[R-sig-ME] Bradley Terry GLMM in R ?
Shira Mitchell
@h|r@qotj @end|ng |rom gm@||@com
Fri Dec 9 15:53:05 CET 2022
Hi Dr van Paridon,
Thank you so much !
We are returning to this after our busy election season. We are using your
awesome lmerMultiMember package and have questions.
We have voter-specific variables x that influence which political message
(i vs j) wins for them:
logit[pr(i beats j | person with covariate x)] = lambda_i - lambda_j +
(beta_i - beta_j) x
We then model parameters as random effects:
lambda_i ~ N(0, sigma_lambda)
beta_i ~ N(0, sigma_beta)
m <- lmerMultiMember::glmer(depvar ~ 1 + (1 | indicators) + (x |
indicators),
family = binomial,
memberships =
list(indicators = W),
data = dat_train)
This runs beautifully. :)
Now suppose we want the strength of message i among people with covariates
x (e.g. a specific age). In reality we have a few covariates, both
continuous (x | indicators) and categorical groups (1 | indicators:group).
pr(i beats a hypothetical average message | person with covariate x) =
logit^-1 ( lambda_i + beta_i x)
We have a data set that crosses all population x values with all messages,
dat_population_all_messages.
Also, if we want to predict specific match-ups from the training data
dat_train, how do we do that ?
Thanks again !!
Shira
---------
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2022q4/030224.html
In case it's helpful to anyone following this email thread: I wrote a
vignette explaining how to fit a Bradley-Terry model in lme4 using
lmerMultiMember. You can find it at
https://jvparidon.github.io/lmerMultiMember/articles/bradleyterry_models.html
Cheers,
JP van Paridon (he/him)
Research Associate, Lupyan Lab
University of Wisconsin-Madisonhttps://github.com/jvparidon
________________________________
From: Jeroen van Paridon <vanparidon using wisc.edu
<https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>
Sent: Thursday, October 20, 2022 1:42 AM
To: r-sig-mixed-models using r-project.org
<https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
<r-sig-mixed-models using r-project.org
<https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>>
Subject: Re: [R-sig-ME] Bradley Terry GLMM in R ?
Hi,
Just to expand on Ben's last email: In principle, lmerMultiMember
allows you to pass arbitrary indicator/weight matrices for the random
effects to lme4 for model fitting as long as they have the correct
shape. The package contains helper functions for generating more
conventional multiple membership matrices since that was my own
use-case, but if you create your own matrix with opposed (1 and -1)
weights I see no reason why it shouldn't work.
Membership matrices need to be sparse matrices of class
Matrix::dgCMatrix and shape n_groups x n_obs. You can probably just
take whatever indicator matrix you already have, transpose it, and
then cast it to the sparse format.
If you're going this route and run into any issues, feel free to reach
out to me, directly.
Cheers,
JP van Paridon (he/him)
Research Associate, Lupyan Lab
University of Wisconsin-Madisonhttps://github.com/jvparidon
________________________________
On Mon, Oct 17, 2022 at 10:02 PM Shira Mitchell <shiraqotj using gmail.com> wrote:
> Questions for Ben Bolker about the excellent GLMM FAQ:
>
> Where does the hglm package fit into this very helpful table ?
>
> https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#what-methods-are-available-to-fit-estimate-glmms
>
> I wonder also about differences in model formula specifications, since
> some packages (e.g. lme4) don't seem to accommodate Bradley-Terry, whereas
> some packages (e.g. INLA, hglm, MCMCglmm) can accommodate.
> https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#model-specification
>
>
>
>
> On Mon, Oct 17, 2022 at 3:55 PM Shira Mitchell <shiraqotj using gmail.com>
> wrote:
>
>> Thanks so much, Jarrod ! Not too late at all. Very interesting to compare
>> MCMC with the approximations (INLA, hglm's extended quasi likelihood). I
>> don't think I have the priors lined up yet across packages. The random
>> effects seem more dispersed according to MCMCglmm than in INLA or hglm, but
>> this could be due to priors not fit algorithm. Will look into the package
>> prior defaults.
>>
>> On Mon, Oct 17, 2022 at 4:45 AM Jarrod Hadfield <j.hadfield using ed.ac.uk>
>> wrote:
>>
>>> Hi Shira,
>>>
>>> Perhaps a little late to be useful, but MCMCglmm also fits random-effect
>>> Bradley-Terry models. Just specify ~mm(opponent1-opponent2) in the random
>>> effect formula. The mm stands for multimembership - the BT model is like a
>>> multimembership model where some effects have been multiplied by -1, hence
>>> the ‘-' rather than ‘+’ in the mm model formula.
>>>
>>> Cheers,
>>>
>>> Jarrod
>>>
>>>
>>> > On 16 Oct 2022, at 22:49, Shira Mitchell <shiraqotj using gmail.com> wrote:
>>> >
>>> > This email was sent to you by someone outside the University.
>>> > You should only click on links or attachments if you are certain that
>>> the email is genuine and the content is safe.
>>> >
>>> > Update: Dr Heather Turner <https://www.heatherturner.net/> (author of
>>> > BradleyTerry2) suggested the hglm package, which unlike lme4 allows
>>> you to
>>> > specify generic design matrices (no longer constrained to lme4
>>> formulas !)
>>> > Results look really similar to INLA so far. Yay !
>>> >
>>> > On Sun, Oct 16, 2022 at 2:19 PM Shira Mitchell <shiraqotj using gmail.com>
>>> wrote:
>>> >
>>> >> Super helpful ! Thank you so much !
>>> >>
>>> >> Out of curiosity, is there a way to fit this type of Bradley-Terry
>>> model
>>> >> in lme4 ? lme4 formulas include random effect via syntax:
>>> >> https://cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf
>>> >> "(expr | factor). The expression expr is evaluated as a linear model
>>> >> formula, producing a model matrix following the same rules used in
>>> standard
>>> >> R modeling functions (e.g., `lm` or `glm`). The expression factor is
>>> >> evaluated as an `R` factor. One way to think about the vertical bar
>>> >> operator is as a special kind of interaction between the model matrix
>>> and
>>> >> the grouping factor. This interaction ensures that the columns of the
>>> model
>>> >> matrix have different effects for each level of the grouping factor."
>>> >>
>>> >> So (expr | factor) is X_expr * alpha_factor.
>>> >>
>>> >> So naively writing ~ (1 | m_1) + (1 | m_2) is alpha_{m_1}^{(1)} +
>>> >> alpha_{m_2}^{(2)}, twice as many parameters as what we want which is
>>> >> alpha_{m_1} - alpha_{m_2}.
>>> >>
>>> >> But then see this stackexchange:
>>> >>
>>> >>
>>> https://stats.stackexchange.com/questions/483833/opposing-effects-in-lme4-formulae-bradley-terry-model
>>> >> "I could just make a design matrix, where player 1 gets the value 1,
>>> and
>>> >> player 2 gets the value −1. However, unless I'm missing a trick, this
>>> would
>>> >> require having a separate column for each player, and plugging each
>>> player
>>> >> column's name into the formula"
>>> >>
>>> >> But suppose we create columns for all m = 1,...,M messages:
>>> >>
>>> >> A_m = 1 if m = m_1
>>> >> -1 if m = m_2
>>> >> 0 otherwise
>>> >>
>>> >> I think then ~ (A_1 + ... + A_M | m_1) is alpha_{m_1}^{(m_1)} -
>>> >> alpha_{m_1}^{(m_2)}, also not what we would want.
>>> >>
>>> >> Back to INLA. Suppose we now want to add random message-specific
>>> slopes
>>> >> for variable X_i in addition to random message-specific intercepts:
>>> >>
>>> >> P[i chooses m_1] = logit^-1 (beta_0 + (alpha_{m_1} - alpha_{m_2}) +
>>> >> (beta_{m_1} - beta_{m_2})X_i)
>>> >>
>>> >> alpha_1,...,alpha_M ~ N(0,sigma_intercept)
>>> >> beta_1,...,beta_M ~ N(0,sigma_slope)
>>> >>
>>> >> I see some resources about this, but nothing super comprehensive. Any
>>> >> advice where to look for complete documentation ?
>>> >>
>>> >>
>>> https://groups.google.com/g/r-inla-discussion-group/c/iQELaQF8M9Q/m/q7f4-W8YQksJ
>>> >> (
>>> >>
>>> https://becarioprecario.bitbucket.io/inla-gitbook/ch-multilevel.html#multilevel-models-for-longitudinal-data
>>> >> https://rpubs.com/corey_sparks/431920
>>> >> https://avianecologist.com/2016/10/05/multilevel-models/
>>> >>
>>> >> Here is what we did:
>>> >>
>>> >> data$w_X = -data$X
>>> >> data$m_1_beta = data$m_1
>>> >> data$m_2_beta = data$m_2
>>> >>
>>> >> inla(depvar ~ f(m_1, model="iid", values = issues) +
>>> >> f(m_2, w, copy = "m_1") +
>>> >> f(m_1_beta, X, model="iid", values =
>>> issues) +
>>> >> f(m_2_beta, w_X, copy = "m_1_beta"),
>>> >> family="binomial",
>>> >> data=data)
>>> >>
>>> >>
>>> >>
>>> >>
>>> >> On Mon, Oct 10, 2022 at 4:24 AM Thierry Onkelinx <
>>> thierry.onkelinx using inbo.be>
>>> >> wrote:
>>> >>
>>> >>> Dear Shira,
>>> >>>
>>> >>> - in a formula object means remove that object from the formula. Use
>>> a
>>> >>> weight of -1 instead.
>>> >>>
>>> >>> f(home, model = "iid")) + f(away, w = -1, copy = "home")
>>> >>>
>>> >>> Best regards,
>>> >>>
>>> >>> ir. Thierry Onkelinx
>>> >>> Statisticus / Statistician
>>> >>>
>>> >>> Vlaamse Overheid / Government of Flanders
>>> >>> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR
>>> NATURE
>>> >>> AND FOREST
>>> >>> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
>>> >>> thierry.onkelinx using inbo.be
>>> >>> Havenlaan 88 bus 73, 1000 Brussel
>>> >>> www.inbo.be
>>> >>>
>>> >>>
>>> >>>
>>> ///////////////////////////////////////////////////////////////////////////////////////////
>>> >>> 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
>>> >>>
>>> >>>
>>> ///////////////////////////////////////////////////////////////////////////////////////////
>>> >>>
>>> >>> <https://www.inbo.be>
>>> >>>
>>> >>>
>>> >>> Op vr 7 okt. 2022 om 23:36 schreef Shira Mitchell <
>>> shiraqotj using gmail.com>:
>>> >>>
>>> >>>> Thanks so much, Thierry ! This is great.
>>> >>>>
>>> >>>> This works except that I cannot subtract because:
>>> >>>> f(home, model = "iid")) - f(away, copy = "home")
>>> >>>>
>>> >>>> just drops the second term. Apologies that I'm not super familiar
>>> with
>>> >>>> INLA syntax yet.
>>> >>>>
>>> >>>>
>>> >>>>
>>> >>>> On Fri, Oct 7, 2022 at 10:19 AM Thierry Onkelinx <
>>> >>>> thierry.onkelinx using inbo.be> wrote:
>>> >>>>
>>> >>>>> Hi Shira,
>>> >>>>>
>>> >>>>> I fit such models with the INLA package (https://www.r-inla.org/).
>>> The
>>> >>>>> trick is to define two random effects but force their parameter
>>> estimates
>>> >>>>> to be identical.
>>> >>>>>
>>> >>>>> The code would contain something like f(home, model = "iid")) +
>>> f(away,
>>> >>>>> copy = "home"). Meaning home ~ N(0, sigma_beta_i) and home[i] =
>>> away[i]
>>> >>>>>
>>> >>>>> Best regards,
>>> >>>>>
>>> >>>>> ir. Thierry Onkelinx
>>> >>>>> Statisticus / Statistician
>>> >>>>>
>>> >>>>> Vlaamse Overheid / Government of Flanders
>>> >>>>> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR
>>> NATURE
>>> >>>>> AND FOREST
>>> >>>>> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality
>>> Assurance
>>> >>>>> thierry.onkelinx using inbo.be
>>> >>>>> Havenlaan 88 bus 73, 1000 Brussel
>>> >>>>> www.inbo.be
>>> >>>>>
>>> >>>>>
>>> >>>>>
>>> ///////////////////////////////////////////////////////////////////////////////////////////
>>> >>>>> 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
>>> >>>>>
>>> >>>>>
>>> ///////////////////////////////////////////////////////////////////////////////////////////
>>> >>>>>
>>> >>>>> <https://www.inbo.be>
>>> >>>>>
>>> >>>>>
>>> >>>>> Op vr 7 okt. 2022 om 15:00 schreef Shira Mitchell <
>>> shiraqotj using gmail.com
>>> >>>>>> :
>>> >>>>>
>>> >>>>>> We want to fit Bradley-Terry-style GLMM models in R. We looked
>>> into:
>>> >>>>>>
>>> >>>>>>
>>> >>>>>>
>>> https://cran.r-project.org/web/packages/BradleyTerry2/vignettes/BradleyTerry.pdf
>>> >>>>>> and
>>> >>>>>> http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html
>>> >>>>>>
>>> >>>>>> We have voter-specific variables x that influence which political
>>> >>>>>> message
>>> >>>>>> (i vs j) wins for them:
>>> >>>>>>
>>> >>>>>> logit[pr(i beats j | person with covariate x)] = lambda_i -
>>> lambda_j +
>>> >>>>>> (beta_i - beta_j) x
>>> >>>>>>
>>> >>>>>> We then model parameters as random effects:
>>> >>>>>> lambda_i ~ N(0, sigma_lambda)
>>> >>>>>> beta_i ~ N(0, sigma_beta)
>>> >>>>>>
>>> >>>>>> Is there a way to do this in R ? We do this in TensorFlow in
>>> Python by
>>> >>>>>> directly specifying design matrices with the 0,-1,1 or 0,-x,x
>>> entries.
>>> >>>>>> However, I do not see how to do this in R using lme4,
>>> BradleyTerry2,
>>> >>>>>> mgcv,
>>> >>>>>> etc.
>>> >>>>>>
>>> >>>>>> Thanks so much,
>>> >>>>>> Shira
>>> >>>>>>
>>> >>>>>> [[alternative HTML version deleted]]
>>> >>>>>>
>>> >>>>>> _______________________________________________
>>> >>>>>> R-sig-mixed-models using r-project.org mailing list
>>> >>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>> >>>>>>
>>> >>>>>
>>> >
>>> > [[alternative HTML version deleted]]
>>> >
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>>
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