llm {bhm}

Fit an L-shape linear model

Description

Fit an L-shape linear model with the cut point estimated by the profile likelihood method.

Usage

## S3 method for class 'formula'
llm(formula, data=list(...), epsilon = 0.025, ...)

Arguments

formula

an object of class "formula": a sympolic description of the model to be fitted. The details of model specificatoin are given under 'Details'.

data

an optional data frame, list or enviroment containing the variables in the model.

epsilon

Step width for the profile likelihood method, default is 0.025

...

additional arguments to be passed to the low level regression fitting functions (see below).

Details

Define a L shape linear funcation that change slope at c0:

when x <c0, y = b1 + b2*x

when x>=c0, y = b1 + b2*x + b3*(x-x0) = (b1-b3*c0) + (b2+b3)*x

Value

llm returns an object of class inheriting from "llm" which inherits from the class glm. See later in this section.

An object of class "llm" is a list containing at least the following components:

coefficients

a named vector of coefficients from 'llm'

residuals

the residuals, that is response minus fitted values.

fitted.values

the fitted mean values.

rank

the numeric rank of the fitted linear model.

df.residual

the residual degrees of freedom.

call

the matched call.

terms

the 'terms' object used.

c.max

the maximum likelihood estimate for the threshold parameter(s).

loglik

the log-likelihood with the final values of the coefficients.

Author(s)

Bingshu E. Chen ([e-mail])

References

Liu, S. S. and Chen, B. E. (2020). Continuous threshold models with two-way interactions in survival analysis. Canadian Journal of Statistics. Vol. 48, page 751-772.

See Also

brm, lm, glm

Examples

#### simulate the data and fit a L-shape model.
n = 50 ; p <- 2
X = matrix(rnorm(n * p), n, p) # no intercept!
w = X[, 1]; age = X[, 2]

wc = w - 0.2; sigma = 0.25
y = rnorm(n, -0.1+0.7*w-1.2*ifelse(wc>0, wc, 0), sigma)

fit=llm(y~w+age)
print(fit)
print(summary(fit))
#### to plot the L-shape function
# plot(fit)