I have a linear regression of the form
Y = a + b1 * X1 + b2 * X2 + b3 * X4
I would like to constrain the intercept parameter a to be a => 0 (i.e., a should be a non-negative value).
What are possible ways to do this in R? Specifically, I would be interested in solutions using the caret package.
Thank you for your answers.
A linear model.
m0 <- lm(wt ~ qsec + hp + disp, data = mtcars)
m0
#
# Call:
# lm(formula = wt ~ qsec + hp + disp, data = mtcars)
#
# Coefficients:
# (Intercept) qsec hp disp
# -2.450047 0.201713 0.003466 0.006755
Force the intercept to be zero.
m1 <- lm(wt ~ qsec + hp + disp - 1, data = mtcars)
m1
#
# Call:
# lm(formula = wt ~ qsec + hp + disp - 1, data = mtcars)
#
# Coefficients:
# qsec hp disp
# 0.0842281 0.0002622 0.0072967
You can use nls to apply limits to the paramaters (in this case the lower limit).
m1n <- nls(wt ~ a + b1 * qsec + b2 * hp + b3 * disp,
data = mtcars,
start = list(a = 1, b1 = 1, b2 = 1, b3 = 1),
lower = c(0, -Inf, -Inf, -Inf), algorithm = "port")
m1n
# Nonlinear regression model
# model: wt ~ a + b1 * qsec + b2 * hp + b3 * disp
# data: mtcars
# a b1 b2 b3
# 0.0000000 0.0842281 0.0002622 0.0072967
# residual sum-of-squares: 4.926
#
# Algorithm "port", convergence message: relative convergence (4)
See here for other example solutions.