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

Jarrod Hadfield j@h@d||e|d @end|ng |rom ed@@c@uk
Mon Oct 17 10:45:27 CEST 2022 

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:
>
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>
> 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
>>>>>>
>>>>>
>
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