Perform non-linear hypothesis testing for all model parameters.

```
# S3 method for brmsfit
hypothesis(
x,
hypothesis,
class = "b",
group = "",
scope = c("standard", "ranef", "coef"),
alpha = 0.05,
robust = FALSE,
seed = NULL,
...
)
hypothesis(x, ...)
# S3 method for default
hypothesis(x, hypothesis, alpha = 0.05, robust = FALSE, ...)
```

- x
An

`R`

object. If it is no`brmsfit`

object, it must be coercible to a`data.frame`

. In the latter case, the variables used in the`hypothesis`

argument need to correspond to column names of`x`

, while the rows are treated as representing posterior draws of the variables.- hypothesis
A character vector specifying one or more non-linear hypothesis concerning parameters of the model.

- class
A string specifying the class of parameters being tested. Default is "b" for population-level effects. Other typical options are "sd" or "cor". If

`class = NULL`

, all parameters can be tested against each other, but have to be specified with their full name (see also`variables`

)- group
Name of a grouping factor to evaluate only group-level effects parameters related to this grouping factor.

- scope
Indicates where to look for the variables specified in

`hypothesis`

. If`"standard"`

, use the full parameter names (subject to the restriction given by`class`

and`group`

). If`"coef"`

or`"ranef"`

, compute the hypothesis for all levels of the grouping factor given in`"group"`

, based on the output of`coef.brmsfit`

and`ranef.brmsfit`

, respectively.- alpha
The alpha-level of the tests (default is 0.05; see 'Details' for more information).

- robust
If

`FALSE`

(the default) the mean is used as the measure of central tendency and the standard deviation as the measure of variability. If`TRUE`

, the median and the median absolute deviation (MAD) are applied instead.- seed
A single numeric value passed to

`set.seed`

to make results reproducible.- ...
Currently ignored.

A `brmshypothesis`

object.

Among others, `hypothesis`

computes an evidence ratio
(`Evid.Ratio`

) for each hypothesis. For a one-sided hypothesis, this
is just the posterior probability (`Post.Prob`

) under the hypothesis
against its alternative. That is, when the hypothesis is of the form
`a > b`

, the evidence ratio is the ratio of the posterior probability
of `a > b`

and the posterior probability of `a < b`

. In this
example, values greater than one indicate that the evidence in favor of
`a > b`

is larger than evidence in favor of `a < b`

. For an
two-sided (point) hypothesis, the evidence ratio is a Bayes factor between
the hypothesis and its alternative computed via the Savage-Dickey density
ratio method. That is the posterior density at the point of interest
divided by the prior density at that point. Values greater than one
indicate that evidence in favor of the point hypothesis has increased after
seeing the data. In order to calculate this Bayes factor, all parameters
related to the hypothesis must have proper priors and argument
`sample_prior`

of function `brm`

must be set to `"yes"`

.
Otherwise `Evid.Ratio`

(and `Post.Prob`

) will be `NA`

.
Please note that, for technical reasons, we cannot sample from priors of
certain parameters classes. Most notably, these include overall intercept
parameters (prior class `"Intercept"`

) as well as group-level
coefficients. When interpreting Bayes factors, make sure that your priors
are reasonable and carefully chosen, as the result will depend heavily on
the priors. In particular, avoid using default priors.

The `Evid.Ratio`

may sometimes be `0`

or `Inf`

implying very
small or large evidence, respectively, in favor of the tested hypothesis.
For one-sided hypotheses pairs, this basically means that all posterior
draws are on the same side of the value dividing the two hypotheses. In
that sense, instead of `0`

or `Inf,`

you may rather read it as
`Evid.Ratio`

smaller `1 / S`

or greater `S`

, respectively,
where `S`

denotes the number of posterior draws used in the
computations.

The argument `alpha`

specifies the size of the credible interval
(i.e., Bayesian confidence interval). For instance, if we tested a
two-sided hypothesis and set `alpha = 0.05`

(5%) an, the credible
interval will contain `1 - alpha = 0.95`

(95%) of the posterior
values. Hence, `alpha * 100`

% of the posterior values will
lie outside of the credible interval. Although this allows testing of
hypotheses in a similar manner as in the frequentist null-hypothesis
testing framework, we strongly argue against using arbitrary cutoffs (e.g.,
`p < .05`

) to determine the 'existence' of an effect.

```
if (FALSE) {
## define priors
prior <- c(set_prior("normal(0,2)", class = "b"),
set_prior("student_t(10,0,1)", class = "sigma"),
set_prior("student_t(10,0,1)", class = "sd"))
## fit a linear mixed effects models
fit <- brm(time ~ age + sex + disease + (1 + age|patient),
data = kidney, family = lognormal(),
prior = prior, sample_prior = "yes",
control = list(adapt_delta = 0.95))
## perform two-sided hypothesis testing
(hyp1 <- hypothesis(fit, "sexfemale = age + diseasePKD"))
plot(hyp1)
hypothesis(fit, "exp(age) - 3 = 0", alpha = 0.01)
## perform one-sided hypothesis testing
hypothesis(fit, "diseasePKD + diseaseGN - 3 < 0")
hypothesis(fit, "age < Intercept",
class = "sd", group = "patient")
## test the amount of random intercept variance on all variance
h <- paste("sd_patient__Intercept^2 / (sd_patient__Intercept^2 +",
"sd_patient__age^2 + sigma^2) = 0")
(hyp2 <- hypothesis(fit, h, class = NULL))
plot(hyp2)
## test more than one hypothesis at once
h <- c("diseaseGN = diseaseAN", "2 * diseaseGN - diseasePKD = 0")
(hyp3 <- hypothesis(fit, h))
plot(hyp3, ignore_prior = TRUE)
## compute hypotheses for all levels of a grouping factor
hypothesis(fit, "age = 0", scope = "coef", group = "patient")
## use the default method
dat <- as.data.frame(fit)
str(dat)
hypothesis(dat, "b_age > 0")
}
```