# hypothesis

From brms v0.6.0
by PaulChristian Buerkner

##### Non-linear hypothesis testing

Perform non-linear hypothesis testing of fixed effects parameters

##### Usage

`hypothesis(x, hypothesis, class = "b", group = "", alpha = 0.05, ...)`

##### Arguments

- x
- An
`R`

object typically of class`brmsfit`

- 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 fixed 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 - group
- Name of a grouping factor to evaluate only random effects parameters related to this grouping factor.
Ignored if
`class`

is not`"sd"`

or`"cor"`

. - alpha
- the alpha-level of the tests (default is 0.05)
- ...
- Currently ignored

##### Details

Among others, `hypothesis`

calculates an evidence ratio for each hypothesis.
For a directed hypothesis, this is just the posterior probability under the hypothesis against its alternative.
For an undirected (i.e. point) hypothesis the evidence ratio is a Bayes factor between the hypothesis and its alternative.
In order to calculate this Bayes factor, all parameters related to the hypothesis must have proper priors
and argument `sample.priors`

of function `brm`

must be set to `TRUE`

.
When interpreting Bayes factors, make sure that your priors are reasonable and carefully chosen,
as the result will depend heavily on the priors. It particular, avoid using default priors.

##### Value

- Summary statistics of the posterior distributions related to the hypotheses.

##### Examples

```
fit_i <- brm(rating ~ treat + period + carry + (1+treat|subject),
data = inhaler, family = "gaussian", sample.prior = TRUE,
prior = set_prior("normal(0,2)", class = "b"), n.cluster = 2)
hypothesis(fit_i, "treat = period + carry")
hypothesis(fit_i, "exp(treat) - 3 = 0")
## perform one-sided hypothesis testing
hypothesis(fit_i, "period + carry - 3 < 0")
## compare random effects standard deviations
hypothesis(fit_i, "treat < Intercept", class = "sd", group = "subject")
## test the amount of random intercept variance on all variance
h <- paste("sd_subject_Intercept^2 / (sd_subject_Intercept^2 +",
"sd_subject_treat^2 + sigma_rating^2) = 0")
hypothesis(fit_i, h, class = NULL)
## test more than one hypothesis at once
hypothesis(fit_i, c("treat = period + carry", "exp(treat) - 3 = 0"))
```

*Documentation reproduced from package brms, version 0.6.0, License: GPL (>= 3)*

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