:10.1080/02664763.02662016.01193725

Johnson, P. C. D. (2014). Extension of Nakagawa & Schielzeth's R2 GLMM to random slopes models. Methods in Ecology and Evolution, 5(9), 944-946. doi:10.1111/2041-210X.12225

Kramer, M. (2005). R2 statistics for mixed models. Proceedings of the Conference on Applied Statistics in Agriculture, 17, 148-160. Retrieved from https://urldefense.proofpoint.com/v2/url?u=http-3A__www.ars.usda.gov_sp2UserFiles_ad-5Fhoc_12000000SpatialWorkshop_19KramerSupplRsq.pdf&d=DwIFaQ&c=nE__W8dFE-shTxStwXtp0A&r=dEfYO8VG_HWacfGbkUWF38w6kNYYVHYjNQca-3cvt28&m=xAL238UzZyrNK2ncSfWTTCX6WI2RUEcC-_31bAF5_1A&s=iRjwqX5RGOT3CuzuRcm_J3Do-EH1F_0eZsOA9afygec&e= 

LaHuis, D. M., Hartman, M. J., Hakoyama, S., & Clark, P. C. (2014). Explained variance measures for multilevel models. Organizational Research Methods, 17(4), 433-451. doi:10.1177/1094428114541701

Liu, H., Zheng, Y., & Shen, J. (2008). Goodness-of-fit measures of R2 for repeated measures mixed effect models. Journal of Applied Statistics, 35, 1081–1092. 

Nakagawa, S., & Schielzeth, H. (2013). A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution, 4(2), 133-142. doi:10.1111/j.2041-210x.2012.00261.x

Nakagawa, S., & Schielzeth, H. (2016). Extending R2 and intra-class correlation coefficient from generalized linear mixed-effects models: capturing and characterizing biological variation. bioRxiv. doi:10.1101/095851

Orelien, J. G., & Edwards, L. J. (2008). Fixed-effect variable selection in linear mixed models using R2 statistics. Computational Statistics & Data Analysis, 52(4), 1896-1907. doi:10.1016/j.csda.2007.06.006

Roberts, J. K., Monaco, J. P., Stovall, H., & Foster, V. (2011). Explained variance in multilevel models. In J. J. Hox & J. K. Roberts (Eds.), Handbook of advanced multilevel analysis (pp. 219-230). New York, NY: Routledge.

Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel analysis: An introduction to basic and advanced multilevel modeling (2nd ed.). London, UK: Sage.

Xu, R. (2003). Measuring explained variation in linear mixed effects models. Statistics in Medicine, 22(22), 3527-3541. doi:10.1002/sim.1572

Steven J. Pierce
E-mail: pierces1 at msu.edu

-----Original Message-----
From: Joaquín Aldabe [mailto:joaquin.aldabe at gmail.com] 
Sent: Tuesday, July 11, 2017 7:28 AM
To: Ben Bolker <bbolker at gmail.com>
Cc: r-sig-mixed-models <r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] Question on random effect

Thank you Ben. Another question: is there any kind of R2 in mixed models
that allow me to estimate the explanatory power of the model?
Thanks again. Joaquin

2017-07-11 8:22 GMT-03:00 Ben Bolker <bbolker at gmail.com>:

> Yes, the assumption is that the random effects are (conditionally)
> independent.  It can help to specify covariates  (such as
> latitude/longitude or eastings/northings, or environmental conditions
> [temperature, elevation, etc.]) for sites to mop up some of the
> independence. It is theoretically possible, although I don't know of
> an easy off-the-shelf way to do it, to impose (e.g.) spatial
> correlation structures at the level of the random effects ...  or you
> could examine the spatial dependence of the conditional modes/random
> effects and try to convince yourself it was weak ...
>
> On Tue, Jul 11, 2017 at 7:14 AM, Joaquín Aldabe
> <joaquin.aldabe at gmail.com> wrote:
> > Hi all, when working with mixed models, do the levels of the random
> effect
> > have to be independent? For example, if my random effect is the identity
> of
> > sites and it is associated to the intercept, do sites have to be
> > independent?
> >
> > I appreciate comments and bibliographic references.
> >
> > Thank you very much in advanced,
> >
> > Joaquin
> >
> > --
> > *Joaquín Aldabe*
> >
> > *Grupo Biodiversidad, Ambiente y Sociedad*
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> > Ruta 15 (y Ruta 9), Km 28.500, Departamento de Rocha
> >
> > *Departamento de Conservación*
> > Aves Uruguay
> > BirdLife International
> > Canelones 1164, Montevideo
> >
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-- 
*Joaquín Aldabe*

*Grupo Biodiversidad, Ambiente y Sociedad*
Centro Universitario de la Región Este, Universidad de la República
Ruta 15 (y Ruta 9), Km 28.500, Departamento de Rocha

*Departamento de Conservación*
Aves Uruguay
BirdLife International
Canelones 1164, Montevideo

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