MRS (version 1.3.2)

andova: Multi Resolution Scanning for one-way ANDOVA using the multi-scale Beta-Binomial model

Description

This function executes the Multi Resolution Scanning algorithm to detect differences across the distributions of multiple groups having multiple replicates.

Usage

andova(
  X,
  G,
  H,
  n_groups = length(unique(G)),
  n_subgroups = NULL,
  Omega = "default",
  K = 6,
  init_state = c(0.8, 0.2, 0),
  beta = 1,
  gamma = 0.07,
  delta = 0.4,
  eta = 0,
  alpha = 0.5,
  nu_vec = 10^(seq(-1, 4)),
  return_global_null = TRUE,
  return_tree = TRUE,
  n_post_samples = 0,
  baseline = 0,
  method = "newton",
  n_grid_theta = 4
)

Value

An mrs object.

Arguments

X

Matrix of the data. Each row represents an observation.

G

Numeric vector of the group label of each observation. Labels are integers starting from 1.

H

Numeric vector of the replicate label of each observation. Labels are integers starting from 1.

n_groups

Number of groups.

n_subgroups

Vector indicating the number of replicates for each group.

Omega

Matrix defining the vertices of the sample space. The "default" option defines a hyperrectangle containing all the data points. Otherwise the user can define a matrix where each row represents a dimension, and the two columns contain the associated lower and upper limit.

K

Depth of the tree. Default is K = 6, while the maximum is K = 14.

init_state

Initial state of the hidden Markov process. The three states are null, alternative and prune, respectively.

beta

Spatial clustering parameter of the transition probability matrix. Default is beta = 1.0.

gamma

Parameter of the transition probability matrix. Default is gamma = 0.07.

delta

Parameter of the transition probability matrix. Default is delta = 0.4.

eta

Parameter of the transition probability matrix. Default is eta = 0.0.

alpha

Pseudo-counts of the Beta random probability assignments.

nu_vec

The support of the discrete uniform prior on nu.

return_global_null

Boolean indicating whether to return the marginal posterior probability of the global null.

return_tree

Boolean indicating whether to return the posterior representative tree.

n_post_samples

Number of posterior trees to sample. Default is zero.

baseline

Group used as the baseline for effect sizes. A value of zero uses the pooled mean as the baseline.

method

Numerical integration method, either "newton" or "riemann".

n_grid_theta

Number of grid points used by the numerical integration. The default of four uses the same midpoint quadrature rule as version 1.2.6.

References

Ma L. and Soriano J. (2018). Analysis of distributional variation through multi-scale Beta-Binomial modeling. Journal of Computational and Graphical Statistics, 27(3), 529--541. tools:::Rd_expr_doi("10.1080/10618600.2017.1402774")

Examples

set.seed(12345)
n = 1000
M = 5
class_1 = sample(M, n, prob= 1:5, replace=TRUE  )
class_2 = sample(M, n, prob = 5:1, replace=TRUE )

Y_1 = rnorm(n, mean=class_1, sd = .2)
Y_2 = rnorm(n, mean=class_2, sd = .2)

X = matrix( c(Y_1, Y_2), ncol = 1)
G = c(rep(1,n),rep(2,n))
H = sample(3,2*n, replace = TRUE  )

ans = andova(X, G, H)
ans$PostGlobNull
plot1D(ans)