This function produces an analysis-of-variance-like 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
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, cov.reduce = range, ...)
character names of
logical value; if
additional arguments passed to
In models with only factors, no covariates, we believe these tests correspond
to “type III” tests a la SAS, as long as equal-weighted
averaging is used and there are no estimability issues. When covariates are
present and interact with factors, the results depend on how the covariate is
handled in constructing the reference grid. See the example at the end of
this documentation. 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.
summary_emm object (same as is produced by
summary.emmGrid). All effects for which there are no
estimable contrasts are omitted from the results.
pigs.lm <- lm(log(conc) ~ source * factor(percent), data = pigs) joint_tests(pigs.lm) ## will be same as type III ANOVA joint_tests(pigs.lm, weights = "outer") ## differently weighted joint_tests(pigs.lm, by = "source") ## separate joint tests of 'percent' ### Comparisons with type III tests 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) joint_tests(toy.fac) joint_tests(toy.cov) # female is regarded as a 2-level factor by default joint_tests(toy.cov, at = list(female = 0.5)) joint_tests(toy.cov, cov.keep = 0) # i.e., female = mean(toy$female) joint_tests(toy.cov, at = list(female = 0)) # -- Compare with SAS output -- female as factor -- ## 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 # # -- Compare with SAS output -- female as covariate -- ## 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
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