loo.stanfit {rstan}  R Documentation 
Approximate leaveoneout crossvalidation
Description
A loo
method that is customized for stanfit objects.
The loo
method for stanfit objects —a wrapper around the array
method for loo
in the loo package — computes PSISLOO CV,
approximate leaveoneout crossvalidation using Pareto smoothed importance
sampling (Vehtari, Gelman, and Gabry, 2017a,2017b).
Usage
## S3 method for class 'stanfit'
loo(x,
pars = "log_lik",
save_psis = FALSE,
cores = getOption("mc.cores", 1),
moment_match = FALSE,
k_threshold = 0.7,
...)
Arguments
x 
An object of S4 class 
pars 
Name of transformed parameter or generated quantity in
the Stan program corresponding to the pointwise loglikelihood. If not
specified the default behavior is to look for 
save_psis 
Should the intermediate results from 
cores 
Number of cores to use for parallelization. The default is 1 unless

moment_match 
Logical; Whether to use the moment matching algorithm for
observations with high Pareto k values to improve accuracy. Note:
because the moment matching algorithm relies on the 
k_threshold 
Threshold value for Pareto k values above which
the moment matching algorithm is used. If 
... 
Ignored. 
Details
Stan does not automatically compute and store the loglikelihood. It is up to the user to incorporate it into the Stan program if it is to be extracted after fitting the model. In a Stan program, the pointwise log likelihood can be coded as a vector in the transformed parameters block (and then summed up in the model block) or it can be coded entirely in the generated quantities block. We recommend using the generated quantities block so that the computations are carried out only once per iteration rather than once per HMC leapfrog step.
For example, the following is the generated quantities
block for
computing and saving the loglikelihood for a linear regression model with
N
data points, outcome y
, predictor matrix X
(including
column of 1s for intercept), coefficients beta
,
and standard deviation sigma
:
vector[N] log_lik;
for (n in 1:N) log_lik[n] = normal_lpdf(y[n]  X[n, ] * beta, sigma);
This function automatically uses Pareto k diagnostics for assessing the accuracy of importance sampling for each observation. When the diagnostics indicate that importance sampling for certain observations is inaccurate, a moment matching algorithm can be used, which can improve the accuracy (Paananen et al., 2020).
Value
A list with class c("psis_loo", "loo")
, as detailed in the
loo
documentation.
References
Vehtari, A., Gelman, A., and Gabry, J. (2017a).
Practical Bayesian model evaluation using leaveoneout crossvalidation and WAIC.
Statistics and Computing. 27(5), 14131432.
doi:10.1007/s1122201696964
.
https://arxiv.org/abs/1507.04544,
https://link.springer.com/article/10.1007/s1122201696964
Vehtari, A., Gelman, A., and Gabry, J. (2017b). Pareto smoothed importance sampling. arXiv preprint: https://arxiv.org/abs/1507.02646
Yao, Y., Vehtari, A., Simpson, D., and Gelman, A. (2018).
Using stacking to average Bayesian predictive distributions.
Bayesian Analysis, advance publication, doi:10.1214/17BA1091
.
Paananen, T., Piironen, J., Buerkner, P.C., Vehtari, A. (2020). Implicitly Adaptive Importance Sampling. arXiv preprint: https://arxiv.org/abs/1906.08850.
See Also
The loo package documentation, including the vignettes for many examples (https://mcstan.org/loo/).

loo_moment_match
for the moment matching algorithm. 
loo_model_weights
for model averaging/weighting via stacking or pseudoBMA weighting.
Examples
## Not run:
# Generate a dataset from N(0,1)
N < 100
y < rnorm(N, 0, 1)
# Suppose we have three models for y:
# 1) y ~ N(1, sigma)
# 2) y ~ N(0.5, sigma)
# 3) y ~ N(0.6,sigma)
#
stan_code < "
data {
int N;
vector[N] y;
real mu_fixed;
}
parameters {
real<lower=0> sigma;
}
model {
sigma ~ exponential(1);
y ~ normal(mu_fixed, sigma);
}
generated quantities {
vector[N] log_lik;
for (n in 1:N) log_lik[n] = normal_lpdf(y[n] mu_fixed, sigma);
}"
mod < stan_model(model_code = stan_code)
fit1 < sampling(mod, data=list(N=N, y=y, mu_fixed=1))
fit2 < sampling(mod, data=list(N=N, y=y, mu_fixed=0.5))
fit3 < sampling(mod, data=list(N=N, y=y, mu_fixed=0.6))
# use the loo method for stanfit objects
loo1 < loo(fit1, pars = "log_lik")
print(loo1)
# which is equivalent to
LL < as.array(fit1, pars = "log_lik")
r_eff < loo::relative_eff(exp(LL))
loo1b < loo::loo.array(LL, r_eff = r_eff)
print(loo1b)
# compute loo for the other models
loo2 < loo(fit2)
loo3 < loo(fit3)
# stacking weights
wts < loo::loo_model_weights(list(loo1, loo2, loo3), method = "stacking")
print(wts)
# use the moment matching for loo with a stanfit object
loo_mm < loo(fit1, pars = "log_lik", moment_match = TRUE)
print(loo_mm)
## End(Not run)