| Title: | Lind/Mehlum Utest |
| Version: | 0.4.0 |
| Description: | An implementation of Lind and Mehlum's (2010) <doi:10.1111/j.1468-0084.2009.00569.x> Utest to test for the presence of a U shaped or inverted U shaped relationship between variables in (generalized) linear models. It also implements a test of upward/downward sloping relationships at the lower and upper boundary of the data range. |
| URL: | https://github.com/jotlind/utest |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Suggests: | testthat |
| NeedsCompilation: | no |
| Packaged: | 2025-08-21 08:13:52 UTC; jlind |
| Author: | Jo Thori Lind 
[aut, cre],
Halvor Mehlum [aut] |
| Maintainer: | Jo Thori Lind <j.t.lind@econ.uio.no> |
| Repository: | CRAN |
| Date/Publication: | 2025-08-26 19:50:02 UTC |
utest: Lind/Mehlum Utest
Description
An implementation of Lind and Mehlum's (2010) doi:10.1111/j.1468-0084.2009.00569.x Utest to test for the presence of a U shaped or inverted U shaped relationship between variables in (generalized) linear models. It also implements a test of upward/downward sloping relationships at the lower and upper boundary of the data range.
Author(s)
Maintainer: Jo Thori Lind j.t.lind@econ.uio.no (ORCID)
Authors:
Halvor Mehlum halvor.mehlum@econ.uio.no
See Also
Useful links:
Estimates slopes at extremes
Description
This function estimates the slope of the relationship at the lower and upper extreme points of the independent variable
Usage
uslopes(lmObject, vars, .vcov = NULL, x.min = NULL, x.max = NULL)
Arguments
lmObject |
The model to be tested |
vars |
A vector with the name of the linear and squared terms. Can also be provided as a formula |
.vcov |
The covariance matrix to use |
x.min |
Lower bound of interval. If |
x.max |
Upper bound of interval. If |
Details
The function computes slopes of a quadratic relationship at the lower and upper bound defined by x.min and x.max. Standard errors of the
estimated slopes, t-values, and p-values from a one-sided test of a flat relationship as well as the extreme point of the estimated relationship are also provided.
Value
A list with class "uslopes" containing the following components:
interval |
a vector with the interval for the independent varaible. |
slope |
a vector with the slope of the relationship at the extremes. |
tval |
a vector with the t-value of the relationship at the extremes. |
pval |
a vector with the p-value from a one-sided test a the extremes of the interval. |
extreme |
the estimated extreme point of the relationship. |
See Also
Examples
x <- runif(100,min=-1,max=1)
xsq <- x^2
y <- x^2+rnorm(100)
mod <- lm(y~x+xsq)
uslopes(mod,c("x","xsq"))
uslopes(mod,~x+xsq,x.max=0.8)
Perform Utest
Description
This function computes the Lind/Mehlum test of a U shaped relationship.
Usage
utest(lmObject, vars, .vcov = NULL, x.min = NULL, x.max = NULL)
Arguments
lmObject |
The model to be tested |
vars |
A vector with the name of the linear and squared terms. Can also be provided as a formula |
.vcov |
The covariance matrix to use |
x.min |
Lower bound of interval. If |
x.max |
Upper bound of interval. If |
Details
To test for a U shaped or inverse U shaped relationship, it is necessary to provide an interval where the shape is located. A U shaped relationship is downward sloping at the lower bound and upward sloping at the upper bound, and vice versa for an inverted U shape.
The function assumes inputs from a model including a squared specification. The sign of the squared term is used to differentiate between U shaped and inverted U shaped relationships.
The function provides a test of the joint hypothesis of a downward sloping relationship at x.min and an uppward sloping relationship
at x.max for U shaped relationships and vice versa for inverted U shaped relationships, as detailed in Lind and Mehlum (2010) doi:10.1111/j.1468-0084.2009.00569.x.
Value
A list with class "htest" containing the following components:
statistic |
the test statistic. |
p.value |
the p-value for the test. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name(s) of the data. |
alternative |
a character string describing the alternative hypothesis. |
References
J. T. Lind and H. Mehlum (2010) , With or without U? The appropriate test for a U shaped relationship. Oxford Bulletin of Economics and Statistics 72(1): 109-18, doi:10.1111/j.1468-0084.2009.00569.x.
See Also
Examples
x <- runif(100,min=-1,max=1)
xsq <- x^2
y <- x^2+rnorm(100)
mod <- lm(y~x+xsq)
utest(mod,c("x","xsq"))
utest(mod,~x+xsq,x.max=0.8)
mod.logit <- glm((y>0)~x+xsq,family="binomial")
utest(mod.logit,c("x","xsq"))