HBglm: Hierarchical Bayesian Regression for GLMs

In HBglm: Hierarchical Bayesian Regression for GLMs

Description

Convenient and efficient functions for performing 2-level HB regressions analysis for multi-group data. The lowest level may belong to the GLM family while the prior level, which effects pooling, allows for linear regression on lower level covariates. Constraints on all or part of the parameter set maybe specified with ease. A rich set of methods is included to visualize and analyze results.

Usage

hbglm(formula, data, formula.fixed = NULL,
      family = "gaussian", 
      sampler.control = hbglm.sampler.control(),
      model.control = hbglm.model.control(),
      ncores = 1, print.level = 0, ...)
hbglm.sampler.control(num.samples = -1, samp.factor = 50, 
    sampler = c("slice"))
hbglm.model.control(constraints = NULL, 
    initializer = c("user", "regression"), user.init.val = NULL)
## S3 method for class 'hbglm'
print(x, digits = max(3, getOption("digits") -2),
                         width = getOption("width"), nburnin = 0, ...)
## S3 method for class 'hbglm'
predict(object, newdata = NULL, grpID.col = NULL,
                   type = c("link", "response", "ppp.mean", "ppp.dist"),
                   nburnin = 0, times = 0, print.level = 0, ...)
## S3 method for class 'hbglm'
coef(object, nburnin = 0, ...)
## S3 method for class 'hbglm'
summary(object, nburnin = 0, ...)
## S3 method for class 'hbglm'
print.summary(x, digits = max(3, getOption("digits") -2),
                                  width = getOption("width"), ...)

Arguments

formula	formula object or string specifying the model to be estimated (see Note).
data	A data.frame object with data organized in the 'long' format or as a list of lists (see Note).
formula.fixed	formula specifying the fixed effects included in the model.
family	Name of a GLM family member. Currently allowed "gaussian", "binomial", "poisson" with standard link functions.
sampler.control	List to control MCMC sampling.
model.control	List to specify initial values, constraints.
ncores	Number of cores to run on. Currently fixed at 1.
print.level	Positive integer to print stuff while running.
num.samples	Number of MCMC samples to draw. Default '-1' will cause internal default values to kick-in.
samp.factor	Used in setting internal default for number of MCMC samples to draw. Must be a positive integer
sampler	Name of MCMC sampler to use. Currently fixed at the slice sampler.
constraints	User specified constraints.
initializer	How to obtain initial values.
user.init.val	User specified initial values.
x, object	A hbglm class object.
width	Printing control options.
nburnin	Number of burn-in samples. These samples, starting fromt the initial, are discarded from print, summary and predict.
digits	Printing control options.
newdata	Same format as data argument. Used in predction.
grpID.col	Name of column in data which has group information for each observation.
type	Used in predict. 'link' and 'response' are non-Bayesian predictions and return the avg response on the linear predictor and the response scale, respectively. They are computed by using model coefficients obtained by averaging MCMC samples. 'ppp.mean' return the distribution of means of the response posterior predcitive probability (PPP) distribution. 'ppp.dist' returns samples drawn from the full response PPP distribution.
times	Used in predict when type = 'ppp.dist' to specify number of samples desired from the response PPP distribution. When 0, a default internal value is used.
...	Currently unused.

Value

An object of class hbglm, with elements:

formula	the model formula object
formula.fixed	the fixed effects formula object
nsamples	the number of samples drawn
model.control	list of model control args
sampler.control	list of sampler control args
grpID.col	Data column with grp ID information
call	the hbglm function call that user made,
model	List with number of parameters and model matrices
family	List with functions such as loglikelihood and inverse link for the GLM family.
samples	A list with the MCMC samples drawn; organized by coeff type.

Note

1. The data must be in the 'long' or the 'list' format. In 'list' format there must bebe 2 keys 'lower' and 'upper' specifying two data.frames for the lower and upper level models respectively. Lower level contains data related to the fixed and random effects, while upper level contains data about the groups. In 'long' the 'upper' and 'lower' level data must be consolidated in a single data.frame (the upper level data will have to suitably replicated).

2. The 'formula' argument should be specified in the format: responseVar ~ choice specific variables with generic coefficients | individual specific variables | choice specific variables with choice specific coefficients. These are the 3 available variable types.

3. Random effects are mandatory in the formula.

Author(s)

Asad Hasan, Alireza S. Mahani

Examples

  library(HBglm)
  data("linear_list", package = "HBglm")
  fm <- formula(y ~ x1 + x2 + x3 - 1 | z1 + z2 + z3 - 1 | grpID)
  fm.fixed <- formula(y ~ f1 + f2)
  samp.control = hbglm.sampler.control(num.samples = 20)
  ## Not run: 
    fit <- hbglm(fm, linear_list, formula.fixed = fm.fixed, family="gaussian",
                sampler.control = samp.control, print.level=0)
    print(fit)
  
## End(Not run)

Example output

2-level Hierarchical Bayesian Regression model estimation ..

Mean coeffcient values are:
beta (random eff)
          x1         x2           x3
1 -0.0850907 -2.2585852 -2.246644235
2 -2.3549977  0.4231252  0.957216184
3 -0.1826344 -0.1170798 -0.009816962
4  0.9008816  2.3149467  0.887721489
5  0.4262071 -1.5951313 -3.706811638

alpha (fixed eff)
(Intercept)          f1          f2 
  0.2638125   0.1414105  -0.4017317 

tau
       1        2        3        4        5 
1.077133 0.974024 1.216256 1.185883 1.974440 

theta (prior coeff)
           x1         x2        x3
z1 -2.1535432  1.2341807  1.336635
z2  1.5056469  1.8298105  2.262980
z3 -0.8605801 -0.4958652 -1.918863

Sigma (prior Covariance)
           x1        x2         x3
x1  1.3069760 0.4500396 -0.1537707
x2  0.4500396 1.5510669  0.0930031
x3 -0.1537707 0.0930031  0.9391468

HBglm documentation built on May 2, 2019, 1:28 a.m.