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Bayesian Generalized Linear models Using iid sampling procedures

R 66.55% C++ 33.45%

glmbayes's Introduction

glmbayes

The glmbayes package produces iid samples for Bayesian Genereralized Linear Models and is intended as a Bayesian version of the glm function for classical models.

Details

Estimation can be performed using three main functions. For models with fixed dispersion parameters, the rglmb function is the workhorse function and comes with a minimialistic interface for the input and output. It is also suitable for use as part of block Gibbs sampling procedures. The glmb function is essentially a wrapper function for the rglmb function that provides an interface closer to that of the glm function. The rglmbdisp function can be leveraged in order to produce samples for the dispersion parameters associated with the gaussian and Gamma link functions. Most methods defined for the output of the glm function are also defined for the glmb, rglmb and rglmbdisp functions (see their respective documentation for details).

For the regression parameters, multivariate normal priors are assumed. Simulation for the gaussian family with the identify link function is performed using standard procedures for multivariate normal densities. For all other families and link functions, simulation is performed using the likelihood subgradient approach of Nygren and Nygren (2006). This approach involves the construction of an enveloping function for the full posterior density followed by accept-reject sampling. For models that are approximately multivariate normal, the expected number of draws required per acceptance are bounded from above as noted in Nygren and Nygren (2006).

Currently implemented models include the gaussian (identity link), poisson/quasipoisson (log link), binomial/quasibinomial (logit, probit, and cloglog links), and Gamma (log link) families. These models all have log-concave likelihood functions that allow us to leverage the likelihood-subgradient approach for the iid sampling. Models that fail to have log-concave likelihood functions are not implemented. Our demos (viewable by entering the demo() command) provides examples of each of these families and links.

The current implementation requires separate use of the rglmbdisp function in order to generate samples for dispersion parameters (gaussian, Gammma, quasipoisson, quasibinomaial families). Our demos include examples of the joint use of the rglmb and rglmbdisp to produce samples for both regression and dispersion parameters using two-block Gibbs samplers. As these two-block Gibbs samplers likely are geometrically ergodic, future implementations may incorporate these two-block Gibbs samplers into the rglmb and glmb functions by leveraging theoretical bounds om convergence rates derived using Rosenthal (1996) type drift and minorization conditions.

The rglmb function can also be used in Block-Gibbs sampling implementations for Hierarchical Bayesian models. The demos associated with this package contains examples of such models.

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glmbayes's Issues

Try implementing joint density Likelihood sub-gradient approach for the posterior when beta and dispersion have independent priors

Add example for glmbsim_cpp

This currently has no example. Can be essentially same a glmbenvelope_c example.

Add seed option for simulate and most other random generator function so that consistent output can be achieved more easily

Improve optimization inside simulation function for gamma dispersion parameter

The gamma.shape and gamma.dispersion parameters are similar to this on the classical side. Should see if source code is available for gamma.shape (or if references are available in their book) to see how they implemented the optimization. Could add an optimization step and pull out much of simulation for this in gamma case into its own function.

Add warning if number of candidates per draw exceeds the theoretical number by a statistically significant margin

Clean up the .R and .cpp functions

Validate/update/Create/Properly Document generic accessor functions for class "rglmb"

Not clear that generic accessor functions referenced in current documentation exists. As needed, create accessor functions. If they can't be created, remove from documentation for relevant functions.

Add number of candidates per iid draw to printed output for rglmb (and some other) functions.

Make "value" output from rglmb function more consistent with glmb, glm, and lm functions to facilitate use of inherited methods

Update printing in several print and summary functions to use scientific notation (possibly using the formatC(numb, format = "e", digits = 4) ) function

This seems to similar to how glm summary and print functions format the output.

Add R function interface with input/error checks for some of C++ functions

Some of the C++ functions can be problematic when called directly from R without checks that the type of the inputs are correct or checks that the values are consistent and/or valid. Adding an R interface for the functions would avoid potential issues.

Add wrapper functions for f1, f2, and f3 functions

Direct users towards these "safe" wrapper functions and create a single *.Rd file to handle all the various files. Look into possibility of avoiding the need to export all the various functions from C++ (which should remove them from the manual index).

Verify that weights are being applied correctly for simulate.glmb function

Add ability to not use Progressbar for glmb and rglmb functions

When running examples using R CMD check, examples with larger dimensions exhibit weird printing behavior because of the Progressbar (not observed in interactive mode). Would be good to be able to avoid progressbar for such examples. For now, kept examples at lower dimensions

Add print function for Prior_Likelihood_function to display key information and remove warnings.

Place any code related to random effects models in separate lmeb (or possibly nlmeb) package.

Add documentation for menarche data (from MASS package)

Added as data in current package to avoid examples having to link to MASS package. Should still give credit to source of data

Replace call to rwishart within rnorm_gamma_reg with call to rgamma and remove dependence on rwishart from package

Write Vignette to Document Simulation Procedure for rIndependent_Normal_Gamma_reg

Add dispersion to printed outputs (print and print.summary)

Add option for not computing LL in post processing inside glmbsim_NGauss and other related functions.

.When running Gibbs sampling, this computation may simply slow simulation process down.

Create function lmb and corresponding class to mirror lm

The normal-gamma regression should be able to mimic most of the feature of the lm function. This may take substantial amount of work to implement (although estimation of basic model is simple). Can also consider adding optional arguments to run with alternative prior specification over time. One of papers has implementation of iid sampling for alternate specification that works well when the prior is strong but not when prior is weak. Not sure if two-block Gibbs sampler is convergent with tight bound.

Determine if glmbsim_NGauss2 is useful as distinct function from glmbsim_NGauss.

Not clear if this function is useful or not. Need to compare differences and possibly remove or document where it has other uses.

Add example for glmbsim_NGauss

This function currently has no examples. Called from Rglmb.R

Add functions mirroring sigma S3 function for lm and gamma.shape function for object from glm

These are functions that extract and/or estimate the sigma (square root of dispersion) outputs. The rglmb_dispersion function currently serves a similar purpose

Find ways of Registering *.default functions in Namespace.

Only current (6/4/2020) Note when running. R CMD check. All other class related functions are currently registering properly.

Update random number generators not use automatic and not reset rng

Create function to handle model standardization and replace calculations inside glmbsim_NGauss

Calculations insider glmbsim_NGauss are fairly extensive and clutter up the function (make it too long). Moreover, the Rcpp function for calculating eigenvalues/eigenvectors orders the values differently than R so it is hard to replicate some calculation steps outside C++ without exporting the eigenvalue function (which seems un-necessary).

Update Titles in *.Rd files

Review/update titles in *.Rd files to ensure the capture the essence of each file

Add example for glmbsim_gauss and update documentation more generally.

The current example is not for glmbsim_gauss. Documentation is also iffy as it is more tied to glmbsim_ngauss and too light.

Create functions for computing Hessians for log-posterior function and use inside glmbsim_NGauss_cpp

The Hessian currently used is one estimated by the optim function. Simulation Results with current approximation are probably still correct, but the Hessian may fail to be positive definite even in cases when it is supposed to be and may somewhat hurt performance of simulation.