First posting to the list, prior to sending this out I've tried searching the mixed model list, other lists and anything google could pick up. I am currently trying to calculate repeatability estimates (intra-class correlation coefficients) following Nakagawa & Schielzeth (2010, Biol.Rev. Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists. online early). The details of my models shouldn't be important except that I originally fit the models using binomial error structures and a logit link. Nakagawa and Schielzeth (henceforth N&S) specify that repeatability estimates differ based on whether additive or multiplicative overdispersion modelling is conducted. N&S define multiplicative as when the dispersion parameter is estimated but that residual variance is fixed to one. Additive is defined as having the residual variance estimated and the dispersion parameter fixed to one. These definitions are based on Browne et al. (2005, J. Roy. Stat. Soc A, 168:599-613). Based on my reading of the family objects description it seems that using the quasibinomial family would correspond to the multiplicative overdispersion modelling and the binomial family would correspond to additive overdispersion modelling. Is this conclusion about multiplicative vs. additive correct or am I missing something? I do realize that when the dispersion parameter is estimated as being close to one under a quasibinomial model then the results should be close to what you'd get with a binomial approach which makes me think I am missing something (since the multiplicative model would have the residual variance fixed). Thank you for any help you can provide. Ned Dochtermann -- Ned Dochtermann Department of Biology University of Nevada, Reno --
Additive versus multiplicative overdispersion modeling
8 messages · Ned Dochtermann, Shinichi Nakagawa, Jarrod Hadfield +1 more
On Thu, 19 Aug 2010, Ned Dochtermann wrote:
I am currently trying to calculate repeatability estimates (intra-class correlation coefficients) following Nakagawa & Schielzeth (2010, Biol.Rev. Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists. online early). The details of my models shouldn't be important except that I originally fit the models using binomial error structures and a logit link.
Nakagawa and Schielzeth (henceforth N&S) specify that repeatability estimates differ based on whether additive or multiplicative overdispersion modelling is conducted.
[SNIP]
These definitions are based on Browne et al. (2005, J. Roy. Stat. Soc A, 168:599-613). Based on my reading of the family objects description it seems that using the quasibinomial family would correspond to the multiplicative overdispersion modelling and the binomial family would correspond to additive overdispersion modelling.
Yes. Browne et al say they are using the "additive" approach because it has a proper likelihood. If you are interested in repeatability of binary measures, there are lots of perfectly good "direct" measures. The thing about the GLMM variance components is that they are up in the latent variable part of the model. If you are using a probit-normal, you are getting (essentially) tetrachoric correlations, that is, estimating the correlation between the "true" continuous measures that are being arbitrarily dichotomized to give you your binary outcome. For biometrical geneticists, this is a regarded as a good thing (Yule might disagree ;)), but might not be as useful for, say, assessing different clinical tests. It really does depend on your actual problem. Cheers, David Duffy.
| David Duffy (MBBS PhD) ,-_|\ | email: davidD at qimr.edu.au ph: INT+61+7+3362-0217 fax: -0101 / * | Epidemiology Unit, Queensland Institute of Medical Research \_,-._/ | 300 Herston Rd, Brisbane, Queensland 4029, Australia GPG 4D0B994A v
Thanks a lot, if that is indeed the case it makes calculating repeatabilities per N&S quite straightforward for the multiplicative models (quasibinomial & quasipoisson) since the relevant term to include in the denominator would just be (summary(model)@sigma)^2 (multiplied by (pi^2)/3 ). Of course I still can't figure out how to get the needed information from the additive models, i.e. the residual of the distribution specific variance. Ned
On Thu, Aug 19, 2010 at 10:00 PM, David Duffy <davidD at qimr.edu.au> wrote:
On Thu, 19 Aug 2010, Ned Dochtermann wrote:
I am currently trying to calculate repeatability estimates (intra-class correlation coefficients) following Nakagawa & Schielzeth (2010, Biol.Rev. Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists. online early). The details of my models shouldn't be important except that I originally fit the models using binomial error structures and a logit link.
Nakagawa and Schielzeth (henceforth N&S) specify that repeatability estimates differ based on whether additive or multiplicative overdispersion modelling is conducted.
[SNIP]
These definitions are based on Browne et al. (2005, J. Roy. Stat. Soc A, 168:599-613). Based on my reading of the family objects description it seems that using the quasibinomial family would correspond to the multiplicative overdispersion modelling and the binomial family would correspond to additive overdispersion modelling.
Yes. ?Browne et al say they are using the "additive" approach because it has a proper likelihood. If you are interested in repeatability of binary measures, there are lots of perfectly good "direct" measures. ?The thing about the GLMM variance components is that they are up in the latent variable part of the model. If you are using a probit-normal, you are getting (essentially) tetrachoric correlations, that is, estimating the correlation between the "true" continuous measures that are being arbitrarily dichotomized to give you your binary outcome. ?For biometrical geneticists, this is a regarded as a good thing (Yule might disagree ;)), but might not be as useful for, say, assessing different clinical tests. ?It really does depend on your actual problem. Cheers, David Duffy. -- | David Duffy (MBBS PhD) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ,-_|\ | email: davidD at qimr.edu.au ?ph: INT+61+7+3362-0217 fax: -0101 ?/ ? ? * | Epidemiology Unit, Queensland Institute of Medical Research ? \_,-._/ | 300 Herston Rd, Brisbane, Queensland 4029, Australia ?GPG 4D0B994A v
Hi Ned, You can get the additive residual term of N&S by fitting an observation-level random effect (i.e. one effect for each datum). You will need the latest version of lme4 for this (not available for Mac). If the data are binary you can't estimate the residual, so it is usual just to set it to zero. Cheers, Jarrod Quoting Ned Dochtermann <ned.dochtermann at gmail.com>:
Thanks a lot, if that is indeed the case it makes calculating repeatabilities per N&S quite straightforward for the multiplicative models (quasibinomial & quasipoisson) since the relevant term to include in the denominator would just be (summary(model)@sigma)^2 (multiplied by (pi^2)/3 ). Of course I still can't figure out how to get the needed information from the additive models, i.e. the residual of the distribution specific variance. Ned On Thu, Aug 19, 2010 at 10:00 PM, David Duffy <davidD at qimr.edu.au> wrote:
On Thu, 19 Aug 2010, Ned Dochtermann wrote:
I am currently trying to calculate repeatability estimates (intra-class correlation coefficients) following Nakagawa & Schielzeth (2010, Biol.Rev. Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists. online early). The details of my models shouldn't be important except that I originally fit the models using binomial error structures and a logit link.
Nakagawa and Schielzeth (henceforth N&S) specify that repeatability estimates differ based on whether additive or multiplicative overdispersion modelling is conducted.
[SNIP]
These definitions are based on Browne et al. (2005, J. Roy. Stat. Soc A, 168:599-613). Based on my reading of the family objects description it seems that using the quasibinomial family would correspond to the multiplicative overdispersion modelling and the binomial family would correspond to additive overdispersion modelling.
Yes. ?Browne et al say they are using the "additive" approach because it has a proper likelihood. If you are interested in repeatability of binary measures, there are lots of perfectly good "direct" measures. ?The thing about the GLMM variance components is that they are up in the latent variable part of the model. If you are using a probit-normal, you are getting (essentially) tetrachoric correlations, that is, estimating the correlation between the "true" continuous measures that are being arbitrarily dichotomized to give you your binary outcome. ?For biometrical geneticists, this is a regarded as a good thing (Yule might disagree ;)), but might not be as useful for, say, assessing different clinical tests. ?It really does depend on your actual problem. Cheers, David Duffy. -- | David Duffy (MBBS PhD) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ,-_|\ | email: davidD at qimr.edu.au ?ph: INT+61+7+3362-0217 fax: -0101 ?/ ? ? * | Epidemiology Unit, Queensland Institute of Medical Research ? \_,-._/ | 300 Herston Rd, Brisbane, Queensland 4029, Australia ?GPG 4D0B994A v
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Hi, Jarrod I think you can probably install lme4 on Mac - see the blog and its correspondences (I have not tried myself). http://www.stat.columbia.edu/~cook/movabletype/archives/2010/08/multilevel_mode_11.html Thanks for the tip Best wishes Shinichi Shinichi Nakagawa, PhD (Lecturer of Behavioural Ecology) Department of Zoology University of Otago 340 Great King Street P. O. Box 56 Dunedin, New Zealand Tel: +64-3-479-5046 Fax: +64-3-479-7584 http://www.otago.ac.nz/zoology/staff/academic/nakagawa.html
From: Jarrod Hadfield [j.hadfield at ed.ac.uk]
Sent: Saturday, 21 August 2010 7:42 p.m.
To: Ned Dochtermann
Cc: David Duffy; r-sig-mixed-models at r-project.org; Holger Schielzeth; Shinichi Nakagawa
Subject: Re: [R-sig-ME] Additive versus multiplicative overdispersion modeling
Sent: Saturday, 21 August 2010 7:42 p.m.
To: Ned Dochtermann
Cc: David Duffy; r-sig-mixed-models at r-project.org; Holger Schielzeth; Shinichi Nakagawa
Subject: Re: [R-sig-ME] Additive versus multiplicative overdispersion modeling
Hi Ned, You can get the additive residual term of N&S by fitting an observation-level random effect (i.e. one effect for each datum). You will need the latest version of lme4 for this (not available for Mac). If the data are binary you can't estimate the residual, so it is usual just to set it to zero. Cheers, Jarrod Quoting Ned Dochtermann <ned.dochtermann at gmail.com>: > Thanks a lot, if that is indeed the case it makes calculating > repeatabilities per N&S quite straightforward for the multiplicative > models (quasibinomial & quasipoisson) since the relevant term to > include in the denominator would just be (summary(model)@sigma)^2 > (multiplied by (pi^2)/3 ). Of course I still can't figure out how to > get the needed information from the additive models, i.e. the residual > of the distribution specific variance. > > > Ned > > On Thu, Aug 19, 2010 at 10:00 PM, David Duffy <davidD at qimr.edu.au> wrote: >> On Thu, 19 Aug 2010, Ned Dochtermann wrote: >> >>> I am currently trying to calculate repeatability estimates >>> (intra-class correlation coefficients) following Nakagawa & Schielzeth >>> (2010, Biol.Rev. Repeatability for Gaussian and non-Gaussian data: a >>> practical guide for biologists. online early). The details of my >>> models shouldn't be important except that I originally fit the models >>> using binomial error structures and a logit link. >> >>> Nakagawa and Schielzeth (henceforth N&S) specify that repeatability >>> estimates differ based on whether additive or multiplicative overdispersion >>> modelling is conducted. >> >> [SNIP] >>> >>> These definitions are based on Browne et al. >>> (2005, J. Roy. Stat. Soc A, 168:599-613). >>> >>> Based on my reading of the family objects description it seems that >>> using the quasibinomial family would correspond to the multiplicative >>> overdispersion modelling and the binomial family would correspond to >>> additive overdispersion modelling. >> >> Yes. Browne et al say they are using the "additive" approach because it has >> a proper likelihood. >> >> If you are interested in repeatability of binary measures, there are lots of >> perfectly good "direct" measures. The thing about the GLMM variance >> components is that they are up in the latent variable part of the model. If >> you are using a probit-normal, you are getting (essentially) tetrachoric >> correlations, that is, estimating the correlation between the "true" >> continuous measures that are being arbitrarily dichotomized to give you your >> binary outcome. For biometrical geneticists, this is a regarded as a good >> thing (Yule might disagree ;)), but might not be as useful for, say, >> assessing different clinical tests. It really does depend on your >> actual problem. >> >> Cheers, David Duffy. >> -- >> | David Duffy (MBBS PhD) ,-_|\ >> | email: davidD at qimr.edu.au ph: INT+61+7+3362-0217 fax: -0101 / * >> | Epidemiology Unit, Queensland Institute of Medical Research \_,-._/ >> | 300 Herston Rd, Brisbane, Queensland 4029, Australia GPG 4D0B994A v >> > > _______________________________________________ > R-sig-mixed-models at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models > > -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.
Hi Shinichi, Just tried - this works for me. Cheers, Jarrod Quoting Shinichi Nakagawa <shinichi.nakagawa at otago.ac.nz>:
Hi, Jarrod I think you can probably install lme4 on Mac - see the blog and its correspondences (I have not tried myself). http://www.stat.columbia.edu/~cook/movabletype/archives/2010/08/multilevel_mode_11.html Thanks for the tip Best wishes Shinichi Shinichi Nakagawa, PhD (Lecturer of Behavioural Ecology) Department of Zoology University of Otago 340 Great King Street P. O. Box 56 Dunedin, New Zealand Tel: +64-3-479-5046 Fax: +64-3-479-7584 http://www.otago.ac.nz/zoology/staff/academic/nakagawa.html
________________________________________ From: Jarrod Hadfield [j.hadfield at ed.ac.uk] Sent: Saturday, 21 August 2010 7:42 p.m. To: Ned Dochtermann Cc: David Duffy; r-sig-mixed-models at r-project.org; Holger Schielzeth; Shinichi Nakagawa Subject: Re: [R-sig-ME] Additive versus multiplicative overdispersion modeling Hi Ned, You can get the additive residual term of N&S by fitting an observation-level random effect (i.e. one effect for each datum). You will need the latest version of lme4 for this (not available for Mac). If the data are binary you can't estimate the residual, so it is usual just to set it to zero. Cheers, Jarrod Quoting Ned Dochtermann <ned.dochtermann at gmail.com>: Thanks a lot, if that is indeed the case it makes calculating repeatabilities per N&S quite straightforward for the multiplicative models (quasibinomial & quasipoisson) since the relevant term to include in the denominator would just be (summary(model)@sigma)^2 (multiplied by (pi^2)/3 ). Of course I still can't figure out how to get the needed information from the additive models, i.e. the residual of the distribution specific variance. Ned On Thu, Aug 19, 2010 at 10:00 PM, David Duffy <davidD at qimr.edu.au> wrote: On Thu, 19 Aug 2010, Ned Dochtermann wrote: I am currently trying to calculate repeatability estimates (intra-class correlation coefficients) following Nakagawa & Schielzeth (2010, Biol.Rev. Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists. online early). The details of my models shouldn't be important except that I originally fit the models using binomial error structures and a logit link. Nakagawa and Schielzeth (henceforth N&S) specify that repeatability estimates differ based on whether additive or multiplicative overdispersion modelling is conducted. [SNIP] These definitions are based on Browne et al. (2005, J. Roy. Stat. Soc A, 168:599-613). Based on my reading of the family objects description it seems that using the quasibinomial family would correspond to the multiplicative overdispersion modelling and the binomial family would correspond to additive overdispersion modelling. Yes. Browne et al say they are using the "additive" approach because it has a proper likelihood. If you are interested in repeatability of binary measures, there are lots of perfectly good "direct" measures. The thing about the GLMM variance components is that they are up in the latent variable part of the model. If you are using a probit-normal, you are getting (essentially) tetrachoric correlations, that is, estimating the correlation between the "true" continuous measures that are being arbitrarily dichotomized to give you your binary outcome. For biometrical geneticists, this is a regarded as a good thing (Yule might disagree ;)), but might not be as useful for, say, assessing different clinical tests. It really does depend on your actual problem. Cheers, David Duffy. -- | David Duffy (MBBS PhD) ,-_|\ | email: davidD at qimr.edu.au ph: INT+61+7+3362-0217 fax: -0101 / * | Epidemiology Unit, Queensland Institute of Medical Research \_,-._/ | 300 Herston Rd, Brisbane, Queensland 4029, Australia GPG 4D0B994A v _______________________________________________ R-sig-mixed-models at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.
The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.
1 day later
On Fri, 20 Aug 2010, Ned Dochtermann wrote:
Thanks a lot, if that is indeed the case it makes calculating repeatabilities per N&S quite straightforward for the multiplicative models (quasibinomial & quasipoisson) since the relevant term to include in the denominator would just be (summary(model)@sigma)^2 (multiplied by (pi^2)/3 ). Of course I still can't figure out how to get the needed information from the additive models, i.e. the residual of the distribution specific variance.
Method "C" in the Browne paper uses: r = V/(V+pi^2/3) for the logistic link, and r=V/(V+1) for the probit link (the latter is the tetrachoric r). Cheers, David Duffy.
| David Duffy (MBBS PhD) ,-_|\ | email: davidD at qimr.edu.au ph: INT+61+7+3362-0217 fax: -0101 / * | Epidemiology Unit, Queensland Institute of Medical Research \_,-._/ | 300 Herston Rd, Brisbane, Queensland 4029, Australia GPG 4D0B994A v
2 days later
David, To somewhat wrap things up; as I guess would be expected, I get the same repeatability estimate from a quasibinomial model using V/(V+sigma^2*pi^2/3) as with V/(V+pi^2/3) from a binomial model. Thanks again for your and everyone else's help! Ned -- Ned Dochtermann Department of Biology University of Nevada, Reno ned.dochtermann at gmail.com http://wolfweb.unr.edu/homepage/mpeacock/Dochter/ -- -----Original Message----- From: David Duffy [mailto:davidD at qimr.edu.au] Sent: Sunday, August 22, 2010 6:39 PM To: Ned Dochtermann Cc: r-sig-mixed-models at r-project.org Subject: Re: [R-sig-ME] Additive versus multiplicative overdispersion modeling
On Fri, 20 Aug 2010, Ned Dochtermann wrote:
Thanks a lot, if that is indeed the case it makes calculating repeatabilities per N&S quite straightforward for the multiplicative models (quasibinomial & quasipoisson) since the relevant term to include in the denominator would just be (summary(model)@sigma)^2 (multiplied by (pi^2)/3 ). Of course I still can't figure out how to get the needed information from the additive models, i.e. the residual of the distribution specific variance.
Method "C" in the Browne paper uses: r = V/(V+pi^2/3) for the logistic link, and r=V/(V+1) for the probit link (the latter is the tetrachoric r). Cheers, David Duffy.
| David Duffy (MBBS PhD) ,-_|\ | email: davidD at qimr.edu.au ph: INT+61+7+3362-0217 fax: -0101 / * | Epidemiology Unit, Queensland Institute of Medical Research \_,-._/ | 300 Herston Rd, Brisbane, Queensland 4029, Australia GPG 4D0B994A v