glm.fixed.a0: Model fitting for generalized linear models with fixed a0

Description Usage Arguments Details Value References See Also Examples

View source: R/main_func.R

Description

Model fitting using power priors for generalized linear models with fixed a_0

Usage

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glm.fixed.a0(
  data.type,
  data.link,
  y = 0,
  n = 1,
  x = matrix(),
  historical = list(),
  lower.limits = rep(-100, 50),
  upper.limits = rep(100, 50),
  slice.widths = rep(1, 50),
  nMC = 10000,
  nBI = 250,
  current.data = TRUE
)

Arguments

data.type

Character string specifying the type of response. The options are "Normal", "Bernoulli", "Binomial", "Poisson" and "Exponential".

data.link

Character string specifying the link function. The options are "Logistic", "Probit", "Log", "Identity-Positive", "Identity-Probability" and "Complementary Log-Log". Does not apply if data.type is "Normal".

y

Vector of responses.

n

(For binomial data only) vector of integers specifying the number of subjects who have a particular value of the covariate vector. If the data is binary and all covariates are discrete, collapsing Bernoulli data into a binomial structure can make the slice sampler much faster.

x

Matrix of covariates. The first column should be the treatment indicator with 1 indicating treatment group. The number of rows should equal the length of the response vector y.

historical

(Optional) list of historical dataset(s). East historical dataset is stored in a list which contains three named elements: y0, x0 and a0.

  • y0 is a vector of responses.

  • x0 is a matrix of covariates. x0 should NOT have the treatment indicator. Apart from missing the treatent/control indicator, x0 should have the same set of covariates in the same order as x.

  • a0 is a number between 0 and 1 indicating the discounting parameter value for that historical dataset.

For binomial data, an additional element n0 is required.

  • n0 is vector of integers specifying the number of subjects who have a particular value of the covariate vector.

lower.limits

Vector of lower limits for parameters to be used by the slice sampler. The length of the vector should be equal to the total number of parameters, i.e. P+1 where P is the number of covariates. The default is -100 for all parameters (may not be appropriate for all situations). Does not apply if data.type is "Normal".

upper.limits

Vector of upper limits for parameters to be used by the slice sampler. The length of the vector should be equal to the total number of parameters, i.e. P+1 where P is the number of covariates. The default is 100 for all parameters (may not be appropriate for all situations). Does not apply if data.type is "Normal".

slice.widths

Vector of initial slice widths for parameters to be used by the slice sampler. The length of the vector should be equal to the total number of parameters, i.e. P+1 where P is the number of covariates. The default is 1 for all parameter (may not be appropriate for all situations). Does not apply if data.type is "Normal".

nMC

Number of iterations (excluding burn-in samples) for the slice sampler or Gibbs sampler. The default is 10,000.

nBI

Number of burn-in samples for the slice sampler or Gibbs sampler. The default is 250.

current.data

Logical value indicating whether current data is included. The default is TRUE. If FALSE, only historical data is included in the analysis, and the posterior samples can be used as discrete approximation to the sampling prior in

power.glm.fixed.a0.

Details

If data.type is "Normal", the response y_i is assumed to follow N(x_i'β, τ^{-1}) where x_i is the vector of covariates for subject i. Each historical dataset D_{0k} is assumed to have a different precision parameter τ_k. The initial prior for τ is the Jeffery's prior, τ^{-1}, and the initial prior for τ_k is τ_k^{-1}. The initial prior for β is the uniform improper prior. Posterior samples are obtained through Gibbs sampling.

For all other data types, posterior samples are obtained through slice sampling. The initial prior for β is the uniform improper prior. The default lower limits for the parameters are -100. The default upper limits for the parameters are 100. The default slice widths for the parameters are 1. The defaults may not be appropriate for all situations, and the user can specify the appropriate limits and slice width for each parameter.

Value

If data.type is "Normal", posterior samples of β, τ and τ_k's (if historical data is given) are returned. For all other data types, a matrix of posterior samples of β is returned. The first column contains posterior samples of the intercept. The second column contains posterior samples of β_1, the parameter for the treatment indicator.

References

Neal, Radford M. Slice sampling. Ann. Statist. 31 (2003), no. 3, 705–767.

See Also

power.glm.fixed.a0

Examples

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data.type <- "Bernoulli"
data.link <- "Logistic"

# Simulate current data
set.seed(1)
p <- 3
n_total <- 100
y <- rbinom(n_total,size=1,prob=0.6)
# The first column of x is the treatment indicator.
x <- cbind(rbinom(n_total,size=1,prob=0.5),
           matrix(rnorm(p*n_total),ncol=p,nrow=n_total))

# Simulate two historical datasets
# Note that x0 does not have the treatment indicator
historical <- list(list(y0=rbinom(n_total,size=1,prob=0.2),
                        x0=matrix(rnorm(p*n_total),ncol=p,nrow=n_total), a0=0.2),
                   list(y0=rbinom(n_total, size=1, prob=0.5),
                        x0=matrix(rnorm(p*n_total),ncol=p,nrow=n_total), a0=0.3))

# Set parameters of the slice sampler
lower.limits <- rep(-100, 5) # The dimension is the number of columns of x plus 1 (intercept)
upper.limits <- rep(100, 5)
slice.widths <- rep(1, 5)

nMC <- 1000 # nMC should be larger in practice
nBI <- 250
result <- glm.fixed.a0(data.type=data.type, data.link=data.link, y=y, x=x, historical=historical,
                       lower.limits=lower.limits, upper.limits=upper.limits,
                       slice.widths=slice.widths, nMC=nMC, nBI=nBI)

colMeans(result) # posterior mean of beta

BayesPPD documentation built on Sept. 8, 2021, 5:06 p.m.