farm.select {FarmSelect}

Factor-adjusted robust model selection

Description

Given a covariate matrix and output vector, this function first adjusts the covariates for underlying factors and then performs model selection.

Usage

farm.select(X, Y, loss = c("scad", "mcp", "lasso"), robust = TRUE,
  cv = FALSE, tau = 2, lin.reg = TRUE, K.factors = NULL,
  max.iter = 10000, nfolds = ceiling(length(Y)/3), eps = 1e-04,
  verbose = TRUE)

Arguments

X

an n x p covariate matrix with each row being a sample. Must have same number of rows as the size of Y.

Y

a size n outcome vector.

loss

a character string specifying the loss function to be minimized. Must be one of "scad" (default) "mcp" or "lasso". You can just specify the initial letter.

robust

a boolean, specifying whether or not to use robust estimators for mean and variance. Default is TRUE.

cv

a boolean, specifying whether or not to run cross-validation for the tuning parameter. Default is FALSE. Only used if robust is TRUE.

tau

>0, multiplier for the tuning parameter for Huber loss function. Default is 2. Only used if robust is TRUE and cv is FALSE. See details.

lin.reg

a boolean, specifying whether or not to assume that we have a linear regression model (TRUE) or a logit model (FALSE) structure. Default is TRUE.

K.factors

number of factors to be estimated. Otherwise estimated internally. K>0.

max.iter

maximum number of iterations across the regularization path. Default is 10000.

nfolds

the number of cross-validation folds. Default is ceiling(samplesize/3).

eps

Convergence threshhold for model fitting using ncvreg. The algorithm iterates until the RMSD for the change in linear predictors for any coefficient is less than eps. Default is 1e-4.

verbose

a boolean specifying whether to print runtime updates to the console. Default is TRUE.

Details

For formula of how the covariates are adjusted for latent factors, see Section 3.2 in Fan et al.(2017).

The tuning parameter = tau * sigma * optimal rate where optimal rate is the optimal rate for the tuning parameter. For details, see Fan et al.(2017). sigma is the standard deviation of the data.

ncvreg is used to fit the model after decorrelation. This package may output its own warnings about failures to converge and model saturation.

Value

A list with the following items

model.size

the size of the model

beta.chosen

the indices of the covariates chosen in the model

coef.chosen

the coefficients of the chosen covariates

X.residual

the residual covariate matrix after adjusting for factors

nfactors

number of (estimated) factors

n

number of observations

p

number of dimensions

robust

whether robust parameters were used

loss

loss function used

#' @details Number of rows and columns of the covariate matrix must be at least 4 in order to be able to calculate latent factors.

References

Fan J., Ke Y., Wang K., "Decorrelation of Covariates for High Dimensional Sparse Regression." https://arxiv.org/abs/1612.08490

See Also

print.farm.select farm.res

Examples

##linear regression
set.seed(100)
P = 200 #dimension
N = 50 #samples
K = 3 #nfactors
Q = 3 #model size
Lambda = matrix(rnorm(P*K, 0,1), P,K)
F = matrix(rnorm(N*K, 0,1), N,K)
U = matrix(rnorm(P*N, 0,1), P,N)
X = Lambda%*%t(F)+U
X = t(X)
beta_1 = rep(5,Q)
beta = c(beta_1, rep(0,P-Q))
eps = rt(N, 2.5)
Y = X%*%beta+eps

##with default options
output = farm.select(X,Y) #robust, no cross-validation
output$beta.chosen #variables selected
output$coef.chosen #coefficients of selected variables

#examples of other robustification options
output = farm.select(X,Y,robust = FALSE) #non-robust
output = farm.select(X,Y, tau = 3) #robust, no cross-validation, specified tau
#output = farm.select(X,Y, cv= TRUE) #robust, cross-validation: LONG RUNNING!

##changing the loss function and inputting factors
output = farm.select(X, Y,loss = "mcp", K.factors = 4)

##use a logistic regression model, a larger sample size is desired.
## Not run: 
set.seed(100)
P = 400 #dimension
N = 300 #samples
K = 3 #nfactors
Q = 3 #model size
Lambda = matrix(rnorm(P*K, 0,1), P,K)
F = matrix(rnorm(N*K, 0,1), N,K)
U = matrix(rnorm(P*N, 0,1), P,N)
X = Lambda%*%t(F)+U
X = t(X)
beta_1 = rep(5, Q)
beta = c(beta_1, rep(0,P-Q))
eps = rnorm(N)
Prob = 1/(1+exp(-X%*%beta))
Y = rbinom(N, 1, Prob)

output = farm.select(X,Y, lin.reg=FALSE, eps=1e-3)
output$beta.chosen
output$coef.chosen

## End(Not run)