diff --git a/NEWS.md b/NEWS.md
index 6f182376..abb6e481 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,7 @@
 # loo (development version)
 
+* Clarify print output to say "posterior draws" and "log-likelihood terms" instead of the ambiguous "X by Y matrix" format (#198)
+
 # loo 2.9.0
 
 * Avoid under and overflows in stacking by @avehtari in #273
diff --git a/R/elpd.R b/R/elpd.R
index 20724e71..b6736fb4 100644
--- a/R/elpd.R
+++ b/R/elpd.R
@@ -67,9 +67,9 @@ elpd_object <- function(pointwise, dims) {
 }
 #' @export
 print_dims.elpd_generic <- function(x, ...) {
+  dims <- dim(x)
   cat(
-    "Computed from",
-    paste(dim(x), collapse = " by "),
-    "log-likelihood matrix using the generic elpd function\n"
+    "Computed from", dims[1], "posterior draws and",
+    dims[2], "log-likelihood terms using the generic elpd function.\n"
   )
 }
diff --git a/R/print.R b/R/print.R
index f05834d6..096bb4a5 100644
--- a/R/print.R
+++ b/R/print.R
@@ -119,40 +119,40 @@ print_dims <- function(x, ...) UseMethod("print_dims")
 #' @rdname print_dims
 #' @export
 print_dims.importance_sampling <- function(x, ...) {
+  dims <- dim(x)
   cat(
-    "Computed from",
-    paste(dim(x), collapse = " by "),
-    "log-weights matrix.\n"
+    "Computed from", dims[1], "posterior draws and",
+    dims[2], "log-weight terms.\n"
   )
 }
 
 #' @rdname print_dims
 #' @export
 print_dims.psis_loo <- function(x, ...) {
+  dims <- dim(x)
   cat(
-    "Computed from",
-    paste(dim(x), collapse = " by "),
-    "log-likelihood matrix.\n"
+    "Computed from", dims[1], "posterior draws and",
+    dims[2], "log-likelihood terms.\n"
   )
 }
 
 #' @rdname print_dims
 #' @export
 print_dims.importance_sampling_loo <- function(x, ...) {
+  dims <- dim(x)
   cat(
-    "Computed from",
-    paste(dim(x), collapse = " by "),
-    "log-likelihood matrix using", class(x)[1], ".\n"
+    "Computed from", dims[1], "posterior draws and",
+    dims[2], "log-likelihood terms using", class(x)[1], ".\n"
   )
 }
 
 #' @rdname print_dims
 #' @export
 print_dims.waic <- function(x, ...) {
+  dims <- dim(x)
   cat(
-    "Computed from",
-    paste(dim(x), collapse = " by "),
-    "log-likelihood matrix.\n"
+    "Computed from", dims[1], "posterior draws and",
+    dims[2], "log-likelihood terms.\n"
   )
 }
 
@@ -169,9 +169,8 @@ print_dims.kfold <- function(x, ...) {
 #' @export
 print_dims.psis_loo_ss <- function(x, ...) {
   cat(
-    "Computed from",
-    paste(c(dim(x)[1], nobs(x)) , collapse = " by "),
-    "subsampled log-likelihood\nvalues from",
+    "Computed from", dim(x)[1], "posterior draws and",
+    nobs(x), "subsampled log-likelihood\nterms from",
     length(x$loo_subsampling$elpd_loo_approx),
     "total observations.\n"
   )
diff --git a/tests/testthat/_snaps/loo_moment_matching.md b/tests/testthat/_snaps/loo_moment_matching.md
index e34c5d48..a227a3aa 100644
--- a/tests/testthat/_snaps/loo_moment_matching.md
+++ b/tests/testthat/_snaps/loo_moment_matching.md
@@ -13,7 +13,7 @@
       Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.
     Output
       
-      Computed from 4000 by 30 log-likelihood matrix.
+      Computed from 4000 posterior draws and 30 log-likelihood terms.
       
                Estimate   SE
       elpd_loo    -74.0 18.8
diff --git a/tests/testthat/_snaps/psis.md b/tests/testthat/_snaps/psis.md
index 9f2deaf3..d902046d 100644
--- a/tests/testthat/_snaps/psis.md
+++ b/tests/testthat/_snaps/psis.md
@@ -4787,7 +4787,7 @@
     Message
       Replacing NAs in `r_eff` with 1s
     Output
-      Computed from 1000 by 32 log-weights matrix.
+      Computed from 1000 posterior draws and 32 log-weight terms.
       MCSE and ESS estimates assume MCMC draws (r_eff in [0.6, 1.0]).
       
       All Pareto k estimates are good (k < 0.67).
@@ -4803,7 +4803,7 @@
       Warning:
       Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.
     Output
-      Computed from 10 by 32 log-weights matrix.
+      Computed from 10 posterior draws and 32 log-weight terms.
       MCSE and ESS estimates assume independent draws (r_eff=1).
       Pareto k diagnostic values:
                              Count Pct.    Min. ESS
diff --git a/tests/testthat/_snaps/tisis.md b/tests/testthat/_snaps/tisis.md
index 57cf7e30..1f20897f 100644
--- a/tests/testthat/_snaps/tisis.md
+++ b/tests/testthat/_snaps/tisis.md
@@ -5,7 +5,7 @@
     Message
       Replacing NAs in `r_eff` with 1s
     Output
-      Computed from 1000 by 32 log-weights matrix.
+      Computed from 1000 posterior draws and 32 log-weight terms.
       MCSE and ESS estimates assume MCMC draws (r_eff in [0.6, 1.0]).
       
       All Pareto k estimates are good (k < 0.67).
diff --git a/tests/testthat/test_loo_subsampling_cases.R b/tests/testthat/test_loo_subsampling_cases.R
index 1f53192b..61fb5691 100644
--- a/tests/testthat/test_loo_subsampling_cases.R
+++ b/tests/testthat/test_loo_subsampling_cases.R
@@ -171,17 +171,17 @@ test_that("Test loo_subsampling and loo_approx with radon data", {
   ))
   expect_failure(expect_output(
     print(full_loo),
-    "subsampled log-likelihood\nvalues"
+    "subsampled log-likelihood\nterms"
   ))
 
   expect_failure(expect_output(
     print(loo_ss),
     "Posterior approximation correction used\\."
   ))
-  expect_output(print(loo_ss), "subsampled log-likelihood\nvalues")
+  expect_output(print(loo_ss), "subsampled log-likelihood\nterms")
 
   expect_output(print(loo_ap_ss), "Posterior approximation correction used\\.")
-  expect_output(print(loo_ap_ss), "subsampled log-likelihood\nvalues")
+  expect_output(print(loo_ap_ss), "subsampled log-likelihood\nterms")
 
   expect_output(
     print(loo_ap_ss_full),
@@ -189,7 +189,7 @@ test_that("Test loo_subsampling and loo_approx with radon data", {
   )
   expect_failure(expect_output(
     print(loo_ap_ss_full),
-    "subsampled log-likelihood\nvalues"
+    "subsampled log-likelihood\nterms"
   ))
 
   # Test conversion of objects
@@ -344,9 +344,9 @@ test_that("Test the vignette", {
   )
   expect_output(
     print(looss_1),
-    "Computed from 4000 by 100 subsampled log-likelihood"
+    "Computed from 4000 posterior draws and 100 subsampled log-likelihood"
   )
-  expect_output(print(looss_1), "values from 3020 total observations.")
+  expect_output(print(looss_1), "terms from 3020 total observations.")
   expect_output(
     print(looss_1),
     "MCSE and ESS estimates assume independent draws"
@@ -366,9 +366,9 @@ test_that("Test the vignette", {
   )
   expect_output(
     print(looss_1b),
-    "Computed from 4000 by 200 subsampled log-likelihood"
+    "Computed from 4000 posterior draws and 200 subsampled log-likelihood"
   )
-  expect_output(print(looss_1b), "values from 3020 total observations.")
+  expect_output(print(looss_1b), "terms from 3020 total observations.")
   expect_output(
     print(looss_1b),
     "MCSE and ESS estimates assume independent draws"
@@ -391,9 +391,9 @@ test_that("Test the vignette", {
   )
   expect_output(
     print(looss_2),
-    "Computed from 4000 by 100 subsampled log-likelihood"
+    "Computed from 4000 posterior draws and 100 subsampled log-likelihood"
   )
-  expect_output(print(looss_2), "values from 3020 total observations.")
+  expect_output(print(looss_2), "terms from 3020 total observations.")
   expect_output(
     print(looss_2),
     "MCSE and ESS estimates assume independent draws"
@@ -415,7 +415,7 @@ test_that("Test the vignette", {
   )
   expect_output(
     print(aploo_1),
-    "Computed from 2000 by 3020 log-likelihood matrix"
+    "Computed from 2000 posterior draws and 3020 log-likelihood terms"
   )
   expect_output(
     print(aploo_1),
@@ -441,13 +441,13 @@ test_that("Test the vignette", {
   )
   expect_output(
     print(looapss_1),
-    "Computed from 2000 by 100 subsampled log-likelihood"
+    "Computed from 2000 posterior draws and 100 subsampled log-likelihood"
   )
   expect_output(
     print(looapss_1),
     "MCSE and ESS estimates assume independent draws"
   )
-  expect_output(print(looapss_1), "values from 3020 total observations.")
+  expect_output(print(looapss_1), "terms from 3020 total observations.")
   expect_output(print(looapss_1), "elpd_loo  -1968.2 15.6            0.4")
   expect_output(print(looapss_1), "p_loo         2.9  0.1            0.5")
   expect_output(print(looapss_1), "All Pareto k estimates are good")
@@ -474,13 +474,13 @@ test_that("Test the vignette", {
   )
   expect_output(
     print(looss_2),
-    "Computed from 4000 by 100 subsampled log-likelihood"
+    "Computed from 4000 posterior draws and 100 subsampled log-likelihood"
   )
   expect_output(
     print(looss_2),
     "MCSE and ESS estimates assume independent draws"
   )
-  expect_output(print(looss_2), "values from 3020 total observations.")
+  expect_output(print(looss_2), "terms from 3020 total observations.")
   expect_output(print(looss_2), "elpd_loo  -1952.0 16.2            0.2")
   expect_output(print(looss_2), "p_loo         2.6  0.1            0.3")
 
diff --git a/tests/testthat/test_print_plot.R b/tests/testthat/test_print_plot.R
index f69ed6f0..ea0ec03b 100644
--- a/tests/testthat/test_print_plot.R
+++ b/tests/testthat/test_print_plot.R
@@ -41,16 +41,16 @@ test_that("plot methods throw appropriate errors/warnings", {
 lldim_msg <- paste0(
   "Computed from ",
   prod(dim(LLarr)[1:2]),
-  " by ",
+  " posterior draws and ",
   dim(LLarr)[3],
-  " log-likelihood matrix"
+  " log-likelihood terms"
 )
 lwdim_msg <- paste0(
   "Computed from ",
   prod(dim(LLarr)[1:2]),
-  " by ",
+  " posterior draws and ",
   dim(LLarr)[3],
-  " log-weights matrix"
+  " log-weight terms"
 )
 
 test_that("print.waic output is ok", {
diff --git a/vignettes/loo2-large-data.Rmd b/vignettes/loo2-large-data.Rmd
index 0dadaf7e..ff801817 100644
--- a/vignettes/loo2-large-data.Rmd
+++ b/vignettes/loo2-large-data.Rmd
@@ -188,8 +188,8 @@ print(loo_ss_1)
 ```
 
 ```
-Computed from 4000 by 100 subsampled log-likelihood
-values from 3020 total observations.
+Computed from 4000 posterior draws and 100 subsampled log-likelihood
+terms from 3020 total observations.
 
          Estimate   SE subsampling SE
 elpd_loo  -1968.5 15.6            0.3
@@ -240,8 +240,8 @@ print(loo_ss_1b)
 ```
 
 ```
-Computed from 4000 by 200 subsampled log-likelihood
-values from 3020 total observations.
+Computed from 4000 posterior draws and 200 subsampled log-likelihood
+terms from 3020 total observations.
 
          Estimate   SE subsampling SE
 elpd_loo  -1968.3 15.6            0.2
@@ -285,8 +285,8 @@ print(loo_ss_1c)
 
 
 ```
-Computed from 4000 by 100 subsampled log-likelihood
-values from 3020 total observations.
+Computed from 4000 posterior draws and 100 subsampled log-likelihood
+terms from 3020 total observations.
 
          Estimate   SE subsampling SE
 elpd_loo  -1968.9 15.4            0.5
@@ -339,7 +339,7 @@ print(loo_ap_1)
 The function creates a class, `psis_loo_ap` that inherits from `psis_loo, loo`.
 
 ```
-Computed from 2000 by 3020 log-likelihood matrix
+Computed from 2000 posterior draws and 3020 log-likelihood terms
 
          Estimate   SE
 elpd_loo  -1968.4 15.6
@@ -375,8 +375,8 @@ print(loo_ap_ss_1)
 ```
 
 ```
-Computed from 2000 by 100 subsampled log-likelihood
-values from 3020 total observations.
+Computed from 2000 posterior draws and 100 subsampled log-likelihood
+terms from 3020 total observations.
 
          Estimate   SE subsampling SE
 elpd_loo  -1968.2 15.6            0.4
@@ -455,8 +455,8 @@ print(loo_ss_2)
 ```
 
 ```
-Computed from 4000 by 100 subsampled log-likelihood
-values from 3020 total observations.
+Computed from 4000 posterior draws and 100 subsampled log-likelihood
+terms from 3020 total observations.
 
          Estimate   SE subsampling SE
 elpd_loo  -1952.0 16.2            0.2
diff --git a/vignettes/loo2-with-rstan.Rmd b/vignettes/loo2-with-rstan.Rmd
index 23ddf364..9c1fcd05 100644
--- a/vignettes/loo2-with-rstan.Rmd
+++ b/vignettes/loo2-with-rstan.Rmd
@@ -140,7 +140,7 @@ print(loo_1)
 ```
 
 ```
-Computed from 4000 by 3020 log-likelihood matrix
+Computed from 4000 posterior draws and 3020 log-likelihood terms
 
          Estimate   SE
 elpd_loo  -1968.5 15.6
@@ -182,7 +182,7 @@ print(loo_2)
 ```
 
 ```
-Computed from 4000 by 3020 log-likelihood matrix
+Computed from 4000 posterior draws and 3020 log-likelihood terms
 
          Estimate   SE
 elpd_loo  -1952.3 16.2