Joaqu?n,
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=oWPX5qlfffXiVV_
GUw6XfiFzgvZaW1Z21RgAeOJfW1A&m=Uc04YW3KXsYZCbVsPoWqHdWzhNglmq
0ndvtDjCKLF9I&s=6qqs7Vr-WbE2YW1X6OE7_35mJ09siJR077ygMnE2hr0&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: Joaqu?n 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, Joaqu?n Aldabe
<joaquin.aldabe at gmail.com> wrote:
Hi all, when working with mixed models, do the levels of the random
have to be independent? For example, if my random effect is the
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
--
*Joaqu?n Aldabe*
*Grupo Biodiversidad, Ambiente y Sociedad*
Centro Universitario de la Regi?n Este, Universidad de la Rep?blica
Ruta 15 (y Ruta 9), Km 28.500, Departamento de Rocha
*Departamento de Conservaci?n*
Aves Uruguay
BirdLife International
Canelones 1164, Montevideo
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