joint_tests  R Documentation 
This function produces an analysisofvariancelike table based on linear
functions of predictors in a model or emmGrid
object. Specifically,
the function constructs, for each combination of factors (or covariates
reduced to two or more levels), a set of (interaction) contrasts via
contrast
, and then tests them using test
with
joint = TRUE
. Optionally, one or more of the predictors may be used as
by
variable(s), so that separate tables of tests are produced for
each combination of them.
joint_tests(object, by = NULL, show0df = FALSE, showconf = TRUE,
cov.reduce = make.meanint(1), ...)
make.meanint(delta)
meanint(x)
make.symmint(ctr, delta)
symmint(ctr)
object 
a fitted model, 
by 
character names of 
show0df 
logical value; if 
showconf 
logical value.
When we have models with estimability issues (e.g., missing cells), then with

cov.reduce 
a function.
If 
... 
additional arguments passed to 
delta, ctr 
arguments for 
x 
argument for 
In models with only factors, no covariates, these tests correspond to
“type III” tests a la SAS, as long as equalweighted averaging
is used and there are no estimability issues. When covariates are present and
they interact with factors, the results depend on how the covariate is
handled in constructing the reference grid. See the section on covariates
below. The point that one must always remember is that joint_tests
always tests contrasts among EMMs, in the context of the reference grid,
whereas type III tests are tests of model coefficients – which may or may
not have anything to do with EMMs or contrasts.
a summary_emm
object (same as is produced by
summary.emmGrid
). All effects for which there are no
estimable contrasts are omitted from the results.
There may be an additional row named (confounded)
which accounts
for additional degrees of freedom for effects not accounted for in the
preceding rows.
The returned object also includes an "est.fcns"
attribute, which is a
named list containing the linear functions associated with each joint test.
No estimable functions are included for confounded effects.
make.meanint
returns the function
function(x) mean(x) + delta * c(1, 1)
,
and make.symmint(ctr, delta)
returns the function
function(x) ctr + delta * c(1, 1)
(which does not depend on x
).
The cases with delta = 1
, meanint = make.meanint(1)
and symmint(ctr) = make.symmint(ctr, 1)
are retained for backcompatibility reasons.
These functions are available primarily for use with cov.reduce
.
A covariate (or any other predictor) must have more than one value in
the reference grid in order to test its effect and be included in the results.
Therefore, when object
is a model, we default to cov.reduce = meanint
which sets each covariate at a symmetric interval about its mean. But
when object
is an existing reference grid, it often has only one value
for covariates, in which case they are excluded from the joint tests.
Covariates present further complications in that their values in the
reference grid can affect the joint tests of other effects. When
covariates are centered around their means (the default), then the tests we
obtain can be described as joint tests of covariateadjusted means; and that
is our intended use here. However, some software such as SAS and
car::Anova
adopt the convention of centering covariates around zero;
and for that purpose, one can use cov.reduce = symmint(0)
when calling
with a model object (or in constructing a reference grid). However, adjusted
means with covariates set at or around zero do not make much sense in the
context of interpreting estimated marginal means, unless the covariate means
really are zero.
See the examples below with the toy
dataset.
test
pigs.lm < lm(log(conc) ~ source * factor(percent), data = pigs)
(jt < joint_tests(pigs.lm)) ## will be same as type III ANOVA
### Estimable functions associated with "percent"
attr(jt, "est.fcns") $ "percent"
joint_tests(pigs.lm, weights = "outer") ## differently weighted
joint_tests(pigs.lm, by = "source") ## separate joint tests of 'percent'
### Comparisons with type III tests in SAS
toy = data.frame(
treat = rep(c("A", "B"), c(4, 6)),
female = c(1, 0, 0, 1, 0, 0, 0, 1, 1, 0 ),
resp = c(17, 12, 14, 19, 28, 26, 26, 34, 33, 27))
toy.fac = lm(resp ~ treat * factor(female), data = toy)
toy.cov = lm(resp ~ treat * female, data = toy)
# (These two models have identical fitted values and residuals)
#  SAS output we'd get with toy.fac 
## Source DF Type III SS Mean Square F Value Pr > F
## treat 1 488.8928571 488.8928571 404.60 <.0001
## female 1 78.8928571 78.8928571 65.29 0.0002
## treat*female 1 1.7500000 1.7500000 1.45 0.2741
#
#  SAS output we'd get with toy.cov 
## Source DF Type III SS Mean Square F Value Pr > F
## treat 1 252.0833333 252.0833333 208.62 <.0001
## female 1 78.8928571 78.8928571 65.29 0.0002
## female*treat 1 1.7500000 1.7500000 1.45 0.2741
joint_tests(toy.fac)
joint_tests(toy.cov) # female is regarded as a 2level factor by default
## Treat 'female' as a numeric covariate (via cov.keep = 0)
## ... then tests depend on where we center things
# Center around the mean
joint_tests(toy.cov, cov.keep = 0, cov.reduce = make.meanint(delta = 1))
# Center around zero (like SAS's results for toy.cov)
joint_tests(toy.cov, cov.keep = 0, cov.reduce = make.symmint(ctr = 0, delta = 1))
# Center around 0.5 (like SAS's results for toy.fac)
joint_tests(toy.cov, cov.keep = 0, cov.reduce = range)
### Example with empty cells and confounded effects
low3 < unlist(attr(ubds, "cells")[1:3])
ubds.lm < lm(y ~ A*B*C, data = ubds, subset = low3)
# Show overall joint tests by C:
ref_grid(ubds.lm, by = "C") > contrast("consec") > test(joint = TRUE)
# Break each of the above into smaller components:
joint_tests(ubds.lm, by = "C")
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