problems using loo in clogit models

首先，使用 issue 中描述的 stan_clogit 示例和 infert 数据，通过 loo::loo.matrix 重现第三列恒定的 Pareto-k 行为。检查 loo::loo、loo::loo.matrix 和 loo.stanreg 如何划分职责，然后确定预期的行为，并为约定的处理方式定义回归测试覆盖范围。

In a rstanarm branch, I introduced a stan_clogit function which is similar to the clogit function in the survival package but is actually described in more detail by Stata ( http://www.stata.com/manuals13/rclogit.pdf ). So, you will be able to do

post <- stan_clogit(case ~ spontaneous + induced, strata = stratum,
                            data = infert[order(infert$stratum, !infert$case),], QR = TRUE)

The problem is that some groups have the same values on the dummy variables spontaneous and induced, such as

> infert[infert$stratum == 3,]
    education age parity induced case spontaneous stratum pooled.stratum
3      0-5yrs  39      6       2    1           0       3              4
86     0-5yrs  39      6       2    0           0       3              4
168    0-5yrs  39      6       2    0           0       3              4

Thus, no matter what are the posterior realizations of the coefficients on spontaneous and induced, the likelihood for group 3 is the same.

I am pretty sure the correct concept for a clogit model is to imagine leaving out one group rather than one observation, but when I call loo::loo.matrix, the third column of the input is a constant, which causes the Pareto k estimate to be infinite. Since the third group could be omitted and only change the log-likelihood by a constant, this seems to be unreasonable.

The question becomes, what function should be catching this? We could have stan_clogit drop groups that have only one unique row in the design matri{x,ces}. We could have loo.stanreg omit such groups. Or loo::loo could check which Pareto k estimates are infinite and change them to some number when the log likelihoods are finite but constant. Thoughts @avehtari ?