Bivariate Logistic Distribution
Posted: Thu Dec 14, 2023 2:46 pm
Hello,
I am attempting to model two binary responses that represent two agents' decisions on the same task. Decisions are nested within agents which are nested within centres, are influenced by several covariates, and the marginal probabilities of the two decisions are identical except for when the second agent can see the first's response. Agents only ever act within a single centre.
1) Can R2MLwiN model bivariate logistic responses? I have attempted to use c(logit(decision1,cons),logit(decision2,cons)) ~ ... with family = c("Binomial","Binomial") but have received the "invalid link function" error. I have got around this so far by joining the two response columns to make a general 'decision' column and using the 'other' decision as a categorical covariate, effectively modelling the two marginals and the odds ratio between them as described in the beginning of this article https://docs.zeligproject.org/articles/ ... logit.html. However I'm concerned that the variance will be artificially shrunk by doing this.
2) If, in some centres/in the case of disagreements, a third agent was then to use decision1, decision2 and all the other information available to make a final decision for each task, how could this be modelled? Is it possible to also model a third binary response variable?
3) How would it be possible to gain information about an agent's "rate", and how it influences the final decision? Is this inference limited to odds ratios, or can non-multiplicative relationships between the responses be modelled?
4) I am aware that one of the key assumptions of multilevel models is that the predictors are not correlated with the random effects. A popular method to treat this assumption being violated is introducing cluster-means of the predictors in question. Is this necessary when using Monte-Carlo sampling, and if so does it change how the orthogonal fixed effects (orth = 1) argument is used?
For reference, my current call resembles:
model = runMLwiN(logit(decision,cons) ~ 1 + OtherDecisionIndicator + isAgent2Indicator + (1 | Centre) + (1 | AgentID),D = "Binomial",estoptions = list(EstM = 1,xc=FALSE,mcmcOptions = list(orth = 1)), data=decisions)
All variables in the model listed are categorical. Thank you very much for your help and excellent software.
I am attempting to model two binary responses that represent two agents' decisions on the same task. Decisions are nested within agents which are nested within centres, are influenced by several covariates, and the marginal probabilities of the two decisions are identical except for when the second agent can see the first's response. Agents only ever act within a single centre.
1) Can R2MLwiN model bivariate logistic responses? I have attempted to use c(logit(decision1,cons),logit(decision2,cons)) ~ ... with family = c("Binomial","Binomial") but have received the "invalid link function" error. I have got around this so far by joining the two response columns to make a general 'decision' column and using the 'other' decision as a categorical covariate, effectively modelling the two marginals and the odds ratio between them as described in the beginning of this article https://docs.zeligproject.org/articles/ ... logit.html. However I'm concerned that the variance will be artificially shrunk by doing this.
2) If, in some centres/in the case of disagreements, a third agent was then to use decision1, decision2 and all the other information available to make a final decision for each task, how could this be modelled? Is it possible to also model a third binary response variable?
3) How would it be possible to gain information about an agent's "rate", and how it influences the final decision? Is this inference limited to odds ratios, or can non-multiplicative relationships between the responses be modelled?
4) I am aware that one of the key assumptions of multilevel models is that the predictors are not correlated with the random effects. A popular method to treat this assumption being violated is introducing cluster-means of the predictors in question. Is this necessary when using Monte-Carlo sampling, and if so does it change how the orthogonal fixed effects (orth = 1) argument is used?
For reference, my current call resembles:
model = runMLwiN(logit(decision,cons) ~ 1 + OtherDecisionIndicator + isAgent2Indicator + (1 | Centre) + (1 | AgentID),D = "Binomial",estoptions = list(EstM = 1,xc=FALSE,mcmcOptions = list(orth = 1)), data=decisions)
All variables in the model listed are categorical. Thank you very much for your help and excellent software.