summary.tsglm {TensorTest2D}

Summarizing Second-order Tensor Generalized Regression Fits

Description

summary method for self-defined class "tsglm".

Usage

## S3 method for class 'tsglm'
summary(object, ...)

Arguments

object

an object of class "tsglm".

...

further arguments passed to or from other methods.

Details

summary.tsglm is combined with print to provide formatting the coefficients, standard errors, etc. and additionally gives 'significance stars'

Value

summary.tsglm returns a printout similar to summary.glm.

The printout contains the following components:

Call: The formula for fitted model.

Deviance Residuals: The summary statistics of deviance residuals. Provide for model except family = "gaussian".

Residuals: The summary statistics of residuals. Provide for family = "gaussian".

Coefficients: The coefficient table includes estimation, standard deviation, test statistics, and p-value of parameters and significance stars.

Deviance: The deviance of a fitted model. Provide for model except family = "gaussian".

AIC: Akaike information criterion.

Author(s)

Mark Chen

See Also

summary, predict.tsglm

Examples

# Simulation data
n <- 500 # number of observations
n_P <- 3; n_G <- 64 # dimension of 3-D tensor variables.
n_d <- 2 # number of numerical variable, if n_d == 1,  numerical variable equals to intercept.
beta_True <- rep(1, n_d)
B_True <- c(1,1,1)%*%t(rnorm(n_G)) + c(0, .5, .5)%*%t(rnorm(n_G))
B_True <- B_True / 10
W <- matrix(rnorm(n*n_d), n, n_d); W[,1] <- 1
W_named <- W
colnames(W_named) <- paste0("w", 1:ncol(W_named))
X <- array(rnorm(n*n_P*n_G), dim=c(n_P, n_G, n))
X_named <- X
dimnames(X_named) <- list(paste0("R", 1:nrow(X_named)),paste0("C", 1:ncol(X_named)))
## Regression
y_R <- as.vector(W%*%beta_True + X%hp%B_True + rnorm(n))
DATA_R <- list(y = y_R, X = X, W = W)
y_R_named <- as.vector(W_named%*%beta_True + X_named%hp%B_True + rnorm(n))
DATA_R_named <- list(y = y_R_named, X = X_named, W = W_named)
## Binomial
p_B <- exp(W%*%beta_True + X%hp%B_True); p_B <- p_B/(1+p_B)
y_B <- rbinom(n, 1, p_B)
DATA_B <- list(y = y_B, W = W, X = X)
## Poisson
p_P <- exp(W%*%beta_True + X%hp%B_True)
y_P <- rpois(n, p_P)
y_P[which(y_P > 170)] <- 170 # If y_P > 170, factorial(y_P) == inf.
DATA_P <- list(y = y_P, W = W, X = X)

# Execution
## Regression
result_R <- tensorReg2D(y = DATA_R$y, X = DATA_R$X, W=NULL, n_R = 1, family = "gaussian",
opt = 1, max_ite = 100, tol = 10^(-7) )
summary(result_R)
head(predict(result_R, DATA_R$X))

## Regression with specified names
result_R_named <- tensorReg2D(y = DATA_R_named$y, X = DATA_R_named$X, W=DATA_R_named$W,
n_R = 1, family = "gaussian", opt = 1, max_ite = 100, tol = 10^(-7) )
summary(result_R_named)

## Binomial
result_B <- tensorReg2D(y = DATA_B$y, X = DATA_B$X, W=NULL, n_R = 1, family = "binomial",
opt = 1, max_ite = 100, tol = 10^(-7) )
summary(result_B)
head(predict(result_B, DATA_B$X))

## Poisson
result_P <- tensorReg2D(y = DATA_P$y, X = DATA_P$X, W=NULL, n_R = 1, family = "poisson",
opt = 1, max_ite = 100, tol = 10^(-7) )
summary(result_P)
head(predict(result_P, DATA_P$X))