posterior_interval.stapreg.Rd
The posterior_interval
function computes Bayesian posterior
uncertainty intervals. These intervals are also often referred
to as credible intervals.
# S3 method for stapreg posterior_interval(object, prob = 0.9, type = "central", pars = NULL, regex_pars = NULL, ...)
object  A fitted model object returned by one of the
rstap modeling functions. See 

prob  A number \(p \in (0,1)\) indicating the desired
probability mass to include in the intervals. The default is to report
\(90\)% intervals ( 
type  The type of interval to compute. Currently the only option is

pars  An optional character vector of parameter names. 
regex_pars  An optional character vector of regular
expressions to use for parameter selection. 
...  Currently ignored. 
A matrix with two columns and as many rows as model parameters (or
the subset of parameters specified by pars
and/or
regex_pars
). For a given value of prob
, \(p\), the columns
correspond to the lower and upper \(100p\)% interval limits and have the
names \(100\alpha/2\)% and \(100(1  \alpha/2)\)%, where \(\alpha
= 1p\). For example, if prob=0.9
is specified (a \(90\)%
interval), then the column names will be "5%"
and "95%"
,
respectively.
Unlike for a frenquentist confidence interval, it is valid to say that, conditional on the data and model, we believe that with probability \(p\) the value of a parameter is in its \(100p\)% posterior interval. This intuitive interpretation of Bayesian intervals is often erroneously applied to frequentist confidence intervals. See Morey et al. (2015) for more details on this issue and the advantages of using Bayesian posterior uncertainty intervals (also known as credible intervals).
We default to reporting \(90\)% intervals rather than \(95\)% intervals for several reasons:
Computational stability: \(90\)% intervals are more stable than \(95\)% intervals (for which each end relies on only \(2.5\)% of the posterior draws).
Relation to TypeS errors (Gelman and Carlin, 2014): \(95\)% of the mass in a \(90\)% central interval is above the lower value (and \(95\)% is below the upper value). For a parameter \(\theta\), it is therefore easy to see if the posterior probability that \(\theta > 0\) (or \(\theta < 0\)) is larger or smaller than \(95\)%.
Of course, if \(95\)% intervals are desired they can be computed by
specifying prob=0.95
.
Currently posterior_interval
only computes central intervals because
other types of intervals are rarely useful for the models that rstap
can estimate. Additional possibilities may be provided in future releases as
more models become available.
Gelman, A. and Carlin, J. (2014). Beyond power calculations: assessing Type S (sign) and Type M (magnitude) errors. Perspectives on Psychological Science. 9(6), 64151.
Morey, R. D., Hoekstra, R., Rouder, J., Lee, M. D., and Wagenmakers, E. (2016). The fallacy of placing confidence in confidence intervals. Psychonomic Bulletin & Review. 23(1), 103123.
predictive_interval
for predictive intervals.
#> 5% 95% #> (Intercept) 0.337929817 0.85413584 #> centered_income 0.099481707 0.18529452 #> sex 0.168857465 0.61993844 #> centered_age 0.024665565 0.48883692 #> Coffee_Shop 0.025062586 0.01613831 #> Coffee_Shop_spatial_scale 0.928690973 19.31034138 #> Coffee_Shop_temporal_scale 0.932842404 8.04121361 #> b[(Intercept) subj_ID:1] 0.041123496 0.54308090 #> b[(Intercept) subj_ID:2] 0.229638315 0.48366472 #> b[(Intercept) subj_ID:3] 0.162877587 0.33464210 #> b[(Intercept) subj_ID:4] 0.123127495 0.31668256 #> b[(Intercept) subj_ID:5] 0.253356962 0.11250896 #> b[(Intercept) subj_ID:6] 0.057953777 0.23293371 #> b[(Intercept) subj_ID:7] 0.199121476 0.12333933 #> b[(Intercept) subj_ID:8] 0.039992200 0.49281622 #> b[(Intercept) subj_ID:9] 0.199664050 0.13760538 #> b[(Intercept) subj_ID:10] 0.199748384 0.10789194 #> Sigma[subj_ID:(Intercept),(Intercept)] 0.001314344 0.13795537 #> sigma 0.319289265 0.77705298posterior_interval(example_model, regex_pars = "Coffee_Shop")#> 5% 95% #> Coffee_Shop 0.02506259 0.01613831 #> Coffee_Shop_spatial_scale 0.92869097 19.31034138 #> Coffee_Shop_temporal_scale 0.93284240 8.04121361