cv.CGEInfo {GEInfo}

Cross-validation for CGEInfo

Description

Does k-fold cross-validation for CGEInfo, returns the estimation results at best tunings, and produces a heatmap for the identification results.

Usage

cv.CGEInfo(
  E,
  G,
  Y,
  family,
  nfolds = 3,
  xi = 6,
  epsilon = 0,
  max.it = 500,
  thresh = 0.001,
  criterion = "BIC",
  lam1 = NULL,
  lam2 = NULL,
  S_G = NULL,
  S_GE = NULL
)

Arguments

E

Observed matrix of E variables, of dimensions n x q.

G

Observed matrix of G variables, of dimensions n x p.

Y

Response variable, of length n. Quantitative for family="gaussian", or family="poisson" (non-negative counts). For family="binomial" should be a factor with two levels.

family

Model type: one of ("gaussian", "binomial", "poisson").

nfolds

Number of folds. Default is 3. Although nfolds can be as large as the sample size n (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable is nfolds=3. See Details.

xi

Tuning parameter of MCP penalty. Default is 6.

epsilon

Tuning parameter of Ridge penalty which shrinks the coefficients having prior information. Default is 0.

max.it

Maximum number of iterations (total across entire path). Default is 500.

thresh

Convergence threshold for group coordinate descent algorithm. The algorithm iterates until the change for each coefficient is less than thresh. Default is 1e-3.

criterion

Criterion used for cross-validation. Currently five options: MSE, AIC, BIC, EBIC, GCV. Default is BIC. See Details.

lam1

A user supplied lambda1 sequence. Typical usage is to have the program compute its own lambda1 sequence. Supplying a value of lam1 overrides this. Default is lam1=NULL.

lam2

A user supplied lambda2 sequence. Default is lam2=NULL. Typical usage is to have the program compute its own lambda2 sequence. Supplying a value of lam2 overrides this. Default is lam2=NULL.

S_G

A user supplied vector, denoting the subscript of G variables which have prior information. Default is NULL. See Details.

S_GE

A user supplied matrix, denoting the subscript of G-E interactions which have prior information. The first and second columns of S_GE represent the subscript of G variable and the subscript of E variable, respectively. For example, S_GE = matrix( c(1, 2), ncol = 2), indicating that the 1st G variable and the 2nd E variables have an interaction effect on Y. Default is NULL. If both S_G and S_GE are NULL, no prior information is incorporated in the model, in which case this function realizes GEsgMCP approach. See Details.

Details

The function calls CGEInfo nfolds times, each time leaving out 1/nfolds of the data. The cross-validation error is based on the user given "criterion". cv.CGEInfo supports to construct two methods: GEInfo and GEsgMCP, depending on whether S_G and S_GE are NULL. When either S_G or S_GE is not NULL, CGEInfo approach is realized, which completely trusts the prior information. Otherwise, GEsgMCP approach is constructed, in which no prior information is incorporated.

In order to select the optimal tunings, there are five criteria available, which are MSE, AIC, BIC, GCV, and EBIC. Let L be the loss function of the model, MSE=L, AIC=2L+2df, BIC=2L+ln(n)df, GCV=2L/(1-df/n)^2, and EBIC=2L+ln(n)df + 2df ln(nvar) (1-ln(n)/(2ln(nvar))). In most cases, BIC is a good choice. In the case of high dimension, EBIC criterion is recommended first, which has demonstrated satisfactory performance in high-dimensional studies.

Value

An object of class "GEInfo" is returned, which is a list with the ingredients of the cross-validation fit.

best.tuning

A vector of length 2, containing the best lambda1 and lambda2 selected by cross-validation.

a

Coefficient vector of length q for all E variables.

beta

Coefficient vector of length p for all G variables.

gamma

Coefficient matrix of dimensions p*q for G-E interactions.

b

Coefficient vector of length (q+1)*p for W (G variables and G-E interactions).

alpha

Intercept.

coef

A coefficient vector of length (q+1)*(p+1), including the estimates for \alpha (intercept), a (coefficients for all E variables), and b (coefficients for all G variables and G-E interactions).

nvar

Number of non-zero coefficients at the best tunings.

References

Wang X, Xu Y, and Ma S. (2019). Identifying gene-environment interactions incorporating prior information. Statistics in medicine, 38(9): 1620-1633. doi: 10.1002/sim.8064

Examples

n <- 30; p <- 5; q <- 2
E <- MASS::mvrnorm(n, rep(0,q), diag(q))
G <- MASS::mvrnorm(n, rep(0,p), diag(p))
W <- matW(E, G)
alpha <- 0; a <- seq(0.4, 0.6, length=q);
beta <- c(seq(0.2, 0.5, length=3),rep(0, p-3))
vector.gamma <- c(0.8, 0.5, 0, 0)
gamma <- matrix(c(vector.gamma, rep(0, p*q - length(vector.gamma))), nrow=p, byrow=TRUE)
mat.b.gamma <- cbind(beta, gamma)
b <- as.vector (t(mat.b.gamma))
Y <- alpha + E %*% a + W %*% b + rnorm (n, 0, 0.5)
S_G <- c(1)
S_GE <- cbind(c(1), c(1))
fit2 <- cv.CGEInfo(E, G, Y,family='gaussian', S_G=S_G, S_GE=S_GE,lam1=0.4,lam2=0.4)