Package 'MRS' reference manual

Package 'MRS'

Title:	Multi-Resolution Scanning for Cross-Sample Differences
Description:	An implementation of the MRS algorithm for comparison across distributions, as described in Jacopo Soriano, Li Ma (2017) <doi:10.1111/rssb.12180>. The model is based on a nonparametric process taking the form of a Markov model that transitions between a "null" and an "alternative" state on a multi-resolution partition tree of the sample space. MRS effectively detects and characterizes a variety of underlying differences. These differences can be visualized using several plotting functions.
Authors:	Jacopo Soriano and Li Ma
Maintainer:	Li Ma <[email protected]>
License:	GPL (>= 3)
Version:	1.2.6
Built:	2024-09-07 03:19:07 UTC
Source:	https://github.com/cran/MRS

Title:

Multi-Resolution Scanning for Cross-Sample Differences

Description:

An implementation of the MRS algorithm for comparison across distributions, as described in Jacopo Soriano, Li Ma (2017) <doi:10.1111/rssb.12180>. The model is based on a nonparametric process taking the form of a Markov model that transitions between a "null" and an "alternative" state on a multi-resolution partition tree of the sample space. MRS effectively detects and characterizes a variety of underlying differences. These differences can be visualized using several plotting functions.

Authors:

Jacopo Soriano and Li Ma

Maintainer:

Li Ma <[email protected]>

License:

GPL (>= 3)

Version:

1.2.6

Built:

2024-09-07 03:19:07 UTC

Source:

https://github.com/cran/MRS

Help Index

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)
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)

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 grop.
`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, altenrative 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.

Value

An mrs object.

References

Ma L. and Soriano J. (2018). Analysis of distributional variation through multi-scale Beta-Binomial modeling. Journal of Computational and Graphical Statistics. Vol. 27, No. 3, 529-541.. doi:10.1080/10618600.2017.1402774

Examples

set.seed(1)
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)
set.seed(1)
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)

Multi Resolution Scanning

Description

This function executes the Multi Resolution Scanning algorithm to detect differences across multiple distributions.

Usage

mrs(X, G, n_groups = length(unique(G)), Omega = "default", K = 6,
  init_state = NULL, beta = 1, gamma = 0.3, delta = NULL, eta = 0.3,
  alpha = 0.5, return_global_null = TRUE, return_tree = TRUE,
  min_n_node = 0)
mrs(X, G, n_groups = length(unique(G)), Omega = "default", K = 6,
  init_state = NULL, beta = 1, gamma = 0.3, delta = NULL, eta = 0.3,
  alpha = 0.5, return_global_null = TRUE, return_tree = TRUE,
  min_n_node = 0)

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.
`n_groups`	Number of groups.
`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 limits for each dimension.
`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, altenrative and prune, respectively.
`beta`	Spatial clustering parameter of the transition probability matrix. Default is `beta = 1`.
`gamma`	Parameter of the transition probability matrix. Default is `gamma = 0.3`.
`delta`	Optional parameter of the transition probability matrix. Default is `delta = NULL`.
`eta`	Parameter of the transition probability matrix. Default is `eta = 0.3`.
`alpha`	Pseudo-counts of the Beta random probability assignments. Default is `alpha = 0.5`.
`return_global_null`	Boolean indicating whether to return the posterior probability of the global null hypothesis.
`return_tree`	Boolean indicating whether to return the posterior representative tree.
`min_n_node`	Node in the tree is returned if there are more than `min_n_node` data-points in it.

Value

An mrs object.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Examples

set.seed(1)
n = 20
p = 2
X = matrix(c(runif(p*n/2),rbeta(p*n/2, 1, 4)), nrow=n, byrow=TRUE)
G = c(rep(1,n/2), rep(2,n/2))
ans = mrs(X=X, G=G)
set.seed(1)
n = 20
p = 2
X = matrix(c(runif(p*n/2),rbeta(p*n/2, 1, 4)), nrow=n, byrow=TRUE)
G = c(rep(1,n/2), rep(2,n/2))
ans = mrs(X=X, G=G)

Plot regions of the representative tree in 1D

Description

This function visualizes the regions of the representative tree of the output of the mrs function. For each region the posterior probability of difference (PMAP) or the effect size is plotted.

Usage

plot1D(ans, type = "prob", group = 1, dim = 1, regions = rep(1,
  length(ans$RepresentativeTree$Levels)), legend = FALSE, main = "default",
  abs = TRUE)
plot1D(ans, type = "prob", group = 1, dim = 1, regions = rep(1,
  length(ans$RepresentativeTree$Levels)), legend = FALSE, main = "default",
  abs = TRUE)

Arguments

`ans`	An `mrs` object.
`type`	What is represented at each node. The options are `type = c("eff", "prob")`. Default is `type = "prob"`.
`group`	If `type = "eff"`, which group effect size is used. Default is `group = 1`.
`dim`	If the data are multivariate, `dim` is the dimension plotted. Default is `dim = 1`.
`regions`	Binary vector indicating the regions to plot. The default is to plot all regions.
`legend`	Color legend for type. Default is `legend = FALSE`.
`main`	Overall title for the plot.
`abs`	If `TRUE`, plot the absolute value of the effect size. Only used when `type = "eff"`.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Examples

set.seed(1)
p = 1
n1 = 200
n2 = 200
mu1 = matrix( c(0,10), nrow = 2, byrow = TRUE)
mu2 = mu1; mu2[2] = mu1[2] + .01
sigma = c(1,.1)

Z1 = sample(2, n1, replace=TRUE, prob=c(0.9, 0.1))
Z2 = sample(2, n2, replace=TRUE, prob=c(0.9, 0.1))
X1 = mu1[Z1] + matrix(rnorm(n1*p), ncol=p)*sigma[Z1]
X2 = mu2[Z2] + matrix(rnorm(n2*p), ncol=p)*sigma[Z1]
X = rbind(X1, X2)
G = c(rep(1, n1), rep(2,n2))

ans = mrs(X, G, K=10)
plot1D(ans, type = "prob")
plot1D(ans, type = "eff")
set.seed(1)
p = 1
n1 = 200
n2 = 200
mu1 = matrix( c(0,10), nrow = 2, byrow = TRUE)
mu2 = mu1; mu2[2] = mu1[2] + .01
sigma = c(1,.1)

Z1 = sample(2, n1, replace=TRUE, prob=c(0.9, 0.1))
Z2 = sample(2, n2, replace=TRUE, prob=c(0.9, 0.1))
X1 = mu1[Z1] + matrix(rnorm(n1*p), ncol=p)*sigma[Z1]
X2 = mu2[Z2] + matrix(rnorm(n2*p), ncol=p)*sigma[Z1]
X = rbind(X1, X2)
G = c(rep(1, n1), rep(2,n2))

ans = mrs(X, G, K=10)
plot1D(ans, type = "prob")
plot1D(ans, type = "eff")

Plot regions of the representative tree in 2D

Description

This function visualizes the regions of the representative tree of the output of the mrs function.

Usage

plot2D(ans, type = "prob", data.points = "all", background = "none",
  group = 1, dim = c(1, 2),
  levels = sort(unique(ans$RepresentativeTree$Levels)), regions = rep(1,
  length(ans$RepresentativeTree$Levels)), legend = FALSE, main = "default",
  abs = TRUE)
plot2D(ans, type = "prob", data.points = "all", background = "none",
  group = 1, dim = c(1, 2),
  levels = sort(unique(ans$RepresentativeTree$Levels)), regions = rep(1,
  length(ans$RepresentativeTree$Levels)), legend = FALSE, main = "default",
  abs = TRUE)

Arguments

`ans`	An `mrs` object.
`type`	Different options on how to visualize the rectangular regions. The options are `type = c("eff", "prob", "empty", "none")`. Default is `type = "prob"`.
`data.points`	Different options on how to plot the data points. The options are `data.points = c("all", "differential", "none")`. Default is `data.points = "all"`.
`background`	Different options on the background. The options are `background = c("smeared", "none")` .
`group`	If `type = "eff"`, which group effect size is used. Default is `group = 1`.
`dim`	If the data are multivariate, `dim` are the two dimensions plotted. Default is `dim = c(1,2)`.
`levels`	Vector with the level of the regions to plot. The default is to plot regions at all levels.
`regions`	Binary vector indicating the regions to plot. The default is to plot all regions.
`legend`	Color legend for type. Default is `legend = FALSE`.
`main`	Overall title for the legend.
`abs`	If `TRUE`, plot the absolute value of the effect size. Only used when `type = "eff"`.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Examples

set.seed(1)
p = 2
n1 = 200
n2 = 200
mu1 = matrix( c(9,9,0,4,-2,-10,3,6,6,-10), nrow = 5, byrow=TRUE)
mu2 = mu1; mu2[2,] = mu1[2,] + 1

Z1 = sample(5, n1, replace=TRUE)
Z2 = sample(5, n2, replace=TRUE)
X1 = mu1[Z1,] + matrix(rnorm(n1*p), ncol=p)
X2 = mu2[Z2,] + matrix(rnorm(n2*p), ncol=p)
X = rbind(X1, X2)
colnames(X) = c(1,2)
G = c(rep(1, n1), rep(2,n2))

ans = mrs(X, G, K=8)
plot2D(ans, type = "prob", legend = TRUE)

plot2D(ans, type="empty", data.points = "differential",
 background = "none")

plot2D(ans, type="none", data.points = "differential",
 background = "smeared", levels = 4)
set.seed(1)
p = 2
n1 = 200
n2 = 200
mu1 = matrix( c(9,9,0,4,-2,-10,3,6,6,-10), nrow = 5, byrow=TRUE)
mu2 = mu1; mu2[2,] = mu1[2,] + 1

Z1 = sample(5, n1, replace=TRUE)
Z2 = sample(5, n2, replace=TRUE)
X1 = mu1[Z1,] + matrix(rnorm(n1*p), ncol=p)
X2 = mu2[Z2,] + matrix(rnorm(n2*p), ncol=p)
X = rbind(X1, X2)
colnames(X) = c(1,2)
G = c(rep(1, n1), rep(2,n2))

ans = mrs(X, G, K=8)
plot2D(ans, type = "prob", legend = TRUE)

plot2D(ans, type="empty", data.points = "differential",
 background = "none")

plot2D(ans, type="none", data.points = "differential",
 background = "smeared", levels = 4)

Plot nodes of the representative tree

Description

This function visualizes the representative tree of the output of the mrs function. For each node of the representative tree, the posterior probability of difference (PMAP) or the effect size is plotted. Each node in the tree is associated to a region of the sample space. All non-terminal nodes have two children nodes obtained by partitiing the parent region with a dyadic cut along a given direction. The numbers under the vertices represent the cutting direction.

Usage

plotTree(ans, type = "prob", group = 1, legend = FALSE, main = "",
  node.size = 5, abs = TRUE)
plotTree(ans, type = "prob", group = 1, legend = FALSE, main = "",
  node.size = 5, abs = TRUE)

Arguments

`ans`	A `mrs` object.
`type`	What is represented at each node. The options are `type = c("eff", "prob")`.
`group`	If `type = "eff"`, which group effect size is used.
`legend`	Color legend for type. Default is `legend = FALSE`.
`main`	Main title. Default is `main = ""`.
`node.size`	Size of the nodes. Default is `node.size = 5`.
`abs`	If `TRUE`, plot the absolute value of the effect size. Only used when `type = "eff"`.

Note

The package igraph is required.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Examples

set.seed(1)
p = 2
n1 = 200
n2 = 200
mu1 = matrix( c(9,9,0,4,-2,-10,3,6,6,-10), nrow = 5, byrow=TRUE)
mu2 = mu1; mu2[2,] = mu1[2,] + 1

Z1 = sample(5, n1, replace=TRUE)
Z2 = sample(5, n2, replace=TRUE)
X1 = mu1[Z1,] + matrix(rnorm(n1*p), ncol=p)
X2 = mu2[Z2,] + matrix(rnorm(n2*p), ncol=p)
X = rbind(X1, X2)
colnames(X) = c(1,2)
G = c(rep(1, n1), rep(2,n2))

ans = mrs(X, G, K=8)
plotTree(ans, type = "prob", legend = TRUE)
set.seed(1)
p = 2
n1 = 200
n2 = 200
mu1 = matrix( c(9,9,0,4,-2,-10,3,6,6,-10), nrow = 5, byrow=TRUE)
mu2 = mu1; mu2[2,] = mu1[2,] + 1

Z1 = sample(5, n1, replace=TRUE)
Z2 = sample(5, n2, replace=TRUE)
X1 = mu1[Z1,] + matrix(rnorm(n1*p), ncol=p)
X2 = mu2[Z2,] + matrix(rnorm(n2*p), ncol=p)
X = rbind(X1, X2)
colnames(X) = c(1,2)
G = c(rep(1, n1), rep(2,n2))

ans = mrs(X, G, K=8)
plotTree(ans, type = "prob", legend = TRUE)

Print summary of a mrs object

Description

This function print the summary the output of the mrs function. It provides the marginal prior and posterior of the null and the top regions of the representative tree.

Usage

## S3 method for class 'summary.mrs'
print(x, ...)
## S3 method for class 'summary.mrs'
print(x, ...)

Arguments

`x`	A `summary.mrs` object
`...`	Additional print parameters.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Examples

set.seed(1)
n = 100
p = 2
X = matrix(c(runif(p*n/2),rbeta(p*n/2, 1, 4)), nrow=n, byrow=TRUE)
G = c(rep(1,n/2), rep(2,n/2))
x = mrs(X=X, G=G)
fit = summary(x, rho = 0.95, abs_eff = 1)
print(fit)
set.seed(1)
n = 100
p = 2
X = matrix(c(runif(p*n/2),rbeta(p*n/2, 1, 4)), nrow=n, byrow=TRUE)
G = c(rep(1,n/2), rep(2,n/2))
x = mrs(X=X, G=G)
fit = summary(x, rho = 0.95, abs_eff = 1)
print(fit)

Summary of a mrs object

Description

This function summarizes the output of the mrs function. It provides the marginal prior and posterior null and the top regions of the representative tree.

Usage

## S3 method for class 'mrs'
summary(object, rho = 0.5, abs_eff = 0, sort_by = "eff",
  ...)
## S3 method for class 'mrs'
summary(object, rho = 0.5, abs_eff = 0, sort_by = "eff",
  ...)

Arguments

`object`	A `mrs` object
`rho`	Threshold for the posterior alternative probability. All regions with posterior alternative probability larger than `rho` are reported. Default is `rho = 0.5`.
`abs_eff`	Threshold for the effect size. All regions with effect size larger than `abs_eff` in absolute value are reported. Default is `abs_eff = 0`.
`sort_by`	Define in which order the regions are reported. The options are `sort_by = c("eff", "prob")` and the default is `sort_by = "eff"`.
`...`	Additional summary parameters.

Value

A list with information about the top regions.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Examples

set.seed(1)
n = 100
p = 2
X = matrix(c(runif(p*n/2),rbeta(p*n/2, 1, 4)), nrow=n, byrow=TRUE)
G = c(rep(1,n/2), rep(2,n/2))
object = mrs(X=X, G=G)
fit = summary(object, rho = 0.5, abs_eff = 0.1)
set.seed(1)
n = 100
p = 2
X = matrix(c(runif(p*n/2),rbeta(p*n/2, 1, 4)), nrow=n, byrow=TRUE)
G = c(rep(1,n/2), rep(2,n/2))
object = mrs(X=X, G=G)
fit = summary(object, rho = 0.5, abs_eff = 0.1)