| Type: | Package |
| Title: | Robust Mixture Regression |
| Version: | 1.1.0 |
| Date: | 2020-08-03 |
| Author: | Sha Cao [aut, cph, ths], Wennan Chang [aut, cre], Chi Zhang [aut, ctb, ths] |
| Maintainer: | Wennan Chang <wnchang@iu.edu> |
| Description: | Finite mixture models are a popular technique for modelling unobserved heterogeneity or to approximate general distribution functions in a semi-parametric way. They are used in a lot of different areas such as astronomy, biology, economics, marketing or medicine. This package is the implementation of popular robust mixture regression methods based on different algorithms including: fleximix, finite mixture models and latent class regression; CTLERob, component-wise adaptive trimming likelihood estimation; mixbi, bi-square estimation; mixL, Laplacian distribution; mixt, t-distribution; TLE, trimmed likelihood estimation. The implemented algorithms includes: CTLERob stands for Component-wise adaptive Trimming Likelihood Estimation based mixture regression; mixbi stands for mixture regression based on bi-square estimation; mixLstands for mixture regression based on Laplacian distribution; TLE stands for Trimmed Likelihood Estimation based mixture regression. For more detail of the algorithms, please refer to below references. Reference: Chun Yu, Weixin Yao, Kun Chen (2017) <doi:10.1002/cjs.11310>. NeyKov N, Filzmoser P, Dimova R et al. (2007) <doi:10.1016/j.csda.2006.12.024>. Bai X, Yao W. Boyer JE (2012) <doi:10.1016/j.csda.2012.01.016>. Wennan Chang, Xinyu Zhou, Yong Zang, Chi Zhang, Sha Cao (2020) <doi:10.48550/arXiv.2005.11599>. |
| Depends: | R (≥ 3.5.0) |
| License: | GPL-2 | GPL-3 [expanded from: GPL] |
| Encoding: | UTF-8 |
| LazyData: | true |
| Imports: | flexmix, robustbase, gtools, MASS, methods,robust,lars,dplyr,rlang, scales,gplots,grDevices,graphics,RColorBrewer,stats,glmnet |
| RoxygenNote: | 6.1.1 |
| URL: | https://changwn.github.io/RobMixReg/ |
| BugReports: | https://github.com/changwn/RobMixReg/issues |
| NeedsCompilation: | no |
| Packaged: | 2020-08-04 02:28:29 UTC; wnchang |
| Repository: | CRAN |
| Date/Publication: | 2020-08-05 12:00:07 UTC |
RobMixReg package built-in CCLE data.
Description
The list which contain all the information to generate variables used in the real application.
Usage
CCLE_data
Format
A list whose length is 2:
- X
Gene expression dataset.
- Y
AUCC score.
The main function of the RBSL algorithm.
Description
The main function of the RBSL algorithm.
Usage
CSMR(x, y, nit, nc, max_iter)
Arguments
x |
The matrix |
y |
The external supervised variable. |
nit |
xxx? |
nc |
The component number in the mixture model. |
max_iter |
The maximum iteration number. |
Value
A list object consist of coefficient, clustering membership, data x, external variable y, predicted y based on regression model.
Perform the RBSL algorithm one times.
Description
Perform the RBSL algorithm one times.
Usage
CSMR_one(x, y, nit = 1, nc, max_iter)
Arguments
x |
The matrix |
y |
The external supervised variable. |
nit |
xxx? |
nc |
The component number in the mixture model. |
max_iter |
The maximum iteration number. |
Value
A list object consist of coefficient, clustering membership, data x, external variable y, predicted y based on regression model.
The predict function of the CSMR algorithm.
Description
The predict function of the CSMR algorithm.
Usage
CSMR_predict(CSMR_coffs, CSMR.model, xnew, ynew, singleMode = F)
Arguments
CSMR_coffs |
The coefficient matrix. |
CSMR.model |
The trained model. |
xnew |
x variable. |
ynew |
y variable. |
singleMode |
A parameter to set the component to one. |
Value
A list object consist of coefficient, clustering membership, data x, external variable y, predicted y based on regression model.
The train function of the CSMR algorithm.
Description
The train function of the CSMR algorithm.
Usage
CSMR_train(x, y, nit, nc, max_iter)
Arguments
x |
The matrix |
y |
The external supervised variable. |
nit |
xxx |
nc |
The component number in the mixture model. |
max_iter |
The maximum iteration number. |
Value
A list object consist of coefficient, clustering membership, data x, external variable y, predicted y based on regression model.
CTLERob: Robust mixture regression based on component-wise adaptive trimming likelihood estimation.
Description
CTLERob performes robust linear regression with high breakdown point and high efficiency in each mixing components and adaptively remove the outlier samples.
Usage
CTLERob(formula, data, nit = 20, nc = 2, rlr_method = "ltsReg")
## S4 method for signature 'formula,ANY,ANY,numeric'
CTLERob(formula, data, nit = 20,
nc = 2, rlr_method = "ltsReg")
Arguments
formula |
A symbolic description of the model to be fit. |
data |
A data frame containing the predictor and response variables, where the last column is the response varible. |
nit |
Number of iterations. |
nc |
Number of mixture components. |
rlr_method |
The regression methods, default is 'ltsReg'. |
Compute the row space using SVD.
Description
Compute the row space using SVD.
Usage
Compute_Rbase_SVD(bulk_data, tg_R1_lists_selected)
Arguments
bulk_data |
The bulk data.. |
tg_R1_lists_selected |
A list of the marker genes for several cell types. |
Value
A matrix which each row span the row space using cell type specific marker genes.
DeOut : Detect outlier observations.
Description
Detect outlier observations from a vector.
Usage
DeOut(daData, method)
Arguments
daData |
A numerical vector. |
method |
Choose from '3sigma','hampel' and 'boxplot'. |
Value
indices of outlier observations.
The main function of mining the latent relationship among variables.
Description
The main function of mining the latent relationship among variables.
Usage
MLM(ml.method = "rlr", rmr.method = "cat",
b.formulaList = list(formula(y ~ x), formula(y ~ 1)), formula = y ~
x, nit = 1, nc = 2, x = NULL, y = NULL, max_iter = 50,
tRatio = 0.05)
Arguments
ml.method |
The option to select the four methods in vignette. |
rmr.method |
The option to select the robust mixture regression method. |
b.formulaList |
The case b require the user provide the formula list. This enable the flexible mixture regression. |
formula |
The linear relationship between two variables. |
nit |
Number of iterations for CTLE, mixbi, mixLp. |
nc |
Number of mixture components. |
x |
The matrix x of the high dimension situation. |
y |
The external outcome variable. |
max_iter |
Maximum iteration for TLE method. |
tRatio |
The ratio of the outliers in the TLE robust mixture regression method. |
Value
Main result object.
Model selection function for low dimension data.
Description
Model selection function for low dimension data.
Usage
MLM_bic(ml.method = "rlr", x, y, nc = 1, formulaList = NULL, K = 2)
Arguments
ml.method |
The parameter to choose the fitted model for calculating the BIC |
x |
x variable. |
y |
y variable. |
nc |
The component number for low dimensional feature |
formulaList |
The list of target formular |
K |
The component number for high dimensional feature |
Value
BIC value.
Cross validation (fold-5) function for high dimension data.
Description
Cross validation (fold-5) function for high dimension data.
Usage
MLM_cv(x = NULL, y = NULL, nit = 1, nc = 2, max_iter = 50)
Arguments
x |
x variable. |
y |
y variable. |
nit |
Iteration number. |
nc |
The number of component. |
max_iter |
Maximum iteration. |
Value
The correlation between y and y_hat based on five fold cross validation.
Adaptive lasso.
Description
Adaptive lasso.
Usage
Rec_Lm(XX, yy)
Arguments
XX |
The independent variable. |
yy |
The dependent variable. |
Value
A list object consist of index of selected variable and coefficient for all variables.
Class RobMixReg.
Description
Class RobMixReg defines a robust mixture regression class as a S4 object.
Slots
inds_inThe indices of observations used in the parameter estimation.
indoutThe indices of outlier samples, not used in the parameter estimation.
ctleclustersThe cluster membership of each observation.
compcoefRegression coefficients for each component.
comppvalsComponent p values.
compwwwThe posterior of the clustering.
callCall function.
TLE: robust mixture regression based on trimmed likelihood estimation.
Description
The algorithm fits a mixture regression model after trimming a proportion of the observations, given by tRatio.
Usage
TLE(formula, data, nc = 2, tRatio, MaxIt = 200)
## S4 method for signature 'formula,ANY,numeric,numeric,numeric'
TLE(formula, data,
nc = 2, tRatio, MaxIt = 200)
Arguments
formula |
A symbolic description of the model to be fit. |
data |
A data frame containing the predictor and response variables, where the last column is the response varible. |
nc |
Number of mixture components. |
tRatio |
Trimming proportion. |
MaxIt |
Maximum iteration. |
Value
A S4 object of RobMixReg class.
Examples
library("RobMixReg")
formula01=as.formula("y~x")
x=(gaussData$x);y=as.numeric(gaussData$y);
example_data01=data.frame(x,y)
res = TLE(formula01,example_data01, nc=2,tRatio=0.05,MaxIt=200)
biscalew :Robust M-estimates for scale.
Description
Tukey's bisquare family of functions.
Usage
biscalew(t)
Arguments
t |
Numerical input, usually residuals. |
Value
bisquare weight for scale.
bisquare : Robust estimates for mean.
Description
Tukey's bisquare family of functions.
Usage
bisquare(t, k = 4.685)
Arguments
t |
Numerical input, usually residuals. |
k |
A constant tuning parameter, default is 4.685. |
Value
A bi-square weight for mean.
Plot the coefficient matrix.
Description
Plot the coefficient matrix.
Usage
blockMap(rrr)
Arguments
rrr |
The result from CSMR function |
RobMixReg package built-in Colon cancer data.
Description
The list which contain all the information to generate variables used in the real application.
Usage
colon_data
Format
A list whose length is 3:
- rnames
A string contains the name of binding protein and epigenetic regulator.
- x3
The gene expression profile of CREB3L1.
- y3
The methylation profile of cg16012690 on 299 colon adenocarcinoma patients.
- x2
x2
- y2
y2
- x1
x1
- y1
y1
The plot wrapper function.
Description
The plot wrapper function.
Usage
compPlot(type = "rlr", x, y, nc, inds_in, res)
Arguments
type |
The character to choose which type of plot to generate. |
x |
The independent variables |
y |
The external variable |
nc |
The number of components |
inds_in |
A vector indicate the outlier samples. |
res |
The result object returned by MLM function. |
denLp : Density function for Laplace distribution.
Description
Laplace distribution.
Usage
denLp(rr, sig)
Arguments
rr |
Shift from the location parameter |
sig |
Scale parameter. |
Value
Laplace density.
flexmix_2: Multiple runs of MLE based mixture regression to stabilize the output.
Description
Mixture regression based on MLE could be unstable when assuming unequal variance. Multiple runs of flexmix is performed to stabilize the results.
Usage
flexmix_2(formula, data1, k, mprior)
Arguments
formula |
A symbolic description of the model to be fit. |
data1 |
A data frame containing the predictor and response variables, where the last column is the response varible. |
k |
Number of mixture components. |
mprior |
A numeric number in (0,1) that specifies the minimum proportion of samples in each mixing components. |
Value
A S4 object of flexmix class. xxx
RobMixReg package built-in gaussian example data.
Description
A dataset generated from gaussian distribution in RobMixReg package.
Usage
gaussData
Format
A data frame with 100 rows and 3 variables:
- x
x variable
- y
y variable
- c
cluster information
lars variant for LSA.
Description
lars variant for LSA.
Usage
lars.lsa(Sigma0, b0, intercept, n, type = c("lasso", "lar"),
eps = .Machine$double.eps, max.steps)
Arguments
Sigma0 |
The parameter. |
b0 |
The intercept of the regression line. |
intercept |
The bool variable of whether consider the intercept situation |
n |
The number of data point. |
type |
Regression options, choose form "lasso" or "lar". |
eps |
The converge threshold defined by the machine. |
max.steps |
The maximum iteration times to stop. |
Value
object.
Author(s)
Reference Wang, H. and Leng, C. (2006) and Efron et al. (2004).
Obtain Log-likelihood from a mixtureReg Object
Description
S3 method for class 'mixtureReg'. However, it doesn't return a 'logLik' object. For simlicity, it returns a 'numeric' value.
Usage
logLik_mixtureReg(mixtureModel)
Arguments
mixtureModel |
mixtureReg object, typically result from 'mixtureReg()'. |
Value
Return a numeric value of log likelihood.
Least square approximation. This version Oct 19, 2006.
Description
Least square approximation. This version Oct 19, 2006.
Usage
lsa(obj)
Arguments
obj |
lm/glm/coxph or other object. |
Value
beta.ols: the MLE estimate ; beta.bic: the LSA-BIC estimate ; beta.aic: the LSA-AIC estimate.
Author(s)
Reference Wang, H. and Leng, C. (2006) and Efron et al. (2004).
mixLp : mixLp_one estimates the mixture regression parameters robustly using Laplace distribution based on multiply initial value..
Description
mixLp estimates the mixture regression parameters robustly using bisquare function based on multiple initial values. The solution is found by the modal solution.
Usage
mixLp(formula, data, nc=2, nit=200)
## S4 method for signature 'formula,ANY,numeric,numeric'
mixLp(formula, data, nc = 2,
nit = 20)
Arguments
formula |
A symbolic description of the model to be fit. |
data |
A data frame containing the predictor and response variables, where the last column is the response varible. |
nc |
Number of mixture components. |
nit |
Number of iterations |
Value
Estimated coefficients of all components.
Examples
library("RobMixReg")
formula01=as.formula("y~x")
x=(gaussData$x);y=as.numeric(gaussData$y);
example_data01=data.frame(x,y)
res = mixLp(formula01, example_data01, nc=2, nit=20)
mixLp_one : mixLp_one estimates the mixture regression parameters robustly using Laplace distribution based on one initial value.
Description
Robust mixture regression assuming that the error terms follow a Laplace distribution.
Usage
mixLp_one(formula, data, nc = 2)
Arguments
formula |
A symbolic description of the model to be fit. |
data |
A data frame containing the predictor and response variables, where the last column is the response varible. |
nc |
Number of mixture components. |
Value
Estimated coefficients of all components.
mixlinrb_bi: mixlinrb_bione estimates the mixture regression parameters robustly using bisquare function based on multiply initial value.
Description
An EM-type of parameter estimation by replacing the least square estimation in the M-step with a robust criterior.
Usage
mixlinrb_bi(formula, data, nc = 2, nit = 200)
## S4 method for signature 'formula,ANY,numeric,numeric'
mixlinrb_bi(formula, data,
nc = 2, nit = 20)
Arguments
formula |
A symbolic description of the model to be fit. |
data |
A data frame containing the predictor and response variables, where the last column is the response varible. |
nc |
Number of mixture components. |
nit |
Number of iterations for biSauqre method. |
Value
Estimated coefficients of all components.
mixlinrb_bione : mixlinrb_bione estimates the mixture regression parameters robustly using bisquare function based on one initial value.
Description
An EM-type of parameter estimation by replacing the least square estimation in the M-step with a robust criterior.
Usage
mixlinrb_bione(formula, data, nc = 2)
Arguments
formula |
A symbolic description of the model to be fit. |
data |
A data frame containing the predictor and response variables, where the last column is the response varible. |
nc |
Number of mixture components. |
Value
Estimated coefficients of all components.
Function to Fit Mixture of Regressions
Description
The main function in this package.
Usage
mixtureReg(regData, formulaList, xName = NULL, yName = NULL,
mixingProb = c("Constant", "loess"), initialWList = NULL,
epsilon = 1e-08, max_iter = 10000, max_restart = 15,
min_lambda = 0.01, min_sigmaRatio = 0.1, silently = TRUE)
Arguments
regData |
data frame used in fitting model. |
formulaList |
a list of the regression components that need to be estimated. |
xName |
character; Name used to pick x variable from data. |
yName |
character; Name used to pick y variable from data. |
mixingProb |
character; Specify how the mixing probabilities are estimated in the M step. "Constant" specifies a constant mixing probabilities; "loess" specifies predictor dependent mixing probabilities obtained by loess smoothing. |
initialWList |
a list of weights guesses (provided by user). Typically this is not used, unless the user has a good initial guess. |
epsilon |
a small value that the function consider as zero. The value is used in determine matrix sigularity and in determine convergence. |
max_iter |
the maximum number of iterations. |
max_restart |
the maximum number of restart before giving up. |
min_lambda |
a value used to ensure estimated mixing probabilities (lambda's) are not too close to zero. |
min_sigmaRatio |
a value used to prevent estimated variaces of any regression component from collapsing to zero. |
silently |
a switch to turn off the screen printout. |
Value
A class 'mixtureReg' object.
Author(s)
The mixtureReg package is developed by Tianxia Zhou on github. All right reserved by Tianxia Zhou.
Sort by X Coordinates and Add Line to a Plot
Description
Rearrange X and Y coordinates before calling "lines()" function.
Usage
orderedLines(x, y, ...)
Arguments
x |
X coordinate vectors of points to join. |
y |
Y coordinate vectors of points to join. |
... |
Further graphical parameters. |
plot_CTLE: Plot the mixture/single regression line(s) in a simply function.
Description
CTLERob performes robust linear regression with high breakdown point and high efficiency in each mixing components and adaptively remove the outlier samples.
Usage
plot_CTLE(formula, data, nc = 2, inds_in)
## S4 method for signature 'formula,ANY,numeric'
plot_CTLE(formula, data, nc = 2, inds_in)
Arguments
formula |
A symbolic description of the model to be fit. |
data |
A data frame containing the predictor and response variables, where the last column is the response varible. |
nc |
Number of mixture components. |
inds_in |
The index of the point which belongs to the current regression line. |
Plot Fit and Mixing Probability of a mixtureReg Object
Description
S3 plot method for class 'mixtureReg'.
Usage
plot_mixtureReg(mixtureModel, which = 1:2, xName = NULL,
yName = NULL, xlab = NULL, ylab = NULL, ...)
Arguments
mixtureModel |
mixtureReg object, typically result from 'mixtureReg()'. |
which |
numeric; choose which plot to display. '1' gives a plot of fit; '2' gives a plot of mixing probability. |
xName |
character; Name used to pick x variable from data. |
yName |
character; Name used to pick y variable from data. |
xlab |
character; label that should be put on the x axis. |
ylab |
character; label that should be put on the y axis. |
... |
Further graphical parameters. |
Plot a List of mixtureReg Objects
Description
Feed in a list of mixtureReg models and get an overlayed plot.
Usage
plot_mixtureRegList(mixtureRegList, xName = NULL, yName = NULL, ...)
Arguments
mixtureRegList |
a list of multiple mixtureReg objects. |
xName |
character; Name used to pick x variable from data. |
yName |
character; Name used to pick y variable from data. |
... |
Further graphical parameters. |
The main function of Robust Mixture Regression using five methods.
Description
The main function of Robust Mixture Regression using five methods.
Usage
rmr(lr.method = "flexmix", formula = NULL, data = NULL, nc = 2,
nit = 20, tRatio = 0.05, MaxIt = 200)
Arguments
lr.method |
A robust mixture regression method to be used. Should be one of "flexmix", "TLE", "CTLERob", "mixbi","mixLp". |
formula |
A symbolic description of the model to be fit. |
data |
A data frame containing the predictor and response variables, where the last column is the response varible. |
nc |
Number of mixture components. |
nit |
Number of iterations for CTLE, mixbi, mixLp. |
tRatio |
Trimming proportion for TLE method. |
MaxIt |
Maximum iteration for TLE method. |
Value
An S4 object about the regression result.
Examples
library(RobMixReg)
#library(robust)
library(flexmix)
library(robustbase)
library(MASS)
library(gtools)
# gaussData
x=(gaussData$x);y=as.numeric(gaussData$y);
formula01=as.formula("y~x")
example_data01=data.frame(x,y)
res_rmr = rmr(lr.method='flexmix', formula=formula01, data=example_data01)
res_rmr = rmr(lr.method='CTLERob', formula=formula01, data=example_data01)
RobMixReg package built-in simulated example data.
Description
A simulation dataset from RobMixReg package. This simulation dataset is in dimension 2 and ground truth (include outliers label) of the cluster information also generated.
Usage
simuData
Format
A data frame with 500 rows and 5 variables:
- X1
X1 variable
- X2
X2 variable
- y
y variable
- c
cluster information
- outlier
outlier indicator
Simulate high dimension data for RBSL algorithm validation.
Description
Simulate high dimension data for RBSL algorithm validation.
Usage
simu_data_sparse(n, bet, pr, sigma)
Arguments
n |
Patient number. |
bet |
The coefficient matrix. |
pr |
A vector of probability threshold which simulate the sampling based on uniform distribution. |
sigma |
A vector of noise level. The length should be equal to the component number. |
Value
A list object consist of x, y, true cluster label.
The simulation function for low/high dimensional space.
Description
The simulation function for low/high dimensional space.
Usage
simu_func(beta, sigma, alpha = NULL, n = 400)
Arguments
beta |
The slope vector for low dimensional space or matrix for high dimensional space. |
sigma |
A vector whose k-th element is the standard deviation for the k-th regression component. |
alpha |
The parameter to control the number of outliers for low dimensional space. |
n |
The sample number for high dimensional data. |
Value
A list object.
The simulation function for low dimensional space.
Description
The simulation function for low dimensional space.
Usage
simu_low(beta, inter, alpha = NULL)
Arguments
beta |
The slope vector. |
inter |
The intercept vector. |
alpha |
The parameter to control the number of outliers. |
Value
A list object consists of the x variable in low dimensional space and the external y variable.