PRIME {misPRIME}

Partial Replacement IMputation Estimation (PRIME) for Missing Covariates

Description

partial replacement imputation estimation conducts imputation and regression simultaneously for missing covariates in additive partially linear model.

Usage

PRIME(
  Y,
  X,
  method = c("PRIME", "PRIME-MA"),
  model_structure = NULL,
  intercept = FALSE,
  bw = NULL,
  k_type = NULL,
  weight_type = c("CP", "CV"),
  L = NULL
)

Arguments

Y

a numeric vector, the response variable.

X

a numeric matrix that may include NAs (missing), the covariate matrix.

method

Users can choose PRIME or PRIME-MA. If method="PRIME", users must provide the model structure (nonlinear part index) in the input argument; If method=="PRIME-MA", then the program automatically applies model averaging methods to reduce reduce the loss of misspecification of models without model structure.

model_structure

only available when method="PRIME". It is a 0/1 index vector representing whether each variable is linear/nonlinear in the partially linear model. For details see Example section.

intercept

logical. if TRUE, an intercept is included in the basis; default is FALSE.

bw

a positive value, specify the bandwidth in estimating missing values, default as NULL. When bw=NULL, it is automatically selected by Silverman's rule of thumb method.

k_type

an optional character string, specify the type of kernel used in iterative estimating algorithm and support 'epk', 'biweight', 'triangle', 'gaussian', 'triweight', 'tricube', 'cosine', 'uniform' in current version, default as 'gaussian'.

weight_type

Options for computing weights for PRIME-MA method. Users can choose among CP and CV.

L

an optional positive integer, degree of the piecewise polynomial, default as '3' for cubic splines.

Value

an object of class "prime" is a list containing at least the following components:

coef

only available when method="PRIME". A vector of coefficients of partially linear model.

beta

only available when method="PRIME". A vector of coefficients of linear parts in partially linear model.

Cmat

only available when method="PRIME-MA". A list of coefficients of candidate partially linear models.

weight

only available when method="PRIME-MA". The weights for candidate models, each candidate model involves one nonlinear part and others are linear parts.

Examples

data(PRIME_SimuData)
X = PRIME_SimuData[,-1]
Y = PRIME_SimuData[,1]
model_structure <- c(rep(0,5),1,1,1)

# estimation
result <- PRIME(Y, X, method = 'PRIME', model_structure, intercept = FALSE, weight_type = 'CV')
result$coef
result$beta