llm function

Fit an L-shape linear model

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

## 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 + b2x + b3(x-x0) = (b1-b3*c0) + (b2+b3)*x

Returns

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.

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.

Author(s)

Bingshu E. Chen (bingshu.chen@queensu.ca)

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)