BFs {BayesRep} | R Documentation |
Computes the sceptical Bayes factor
BFs(to, so, tr, sr, truncate = FALSE, zo = NULL, zr = NULL, c = NULL)
to |
Original effect estimate |
so |
Standard error of the original effect estimate |
tr |
Replication effect estimate |
sr |
Standard error of the replication effect estimate |
truncate |
Logical indicating whether advocacy prior should be truncated
to direction of the original effect estimate (i.e., a one-sided test).
Defaults to |
zo |
Original z-value |
zr |
Replication z-value |
c |
Relative variance |
The sceptical Bayes factor is a summary measure of the following two-step reverse-Bayes procedure for assessing replication success:
Use the data from the original study to determine the standard deviation
\tau_{\gamma}
of a sceptical normal prior \theta \sim
\mathrm{N}(0, \tau_{\gamma}^2)
such that the
Bayes factor contrasting the null hypothesis H_0: \theta = 0
to the sceptic's hypothesis H_{\mathrm{S}}: \theta \sim
\mathrm{N}(0, \tau_{\gamma}^2)
equals a
specified level \gamma \in (0, 1]
. This prior
represents a sceptic who remains unconvinced about the presence of an effect
at level \gamma
.
Use the data from the replication study to compare the sceptic's
hypothesis H_{\mathrm{S}}: \theta \sim \mathrm{N}(0,
\tau_{\gamma}^2)
to the advocate's hypothesis
H_{\mathrm{A}}: \theta \sim f(\theta \, | \,
\mathrm{original~study})
. The prior of
the effect size under H_{\mathrm{A}}
is its posterior based on the
original study and a uniform prior, thereby representing the position of an
advocate of the original study. Replication success at level
\gamma
is achieved if the Bayes factor contrasting
H_{\mathrm{S}}
to H_{\mathrm{A}}
is smaller than
\gamma
, which means that the replication data favour the
advocate over the sceptic at a higher level than the sceptic's initial
objection. The sceptical Bayes factor \mathrm{BF}_{\mathrm{S}}
is
the smallest level \gamma
at which replication success can be
established.
The function can be used with two input parametrizations, either on the
absolute effect scale (to
, so
, tr
, sr
) or
alternatively on the relative z-scale (zo
, zr
, c
). If
an argument on the effect scale is missing, the z-scale is automatically
used and the other non-missing arguments on the effect scale ignored.
The sceptical Bayes factor \mathrm{BF}_{\mathrm{S}}
.
\mathrm{BF}_{\mathrm{S}} < 1
indicates replication
success, the smaller the value of \mathrm{BF}_{\mathrm{S}}
the higher the degree of replication success. It is possible that the
result of the replication is so inconclusive that replication success
cannot be established at any level. In this case, the sceptical Bayes
factor does not exist and the function returns NaN
.
Samuel Pawel
Pawel, S. and Held, L. (2022). The sceptical Bayes factor for the assessment of replication success. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84(3): 879-911. doi:10.1111/rssb.12491
to <- 2
tr <- 2.5
so <- 1
sr <- 1
BFs(to = to, so = so, tr = tr, sr = sr)
BFs(zo = to/so, zr = tr/sr, c = so^2/sr^2)