Specify a normal prior

Construct a normal prior for passing to mlumr() via prior_intercept, prior_beta, or prior_sigma. The resulting list is consumed by the Stan models.

Usage

prior_normal(mean = 0, sd = 10, autoscale = FALSE)

Arguments

mean

Prior mean (default 0).

sd

Prior standard deviation (default 10). The default matches the historical "very weak" scale; explicit tighter values are recommended for regression coefficients (see Details).

autoscale

If TRUE and this prior is passed as prior_beta, the scale is divided by each covariate's empirical SD so the prior is weakly-informative regardless of predictor scaling, and for family = "normal" with the identity link also multiplied by the IPD outcome SD, since the coefficients are then in outcome units. Default FALSE to preserve backward-compatible behavior; set to TRUE explicitly when passing unstandardized predictors. Ignored for prior_intercept and prior_sigma.

Value

A list with components distribution, mean, sd, df, autoscale.

Choosing a scale

The default intercept prior normal(0, 10) is very weak on the link scale, and the data usually constrain the intercept strongly. The coefficient default normal(0, 2.5) is a generic starting value on the link scale per unit of covariate, not a calibrated choice; use autoscale = TRUE for predictors on different scales and calibrate with prior predictive checks (Gelman et al., 2008; the Stan prior-choice wiki). prior_sigma is a normal truncated at zero through the Stan <lower=0> constraint, a half-normal at the default mean of 0.

For family = "normal" the identity link is not unit-free: the intercepts and coefficients are in the outcome's units, and so is the residual SD under either link. There the package defaults are read in units of the IPD outcome SD, sd(y): normal(0, 10 * sd(y)) for the intercepts, normal(0, 2.5 * sd(y)) for the coefficients (identity link) and a half-normal with scale 2.5 * sd(y) for the residual SD (either link), and autoscale = TRUE gives a coefficient scale of sd * sd(y) / sd(x). A prior written out by the user is used as given. prior_summary() prints the scales the model used. Run prior_sensitivity() for the relaxed model, whose beta_comparator is identified only by the aggregate likelihood.

References

Gelman, A., Jakulin, A., Pittau, M. G., & Su, Y.-S. (2008). A weakly informative default prior distribution for logistic and other regression models. Annals of Applied Statistics, 2(4), 1360-1383.

Vehtari, A. et al. Prior Choice Recommendations (Stan wiki): https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations.

Examples

# Default weakly-very-weak intercept prior
prior_normal(mean = 0, sd = 10)
#> $distribution
#> [1] "normal"
#> 
#> $mean
#> [1] 0
#> 
#> $sd
#> [1] 10
#> 
#> $df
#> [1] NA
#> 
#> $autoscale
#> [1] FALSE
#> 

# Package starting value for regression coefficients
prior_normal(mean = 0, sd = 2.5)
#> $distribution
#> [1] "normal"
#> 
#> $mean
#> [1] 0
#> 
#> $sd
#> [1] 2.5
#> 
#> $df
#> [1] NA
#> 
#> $autoscale
#> [1] FALSE
#> 

# Autoscaled coefficient prior (dividing 2.5 by each covariate's SD)
prior_normal(mean = 0, sd = 2.5, autoscale = TRUE)
#> $distribution
#> [1] "normal"
#> 
#> $mean
#> [1] 0
#> 
#> $sd
#> [1] 2.5
#> 
#> $df
#> [1] NA
#> 
#> $autoscale
#> [1] TRUE
#>