[R-sig-ME] Bradley Terry GLMM in R ?

Shira Mitchell @h|r@qotj @end|ng |rom gm@||@com
Mon Oct 17 22:02:10 CEST 2022 

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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