This function provides some basic checks on the strength of the prior in the MRLocus slope fitting Bayesian model. It is not desired that the prior overly influences the posterior inference.
priorCheck(res, n = 200, plot = TRUE, type = 1)output of fitSlope
integer, for the plot how many data points to simulate
logical, whether to draw the plots
integer, return type. by default (type=1)
the function returns a table. By setting type=2,
the prior predictive draws for alpha, sigma, beta_a,
and beta_b are returned. See Details regarding the
simulated draws for beta_a
a data.frame with information about prior and posterior SD for alpha and sigma, and two plots are generated (see Details)
The posterior-over-prior SD ratio is calculated
and returned in a table, and two plots are made
that show parameters drawn from the estimated
priors (in MRLocus, two priors are estimated from the data -
the SD of beta, the instrument effects, and the SD of alpha, the slope).
Alternatively, the prior predictive draws themselves can
be returned instead of the table (by setting type=2).
If the posterior-over-prior SD ratio is close to 1 for either alpha or sigma, this indicates undesirable influence of the prior on the posterior inference. For comparison, some consider a posterior-prior SD ratio of 0.1 or higher to be described as an 'informative prior' (from Stan wiki on prior choice recommendations). We note that an 'informative prior' alone is not problematic for MRLocus, and the prior estimation steps have been designed to be informative as to reasonable values for some of the prior parameters of alpha and sigma.
The plots show parameters generated
from the prior and the model. The simulated true values of
beta_a and beta_b are drawn as black
circles (summary statistics would then be drawn from
these according to the reported SEs, but this step
of the model is omitted in this plot).
The two plots differ in that the second plot uses fixed
alpha (fixed to the prior mean) instead of drawing it from the model
(so that the prior for sigma can better be visualized).
The fitted estimates of beta_a and beta_b
from the colocalization step are shown as blue X's.
One exception where parameters are not drawn from the prior is:
beta_a values are instead drawn as uniform
between 0 and 1.1x the maximum value of beta_hat_a
from the colocalization step (for ease of visualization).