gamm4.test (version 0.1.0)

T.L2c: Test the equality of nonparametric curves or surfaces based on L2 distance

Description

This function tests the equality of nonparametric curves and surface estimations based on L2 distance. The specific model considered here is

Usage

T.L2c(formula, test, data, N.boot = 200, degree = 1, criterion = c("aicc",
  "gcv"), family = c("gaussian", "symmetric"), m = 225, user.span = NULL,
  ...)

Arguments

formula

A regression formula. This is like the formula for a lm.

test

An indicator of variable for testing nonparametric curves or surface estimations

data

A data frame or list containing the model response variable and covariates required by the formula.

N.boot

the number of bootstrap replicates. This should be a single positive integer.

degree

the degree of the local polynomials to be used. It can ben 0, 1 or 2.

criterion

the criterion for automatic smoothing parameter selection: ``aicc'' denotes bias-corrected AIC criterion, ``gcv'' denotes generalized cross-validation.

family

if ``gaussian'' fitting is by least-squares, and if ``symmetric'' a re-descending M estimator is used with Tukey's biweight function.

m

the number of the sampling points for the Monte-Carlo integration.

user.span

the user-defined parameter which controls the degree of smoothing.

...

other options from ``loess'' package.

Details

y_ij= m_i(x_ij) + e_ij,

where m_i(.), are semiparametric smooth functions; e_ij are subject-specific errors. The errors e_ij do not have to be independent N(0, sigma^2) errors. The errors can be heteroscedastic, i.e., e_ij = sigma_i(x_ij) * u_ij, where u_ij are independent identically distributed errors with mean 0 and variance 1.

We are interested in the problem of testing the equality of the regression curves (when x is one-dimensional) or surfaces (when x is two-dimensional),

H_0: m_1(.) = m_2(.) = ... v.s. H_1: otherwise

The problem can also be viewed as the test of the equality in the one-sample problem for functional data.

A bootstrap algorithm is applied to test the equality of semiparametric curves or surfaces based on L2 distance.

See Also

gam.grptest

Examples

# NOT RUN {
n1 <- 200
x1 <- runif(n1,min=0, max=3)
sd1 <- 0.2
e1 <- rnorm(n1,sd=sd1)
y1 <- sin(2*x1) + cos(2*x1) + e1

n2 <- 120
x2 <- runif(n2, min=0, max=3)
sd2 <- 0.25
e2 <- rnorm(n2, sd=sd2)
y2 <- sin(2*x2) + cos(2*x2) + x2 + e2

dat <- data.frame(rbind(cbind(x1,y1,1), cbind(x2,y2,2)))
colnames(dat)=c('x','y','group')

t1 <- T.L2c(formula=y~x,test=~group,data=dat)
t1$p.value
########
## Semiparametric test the equality for regression surfaces
## Simulate data sets

n1 <- 200
x11 <- runif(n1,min=0, max=3)
x12 <- runif(n1,min=0, max=3)
sd1 <- 0.2
e1 <- rnorm(n1,sd=sd1)
y1 <- 2*x11^2 + 3*x12^2  + e1

n2 <- 120
x21 <- runif(n2, min=0, max=3)
x22 <- runif(n2, min=0, max=3)
sd2 <- 0.25
e2 <- rnorm(n2, sd=sd2)
y2 <- 2*x21^2 + 3*x22^2 + sin(2*pi*x21) + e2

n3 <- 150
x31 <- runif(n3,min=0, max=3)
x32 <- runif(n3,min=0, max=3)
sd3 <- 0.2
e3 <- rnorm(n3,sd=sd1)
y3 <- 2*x31^2 + 3*x32^2  + e3

data.bind <- data.frame(rbind(cbind(x11, x12 ,y1,1), cbind(x21, x22, y2,2), cbind(x31, x32, y3,3)))
colnames(data.bind)=c('x1','x2', 'y','group')

T.L2c(formula=y~x1+x2,test=~group,data=data.bind)
# }