summary.kspm {KSPM}

Summarizing Kernel Semi parametric Model Fits

Description

summary method for an object of class "kspm"

Usage

## S3 method for class 'kspm'
summary(object, kernel.test = "all",
  global.test = FALSE, ...)

Arguments

object

an object of class "kspm", usually, a result of a call to kspm.

kernel.test

vector of characters indicating for which kernel a test should be performed. Default is "all". If "none", no test will be performed.

global.test

logical, if TRUE, a global test for kernel part is computed.

...

further arguments passed to or from other methods.

Details

the description of the model, including coefficients for the linear part and if asked for, test(s) of variance components associated with kernel part.

Value

Computes and returns the followimg summary statistics of the fitted kernel semi parametric model given in object

residuals

residuals

coefficients

a p \times 4 matrix with columns for the estimated coefficient, its standard error, t statistic and corresponding (two sided) p value for the linear part of the model.

sigma

the square root of the estimated variance of the random error \sigma^2 = \frac{RSS}{edf} where RSS is the residual sum of squares and edf is the effective degree of freedom.

edf

effective degrees of freedom

r.squared

R^2, the fraction of variance explained by the model, 1 - \frac{\sum e_i^2}{\sum(y_i - y^{\ast})^2} where y^{\ast} is the mean of y_i if there is an intercept and zero otherwise.

adj.r.squared

the above R^2 statistics, adjusted, penalizing for higher p.

score.test

a q \times 3 matrix with colums for the estimated lambda, tau and p value for the q kernels for which a test should be performed.

global.p.value

p value from the score test for the global model.

sample.size

sample size (all: global sample size, inc: complete data sample size).

Author(s)

Catherine Schramm, Aurelie Labbe, Celia Greenwood

References

Liu, D., Lin, X., and Ghosh, D. (2007). Semiparametric regression of multidimensional genetic pathway data: least squares kernel machines and linear mixed models. Biometrics, 63(4), 1079:1088.

Schweiger, Regev, et al. "RL SKAT: an exact and efficient score test for heritability and set tests." Genetics (2017): genetics 300395.

Li, Shaoyu, and Yuehua Cui. "Gene centric gene gene interaction: A model based kernel machine method." The Annals of Applied Statistics 6.3 (2012): 1134:1161.

See Also

kspm for fitting model, predict.kspm for predictions, plot.kspm for diagnostics

Examples

x <- 1:15
z1 <- runif(15, 1, 6)
z2 <- rnorm(15, 1, 2)
y <- 3*x + (z1 + z2)^2 + rnorm(15, 0, 2)
fit <- kspm(y, linear = ~ x, kernel = ~ Kernel(~ z1 + z2,
kernel.function = "polynomial", d= 2, rho = 1, gamma = 0))
summary(fit)