Some computational and modeling issues for hierarchical models Andrew Gelman Dept of Statistics and Dept of Political Science, Columbia University, New York (Visiting Sciences Po, Paris, for 2009–2010) 17 Oct 2009 1/13 Andrew Gelman Some computational and modeling issues for hierarchical models
6 challenges in statistical modeling 2/13 Andrew Gelman Some computational and modeling issues for hierarchical models
6 challenges in statistical modeling ◮ Setting up a realistic (i.e., complicated) model 2/13 Andrew Gelman Some computational and modeling issues for hierarchical models
6 challenges in statistical modeling ◮ Setting up a realistic (i.e., complicated) model ◮ Regularization or partial pooling 2/13 Andrew Gelman Some computational and modeling issues for hierarchical models
6 challenges in statistical modeling ◮ Setting up a realistic (i.e., complicated) model ◮ Regularization or partial pooling ◮ Fitting the model 2/13 Andrew Gelman Some computational and modeling issues for hierarchical models
6 challenges in statistical modeling ◮ Setting up a realistic (i.e., complicated) model ◮ Regularization or partial pooling ◮ Fitting the model ◮ Checking the fit to data 2/13 Andrew Gelman Some computational and modeling issues for hierarchical models
6 challenges in statistical modeling ◮ Setting up a realistic (i.e., complicated) model ◮ Regularization or partial pooling ◮ Fitting the model ◮ Checking the fit to data ◮ Confidence building 2/13 Andrew Gelman Some computational and modeling issues for hierarchical models
6 challenges in statistical modeling ◮ Setting up a realistic (i.e., complicated) model ◮ Regularization or partial pooling ◮ Fitting the model ◮ Checking the fit to data ◮ Confidence building ◮ Understanding the fitted model 2/13 Andrew Gelman Some computational and modeling issues for hierarchical models
The models I’m fitting ◮ Hierarchical generalized linear models 3/13 Andrew Gelman Some computational and modeling issues for hierarchical models
The models I’m fitting ◮ Hierarchical generalized linear models ◮ y i = α + β x i + ǫ i 3/13 Andrew Gelman Some computational and modeling issues for hierarchical models
The models I’m fitting ◮ Hierarchical generalized linear models ◮ y i = α + β x i + ǫ i ◮ y i = α j [ i ] + β j [ i ] x i + ǫ i (separate regression in each group) 3/13 Andrew Gelman Some computational and modeling issues for hierarchical models
The models I’m fitting ◮ Hierarchical generalized linear models ◮ y i = α + β x i + ǫ i ◮ y i = α j [ i ] + β j [ i ] x i + ǫ i (separate regression in each group) σ 2 � α j � �� µ α � � �� ρσ α σ β α ∼ N , for j = 1 , . . . , J , ◮ σ 2 ρσ α σ β β j µ β β 3/13 Andrew Gelman Some computational and modeling issues for hierarchical models
The models I’m fitting ◮ Hierarchical generalized linear models ◮ y i = α + β x i + ǫ i ◮ y i = α j [ i ] + β j [ i ] x i + ǫ i (separate regression in each group) σ 2 � α j � �� µ α � � �� ρσ α σ β α ∼ N , for j = 1 , . . . , J , ◮ σ 2 ρσ α σ β β j µ β β ◮ Also can have group-level predictors and nonnested grouping factors 3/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Application: public opinion in population subgroups 4/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Software options 5/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Software options ◮ R, Matlab, etc. (data processing and graphics, general computing) 5/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Software options ◮ R, Matlab, etc. (data processing and graphics, general computing) ◮ C, Fortran, Python, etc. (fast computation) 5/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Software options ◮ R, Matlab, etc. (data processing and graphics, general computing) ◮ C, Fortran, Python, etc. (fast computation) ◮ Bugs etc. 5/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Software options ◮ R, Matlab, etc. (data processing and graphics, general computing) ◮ C, Fortran, Python, etc. (fast computation) ◮ Bugs etc. ◮ Specialized multilevel modeling software (e.g., lmer in R) 5/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Software options ◮ R, Matlab, etc. (data processing and graphics, general computing) ◮ C, Fortran, Python, etc. (fast computation) ◮ Bugs etc. ◮ Specialized multilevel modeling software (e.g., lmer in R) ◮ What’s missing? 5/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Software options ◮ R, Matlab, etc. (data processing and graphics, general computing) ◮ C, Fortran, Python, etc. (fast computation) ◮ Bugs etc. ◮ Specialized multilevel modeling software (e.g., lmer in R) ◮ What’s missing? 5/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Software options ◮ R, Matlab, etc. (data processing and graphics, general computing) ◮ C, Fortran, Python, etc. (fast computation) ◮ Bugs etc. ◮ Specialized multilevel modeling software (e.g., lmer in R) ◮ What’s missing? 5/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Software options ◮ R, Matlab, etc. (data processing and graphics, general computing) ◮ C, Fortran, Python, etc. (fast computation) ◮ Bugs etc. ◮ Specialized multilevel modeling software (e.g., lmer in R) ◮ What’s missing? 5/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Software options ◮ R, Matlab, etc. (data processing and graphics, general computing) ◮ C, Fortran, Python, etc. (fast computation) ◮ Bugs etc. ◮ Specialized multilevel modeling software (e.g., lmer in R) ◮ What’s missing? ◮ Something in between “automatic” and “program it yourself” 5/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Some issues with Bugs, OpenBugs, Jags, etc. 6/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Some issues with Bugs, OpenBugs, Jags, etc. ◮ Difficult to keep track of multiple versions of a model 6/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Some issues with Bugs, OpenBugs, Jags, etc. ◮ Difficult to keep track of multiple versions of a model ◮ Solution: allow unused parameters and data 6/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Some issues with Bugs, OpenBugs, Jags, etc. ◮ Difficult to keep track of multiple versions of a model ◮ Solution: allow unused parameters and data ◮ Code gets long and ugly 6/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Some issues with Bugs, OpenBugs, Jags, etc. ◮ Difficult to keep track of multiple versions of a model ◮ Solution: allow unused parameters and data ◮ Code gets long and ugly ◮ Solution: allow subroutines and macros 6/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Some issues with Bugs, OpenBugs, Jags, etc. ◮ Difficult to keep track of multiple versions of a model ◮ Solution: allow unused parameters and data ◮ Code gets long and ugly ◮ Solution: allow subroutines and macros ◮ How long to run the program? 6/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Some issues with Bugs, OpenBugs, Jags, etc. ◮ Difficult to keep track of multiple versions of a model ◮ Solution: allow unused parameters and data ◮ Code gets long and ugly ◮ Solution: allow subroutines and macros ◮ How long to run the program? ◮ Solution: automatic convergence check 6/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Some issues with Bugs, OpenBugs, Jags, etc. ◮ Difficult to keep track of multiple versions of a model ◮ Solution: allow unused parameters and data ◮ Code gets long and ugly ◮ Solution: allow subroutines and macros ◮ How long to run the program? ◮ Solution: automatic convergence check ◮ Lack of confidence in results. (“My model converged. Now what?”) 6/13 Andrew Gelman Some computational and modeling issues for hierarchical models
Some issues with Bugs, OpenBugs, Jags, etc. ◮ Difficult to keep track of multiple versions of a model ◮ Solution: allow unused parameters and data ◮ Code gets long and ugly ◮ Solution: allow subroutines and macros ◮ How long to run the program? ◮ Solution: automatic convergence check ◮ Lack of confidence in results. (“My model converged. Now what?”) ◮ Solution: automatic fake-data debugging 6/13 Andrew Gelman Some computational and modeling issues for hierarchical models
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