Invisible Fence model selection (Linear Model)

Description

Invisible Fence model selection (Linear Model)

Usage

IF.lm(full, data, B = 100, cpus = 2, lftype = c("abscoef", "pvalue"))

Arguments

Details

This method (Jiang et. al, 2011) is motivated by computational expensive in complex and high dimensional problem. The idea of the method–there is the best model in each dimension (in model space). The boostrapping determines the coverage probability of the selected model in each dimensions. The parsimonious model is the selected model with the highest coverage probabily (except the one for the full model, always probability of 1.)

Value

@note The current Invisible Fence focuses on variable selection. The current routine is applicable to the case in which the subtractive measure is the absolute value of the coefficients, p-value, t-value. However, the method can be extended to other subtractive measures. See Jiang et. al (2011) for more details.

Author(s)

Jiming Jiang Jianyang Zhao J. Sunil Rao Thuan Nguyen

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiming Jiang, Thuan Nguyen and J. Sunil Rao (2011), Invisible fence methods and the identification of differentially expressed gene sets. Statistics and Its Interface, Volume 4, 403-415.

Examples

library(fence)
library(MASS)
library(snow)
r =1234; set.seed(r)
p=10; n=300; rho = 0.6
R = diag(p)
for(i in 1:p){
  for(j in 1:p){
     R[i,j] = rho^(abs(i-j))
  }
}
R = 1*R
x=mvrnorm(n, rep(0, p), R)
colnames(x)=paste('x',1:p, sep='')
X = cbind(rep(1,n),x)
tbetas = c(1,1,1,0,1,1,0,1,0,0,0)  # non-zero beta 1,2,4,5,7
epsilon = rnorm(n)
y = as.matrix(X)%*%tbetas + epsilon
colnames(y) = 'y'
data = data.frame(cbind(X,y))
full = y ~ x1+x2+x3+x4+x5+x6+x7+x8+x9+x10
# Takes greater than 5 seconds (~`17 seconds) to run
# obj1 = IF.lm(full = full, data = data, B = 100, lftype = "abscoef")
# sort((names(obj1$model$coef)[-1]))  
# obj2 = IF.lm(full = full, data = data, B = 100, lftype = "pvalue")
# sort(setdiff(names(data[c(-1,-12)]), names(obj2$model$coef)))

Invisible Fence model selection (Linear Mixed Model)

Description

Invisible Fence model selection (Linear Mixed Model)

Usage

IF.lmer(full, data, B = 100, REML = TRUE, method = c("marginal",
  "conditional"), cpus = parallel::detectCores(), lftype = c("abscoef",
  "tvalue"))

Arguments

Details

This method (Jiang et. al, 2011) is motivated by computational expensive in complex and high dimensional problem. The idea of the method–there is the best model in each dimension (in model space). The boostrapping determines the coverage probability of the selected model in each dimensions. The parsimonious model is the selected model with the highest coverage probabily (except the one for the full model, always probability of 1.)

Value

@note The current Invisible Fence focuses on variable selection. The current routine is applicable to the case in which the subtractive measure is the absolute value of the coefficients, p-value, t-value. However, the method can be extended to other subtractive measures. See Jiang et. al (2011) for more details.

Author(s)

Jiming Jiang Jianyang Zhao J. Sunil Rao Thuan Nguyen

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiming Jiang, Thuan Nguyen and J. Sunil Rao (2011), Invisible fence methods and the identification of differentially expressed gene sets. Statistics and Its Interface, Volume 4, 403-415.

Examples

require(fence)
library(snow)
library(MASS)
data("X.lmer")
data = data.frame(X.lmer)
# non-zero beta I.col.2, I.col.3a, I.col.3b, V5, V7, V8, V9
beta = matrix(c(0, 1, 1, 1, 1, 0, 0.1, 0.05, 0.25, 0), ncol = 1)
set.seed(1234)
alpha = rep(rnorm(100), each = 3)
mu = alpha + as.matrix(data[,-1]) %*% beta
data$id = as.factor(data$id)
data$y = mu + rnorm(300)
raw = "y ~ (1|id)+I.col.2+I.col.3a+I.col.3b"
for (i in 5:10) {
    raw = paste0(raw, "+V", i)
}
full = as.formula(raw)
# The following output takes more than 5 seconds (~70 seconds) to run. 

# obj1.lmer = IF.lmer(full = full, data = data, B = 100, method="conditional",lftype = "abscoef")
# sort(obj1.lmer$model) 

# obj2.lmer = IF.lmer(full = full, data = data, B = 100, method="conditional",lftype = "tvalue")
# sort(obj2.lmer$model)

# Similarly, the following scenarios can be run

# obj2.lmer = IF.lmer(full = full, data = data, B = 100, method="conditional",lftype = "tvalue")
# sort(obj2.lmer$model)
# obj1.lm = IF.lmer(full = full, data = data, B = 100, method="marginal", lftype = "abscoef")
# sort(names(obj1.lm$model$coefficients[-1]))
# obj2.lm = IF.lmer(full = full, data = data, B = 100, method="marginal", lftype = "tvalue")
# sort(names(obj2.lm$model$coefficients[-1]))

Adaptive Fence model selection (Restricted Fence)

Description

Adaptive Fence model selection (Restricted Fence)

Usage

RF(full, data, groups, B = 100, grid = 101, bandwidth = NA,
  plot = FALSE, method = c("marginal", "conditional"), id = "id",
  cpus = parallel::detectCores())

Arguments

Details

In Jiang et. al (2008), the adaptive c value is chosen from the highest peak in the p* vs. c plot. In Jiang et. al (2009), 95% CI is taken into account while choosing such an adaptive choice of c. In Thuan Nguyen et. al (2014), the adaptive c value is chosen from the first peak. This approach works better in the moderate sample size or weak signal situations. Empirically, the first peak becomes highest peak when sample size increases or signals become stronger

Value

Note

bandwidth = (cs[2] - cs[1]) * 3. So it's chosen as 3 times grid between two c values.

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629

• Thuan Nguyen, Jiming Jiang (2012), Restricted fence method for covariate selection in longitudinal data analysis. Biostatistics, 13(2), 303-314

• Thuan Nguyen, Jie Peng, Jiming Jiang (2014), Fence Methods for Backcross Experiments. Statistical Computation and Simulation, 84(3), 644-662

Examples

## Not run: 
r =1234; set.seed(r)
n = 100; p=15; rho = 0.6
beta = c(1,1,1,0,1,1,0,1,0,0,1,0,0,0,0)  # non-zero beta 1,2,3,V6,V7,V9,V12
id = rep(1:n,each=3)
V.1 = rep(1,n*3)
I.1 = rep(c(1,-1),each=150)
I.2a = rep(c(0,1,-1),n)
I.2b = rep(c(0,-1,1),n)
x = matrix(rnorm(n*3*11), nrow=n*3, ncol=11)
x = cbind(id,V.1,I.1,I.2a,I.2b,x)
R = diag(3)
for(i in 1:3){
 for(j in 1:3){
   R[i,j] = rho^(abs(i-j))
 }
} 
e=as.vector(t(mvrnorm(n, rep(0, 3), R)))  
y = as.vector(x[,-1]%*%beta) + e
data = data.frame(x,y)
raw = "y ~ V.1 + I.1 + I.2a +I.2b"
for (i in 6:16) { raw = paste0(raw, "+V", i)}; full = as.formula(raw)
bin1="y ~ V.1 + I.1 + I.2a +I.2b"
for (i in 6:8) { bin1 = paste0(bin1, "+V", i)}; bin1 = as.formula(bin1)
bin2="y ~ V9"
for (i in 10:16){ bin2 = paste0(bin2, "+V", i)}; bin2 = as.formula(bin2)
# May take longer than 30 min since there are two stages in this RF procedure
obj1.RF = RF(full = full, data = data, groups = list(bin1,bin2), method="conditional")
obj1.RF$sel_model
obj2.RF = RF(full = full, data = data, groups = list(bin1,bin2), B=100, method="marginal")
obj2.RF$sel_model

## End(Not run)

X.lmer

Description

Data used in the example for X.lmer

Usage

data(X.lmer)

Format

A data frame with 10 variables:

Adaptive Fence model selection

Description

Adaptive Fence model selection

Usage

adaptivefence(mf, f, ms, d, lf, pf, bs, grid = 101, bandwidth)

Arguments

Value

Author(s)

Jiming Jiang Jianyang Zhao J. Sunil Rao Thuan Nguyen

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629

• Thuan Nguyen, Jie Peng, Jiming Jiang (2014), Fence Methods for Backcross Experiments. Statistical Computation and Simulation, 84(3), 644-662

Examples

## Not run: 
require(fence)

#### Example 1 #####
data(iris)
full = Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width + (1|Species)
test_af = fence.lmer(full, iris)
plot(test_af)
test_af$sel_model

#### Example 2 #####
r =1234; set.seed(r)  
p=8; n=150; rho = 0.6
id = rep(1:50,each=3)
R = diag(p)
for(i in 1:p){
  for(j in 1:p){
     R[i,j] = rho^(abs(i-j))
  }
} 
R = 1*R
x=mvrnorm(n, rep(0, p), R)  # all x's are time-varying dependence #
colnames(x)=paste('x',1:p, sep='')
tbetas = c(0,0.5,1,0,0.5,1,0,0.5)  # non-zero beta 2,3,5,6,8
epsilon = rnorm(150)
y = x%*%tbetas + epsilon
colnames(y) = 'y'
data = data.frame(cbind(x,y,id))
full = y ~ x1+x2+x3+x4+x5+x6+x7+x8+(1|id)
#X = paste('x',1:p, sep='', collapse='+')
#full = as.formula(paste('y~',X,'+(1|id)', sep=""))  #same as previous one
fence_obj = fence.lmer(full,data)   # it takes 3-5 min #
plot(fence_obj)
fence_obj$sel_model

## End(Not run)

Adaptive Fence model selection (Small Area Estmation)

Description

Adaptive Fence model selection (Small Area Estmation)

Usage

adaptivefence.fh(mf, f, ms, d, lf, pf, bs, grid = 101, bandwidth, method)

Arguments

Details

In Jiang et. al (2008), the adaptive c value is chosen from the highest peak in the p* vs. c plot. In Jiang et. al (2009), 95% CI is taken into account while choosing such an adaptive choice of c. In Thuan Nguyen et. al (2014), the adaptive c value is chosen from the first peak. This approach works better in the moderate sample size or weak signal situations. Empirically, the first peak becomes highest peak when sample size increases or signals become stronger

Value

Note

• The current Fence package focuses on variable selection. However, Fence methods can be used to select other parameters of interest, e.g., tunning parameter, variance-covariance structure, etc.

• The number of bootstrap samples is suggested to be increased, e.g., B=1000 when the sample size is small, or signals are weak

Author(s)

Jiming Jiang Jianyang Zhao J. Sunil Rao Thuan Nguyen

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629

• Thuan Nguyen, Jie Peng, Jiming Jiang (2014), Fence Methods for Backcross Experiments. Statistical Computation and Simulation, 84(3), 644-662

Examples

## Not run: 
require(fence)
### example 1 ####
data("kidney")
data = kidney[-which.max(kidney$x),]     # Delete a suspicious data point #
data$x2 = data$x^2
data$x3 = data$x^3
data$x4 = data$x^4
data$D = data$sqrt.D.^2
plot(data$y ~ data$x)
full = y~x+x2+x3+x4
testfh = fence.sae(full, data, B=1000, fence="adaptive", method="F-H", D = D)
testfh$sel_model
testfh$c

## End(Not run)

Fence model selection (Nonparametric Model)

Description

Fence model selection (Noparametric Model)

Usage

fence.NF(full, data, spline, ps = 1:3, qs = NA, B = 100, grid = 101,
  bandwidth = NA, lambda)

Arguments

Value

@note The current Fence method in Nonparametric model focuses on one spline variable. This method can be extended to a general case with more than one spline variables, and includes non-spline variables.

Author(s)

Jiming Jiang Jianyang Zhao J. Sunil Rao Bao-Qui Tran Thuan Nguyen

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629

• Jiang J., Nguyen T., Rao J.S. (2010), Fence Method for Nonparametric Small Area Estimation. Survey Methodology, 36, 1, 3-11

Examples

## Not run: 
require(fence)
n = 100
set.seed(1234)
x=runif(n,0,3)
y = 1-x+x^2- 2*(x-1)^2*(x>1) + 2*(x-2)^2*(x>2) + rnorm(n,sd=.2)
lambda=exp((c(1:60)-30)/3)
data=data.frame(cbind(x,y))   
test_NF = fence.NF(full=y~x, data=data, spline='x', ps=c(1:3), qs=c(2,5), B=1000, lambda=lambda)
plot(test_NF)
summary <- summary(test_NF) 
model_sel <- summary[[1]]
model_sel
lambda_sel <- summary[[2]]
lambda_sel

## End(Not run)

Fence model selection (Linear Mixed Model)

Description

Fence model selection (Linear Mixed Model)

Usage

fence.lmer(full, data, B = 100, grid = 101, fence = c("adaptive",
  "nonadaptive"), cn = NA, REML = TRUE, bandwidth = NA,
  cpus = parallel::detectCores())

Arguments

Details

In Jiang et. al (2008), the adaptive c value is chosen from the highest peak in the p* vs. c plot. In Jiang et. al (2009), 95% CI is taken into account while choosing such an adaptive choice of c. In Thuan Nguyen et. al (2014), the adaptive c value is chosen from the first peak. This approach works better in the moderate sample size or weak signal situations. Empirically, the first peak becomes highest peak when sample size increases or signals become stronger

Value

@note The current Fence package focuses on variable selection. However, Fence methods can be used to select other parameters of interest, e.g., tunning parameter, variance-covariance structure, etc.

Author(s)

Jiming Jiang Jianyang Zhao J. Sunil Rao Thuan Nguyen

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629

• Thuan Nguyen, Jie Peng, Jiming Jiang (2014), Fence Methods for Backcross Experiments. Statistical Computation and Simulation, 84(3), 644-662

Examples

require(fence)
library(snow)

#### Example 1 #####
data(iris)
full = Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width + (1|Species)
# Takes greater than 5 seconds to run
# test_af = fence.lmer(full, iris)
# test_af$c
# test_naf = fence.lmer(full, iris, fence = "nonadaptive", cn = 12)
# plot(test_af)
# test_af$sel_model
# test_naf$sel_model

Fence model selection (Small Area Estmation)

Description

Fence model selection (Small Area Estmation)

Usage

fence.sae(full, data, B = 100, grid = 101, fence = c("adaptive",
  "nonadaptive"), cn = NA, method = c("F-H", "NER"), D = NA,
  REML = FALSE, bandwidth = NA, cpus = parallel::detectCores())

Arguments

Details

In Jiang et. al (2008), the adaptive c value is chosen from the highest peak in the p* vs. c plot. In Jiang et. al (2009), 95% CI is taken into account while choosing such an adaptive choice of c. In Thuan Nguyen et. al (2014), the adaptive c value is chosen from the first peak. This approach works better in the moderate sample size or weak signal situations. Empirically, the first peak becomes highest peak when sample size increases or signals become stronger

Value

Note

• The current Fence package focuses on variable selection. However, Fence methods can be used to select other parameters of interest, e.g., tunning parameter, variance-covariance structure, etc.

• The number of bootstrap samples is suggested to be increased, e.g., B=1000 when the sample size is small, or signals are weak

Author(s)

Jiming Jiang Jianyang Zhao J. Sunil Rao Thuan Nguyen

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629

• Thuan Nguyen, Jie Peng, Jiming Jiang (2014), Fence Methods for Backcross Experiments. Statistical Computation and Simulation, 84(3), 644-662

Examples

require(fence)
library(snow)
### example 1 ####
data("kidney")
data = kidney[-which.max(kidney$x),]     # Delete a suspicious data point #
data$x2 = data$x^2
data$x3 = data$x^3
data$x4 = data$x^4
data$D = data$sqrt.D.^2
plot(data$y ~ data$x)
full = y~x+x2+x3+x4
# Takes more than 5 seconds to run
# testfh = fence.sae(full, data, B=100, fence="adaptive", method="F-H", D = D)
# testfh$sel_model
# testfh$c

Invisible Fence model selection

Description

Invisible Fence model selection

Usage

invisiblefence(mf, f, d, lf, bs)

Arguments

Details

This method (Jiang et. al, 2011) is motivated by computational expensive in complex and high dimensional problem. The idea of the method–there is the best model in each dimension (in model space). The boostrapping determines the coverage probability of the selected model in each dimensions. The parsimonious model is the selected model with the highest coverage probabily (except the one for the full model, always probability of 1.)

Value

@note The current Invisible Fence focuses on variable selection. The current routine is applicable to the case in which the subtractive measure is the absolute value of the coefficients, p-value, t-value. However, the method can be extended to other subtractive measures. See Jiang et. al (2011) for more details.

Author(s)

Jiming Jiang Jianyang Zhao J. Sunil Rao Thuan Nguyen

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiming Jiang, Thuan Nguyen and J. Sunil Rao (2011), Invisible fence methods and the identification of differentially expressed gene sets. Statistics and Its Interface, Volume 4, 403-415.

Examples

## Not run: 
data("X.lmer")
data = data.frame(X.lmer)
beta = matrix(c(0, 1, 1, 1, 1, 0, 0.1, 0.05, 0.25, 0), ncol = 1)
set.seed(1234)
alpha = rep(rnorm(100), each = 3)
mu = alpha + as.matrix(data[,-1]) %*% beta
data$id = as.factor(data$id)
data$y = mu + rnorm(300)
raw = "y ~ (1|id)+I.col.2+I.col.3a+I.col.3b"
for (i in 5:10) {
    raw = paste0(raw, "+V", i)
}
full = as.formula(raw)
obj1.lmer = IF.lmer(full = full, data = data, B = 100, method="conditional",lftype = "abscoef")
obj1.lmer$model$coefficients
obj2.lmer = IF.lmer(full = full, data = data, B = 100, method="conditional",lftype = "tvalue")
obj2.lmer$model$coefficients
obj1.lm = IF.lmer(full = full, data = data, B = 100, method="marginal", lftype = "abscoef")
obj1.lm$model$coefficients
obj2.lm = IF.lmer(full = full, data = data, B = 100, method="marginal", lftype = "tvalue")
obj2.lm$model$coefficients

## End(Not run)

kidney

Description

Data used for kidney example

Usage

kidney

Format

A data frame with 4 variables

Nonadaptive Fence model selection

Description

Nonadaptive Fence model selection

Usage

nonadaptivefence(mf, f, ms, d, lf, pf, cn)

Arguments

Value

Author(s)

Jiming Jiang Jianyang Zhao J. Sunil Rao Thuan Nguyen

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629

• Thuan Nguyen, Jie Peng, Jiming Jiang (2014), Fence Methods for Backcross Experiments. Statistical Computation and Simulation, 84(3), 644-662

Examples

## Not run: 
require(fence)

#### Example 1 #####
data(iris)
full = Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width + (1|Species)
test_naf = fence.lmer(full, iris, fence = "nonadaptive", cn = 12)
test_naf$sel_model

## End(Not run)

Plot Adaptive Fence model selection

Description

Plot Adaptive Fence model selection

Usage

## S3 method for class 'AF'
plot(x = res, ...)

Arguments

Plot Nonparametric Fence model selection

Description

Plot Nonparametric Fence model selection

Usage

## S3 method for class 'NF'
plot(x = res, ...)

Arguments

Summary Adaptive Fence model selection

Description

Summary Adaptive Fence model selection

Usage

## S3 method for class 'AF'
summary(object = res, ...)

Arguments

Summary Nonparametric Fence model selection

Description

Summary Nonparametric Fence model selection

Usage

## S3 method for class 'NF'
summary(object = res, ...)

Arguments