diff --git a/lighthergm/R/estimate_between_param.R b/lighthergm/R/estimate_between_param.R
index 903f70c..1dfd2d4 100644
--- a/lighthergm/R/estimate_between_param.R
+++ b/lighthergm/R/estimate_between_param.R
@@ -47,12 +47,13 @@ estimate_between_param <- function(formula, network, block) {
   varnames <-
     statnet.common::list_rhs.formula(formula) %>%
     as.character()
-  dep_terms <- which(terms %>% purrr::map(function(t) {
-    dep <- t$dependence
-    is_dep <- is.null(dep) || dep
-  }) %>% unlist())
-  between_rhs <- varnames[-dep_terms]
-  between_formula <- as.formula(paste("g_logit ~ ", paste(between_rhs, collapse = " + ")))
+  dep_terms <-
+    terms %>% purrr::map(function(t) {
+      dep <- t$dependence
+      is_dep <- is.null(dep) || dep
+    }) %>% unlist()
+  between_rhs <- varnames[!dep_terms]
+  between_formula <- as.formula(glue::glue("g_logit ~ {paste(between_rhs, collapse = '+')}"))
 
   # Estimate logit
   between_logit <- ergm(
diff --git a/lighthergm/R/gof_lighthergm.R b/lighthergm/R/gof_lighthergm.R
index 2ac389b..7f0d234 100644
--- a/lighthergm/R/gof_lighthergm.R
+++ b/lighthergm/R/gof_lighthergm.R
@@ -63,12 +63,12 @@ separate_formulas <- function(target_formula) {
   net <- get(str_net, envir = environment(target_formula))
   terms <- ergm::ergm_model(target_formula)$terms
   varnames <- statnet.common::list_rhs.formula(target_formula) %>% as.character()
-  dep_terms <- which(terms %>% purrr::map(function(t) {
-    dep <- t$dependence
-    is_dep <- is.null(dep) || dep
-  }) %>% unlist())
-
-  between_rhs <- varnames[-dep_terms]
+  dep_terms <-
+    terms %>% purrr::map(function(t) {
+      dep <- t$dependence
+      is_dep <- is.null(dep) || dep
+    }) %>% unlist()
+  between_rhs <- varnames[!dep_terms]
   within_rhs <- varnames
 
   between_formula <- paste(str_net, "~", paste(between_rhs, collapse = " + "))
diff --git a/lighthergm/inst/extdata/initialized_cluster_data_by_infomap.clu b/lighthergm/inst/extdata/initialized_cluster_data_by_infomap.clu
new file mode 100644
index 0000000..4c0fb8b
--- /dev/null
+++ b/lighthergm/inst/extdata/initialized_cluster_data_by_infomap.clu
@@ -0,0 +1,1009 @@
+# v1.3.0
+# ./Infomap --flow-model undirected --preferred-number-of-modules 50 --clu inst/extdata/initialized_cluster_data_by_infomap.csv inst/extdata --seed 334
+# started at 2021-06-17 17:40:43
+# completed in 0.103162 s
+# partitioned into 2 levels with 50 top modules
+# codelength 9.45098 bits
+# relative codelength savings 5.08335%
+# module level 1
+# node_id module flow
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diff --git a/lighthergm/src/RcppExports.cpp b/lighthergm/src/RcppExports.cpp
index d698382..aaececa 100644
--- a/lighthergm/src/RcppExports.cpp
+++ b/lighthergm/src/RcppExports.cpp
@@ -6,6 +6,11 @@
 
 using namespace Rcpp;
 
+#ifdef RCPP_USE_GLOBAL_ROSTREAM
+Rcpp::Rostream<true>&  Rcpp::Rcout = Rcpp::Rcpp_cout_get();
+Rcpp::Rostream<false>& Rcpp::Rcerr = Rcpp::Rcpp_cerr_get();
+#endif
+
 // eigenvectors_sparse
 arma::mat eigenvectors_sparse(const arma::sp_mat& X, int n_vec);
 RcppExport SEXP _lighthergm_eigenvectors_sparse(SEXP XSEXP, SEXP n_vecSEXP) {
diff --git a/lighthergm/tests/testthat/test-estimate-params.R b/lighthergm/tests/testthat/test-estimate-params.R
index 88c5e74..2fb23b7 100644
--- a/lighthergm/tests/testthat/test-estimate-params.R
+++ b/lighthergm/tests/testthat/test-estimate-params.R
@@ -1,83 +1,83 @@
-test_that("estimating between-block parameters by logit works", {
-  set.seed(334)
-  # Prepare data
-  edgelist <-
-    tibble::tribble(
-      ~head, ~tail,
-      1, 9,
-      2, 6,
-      2, 7,
-      2, 9,
-      3, 5,
-      3, 9,
-      4, 7,
-      4, 11,
-      4, 15,
-      5, 11,
-      5, 15,
-      7, 8,
-      7, 16,
-      9, 13,
-      9, 14,
-      9, 16,
-      10, 14,
-      11, 15,
-      13, 15,
-      13, 16
-    )
-  edgelist <-
-    as.matrix(edgelist)
-  attr(edgelist, "n") <- 16
-  attr(edgelist, "vnames") <-
-    c(
-      "Acciaiuoli", "Albizzi", "Barbadori", "Bischeri", "Castellani", "Ginori",
-      "Guadagni", "Lamberteschi", "Medici", "Pazzi", "Peruzzi", "Pucci", "Ridolfi",
-      "Salviati", "Strozzi", "Tornabuoni"
-    )
-  attr(edgelist, "directed") <- FALSE
-  attr(edgelist, "bipartite") <- FALSE
-  attr(edgelist, "loops") <- FALSE
-  attr(edgelist, "class") <- c("edgelist", "matrix")
+set.seed(334)
+# Prepare data
+edgelist <-
+  tibble::tribble(
+    ~head, ~tail,
+    1, 9,
+    2, 6,
+    2, 7,
+    2, 9,
+    3, 5,
+    3, 9,
+    4, 7,
+    4, 11,
+    4, 15,
+    5, 11,
+    5, 15,
+    7, 8,
+    7, 16,
+    9, 13,
+    9, 14,
+    9, 16,
+    10, 14,
+    11, 15,
+    13, 15,
+    13, 16
+  )
+edgelist <-
+  as.matrix(edgelist)
+attr(edgelist, "n") <- 16
+attr(edgelist, "vnames") <-
+  c(
+    "Acciaiuoli", "Albizzi", "Barbadori", "Bischeri", "Castellani", "Ginori",
+    "Guadagni", "Lamberteschi", "Medici", "Pazzi", "Peruzzi", "Pucci", "Ridolfi",
+    "Salviati", "Strozzi", "Tornabuoni"
+  )
+attr(edgelist, "directed") <- FALSE
+attr(edgelist, "bipartite") <- FALSE
+attr(edgelist, "loops") <- FALSE
+attr(edgelist, "class") <- c("edgelist", "matrix")
 
-  g <- network::network(edgelist, matrix.type = "edgelist", directed = FALSE)
+g <- network::network(edgelist, matrix.type = "edgelist", directed = FALSE)
 
-  x1 <- as.integer(unlist(purrr::rbernoulli(n = g$gal$n)))
-  network::set.vertex.attribute(x = g, attrname = "x1", value = x1)
+x1 <- as.integer(unlist(purrr::rbernoulli(n = g$gal$n)))
+network::set.vertex.attribute(x = g, attrname = "x1", value = x1)
 
-  # Cluster
-  z_memb <- rep(1:4, each = 4)
-  network::set.vertex.attribute(x = g, attrname = "block", value = z_memb)
+# Cluster
+z_memb <- rep(1:4, each = 4)
+network::set.vertex.attribute(x = g, attrname = "block", value = z_memb)
 
-  # Create dataset for test
-  g_link <- intergraph::asDF(g)$edges
-  g_attr <- intergraph::asDF(g)$vertexes
+# Create dataset for test
+g_link <- intergraph::asDF(g)$edges
+g_attr <- intergraph::asDF(g)$vertexes
 
-  df_g <-
-    tibble::tibble(
-      head = 1:g$gal$n,
-      tail = 1:g$gal$n
-    ) %>%
-    tidyr::expand(tail, head) %>%
-    dplyr::filter(tail < head) %>%
-    dplyr::left_join(., g_attr, by = c("tail" = "intergraph_id")) %>%
-    dplyr::left_join(., g_attr, by = c("head" = "intergraph_id")) %>%
-    dplyr::mutate(
-      nodematch.x1 = ifelse(x1.x == x1.y, 1, 0),
-      same_block = ifelse(block.x == block.y, 1, 0)
-    ) %>%
-    dplyr::select(tail, head, nodematch.x1:same_block) %>%
-    dplyr::left_join(., g_link, by = c("tail" = "V1", "head" = "V2")) %>%
-    dplyr::mutate(connected = ifelse(is.na(na), 0, 1)) %>%
-    dplyr::select(-na)
+df_g <-
+  tibble::tibble(
+    head = 1:g$gal$n,
+    tail = 1:g$gal$n
+  ) %>%
+  tidyr::expand(tail, head) %>%
+  dplyr::filter(tail < head) %>%
+  dplyr::left_join(., g_attr, by = c("tail" = "intergraph_id")) %>%
+  dplyr::left_join(., g_attr, by = c("head" = "intergraph_id")) %>%
+  dplyr::mutate(
+    nodematch.x1 = ifelse(x1.x == x1.y, 1, 0),
+    same_block = ifelse(block.x == block.y, 1, 0)
+  ) %>%
+  dplyr::select(tail, head, nodematch.x1:same_block) %>%
+  dplyr::left_join(., g_link, by = c("tail" = "V1", "head" = "V2")) %>%
+  dplyr::mutate(connected = ifelse(is.na(na), 0, 1)) %>%
+  dplyr::select(-na)
 
-  # Estimate the model
-  formula <- g ~ edges + nodematch("x1") + triangle + kstar(2)
-  est_between <- estimate_between_param(
-    formula = formula,
-    network = g,
-    block = z_memb
-  )
+# Estimate the model
+formula <- g ~ edges + nodematch("x1") + triangle + kstar(2)
+est_between <- estimate_between_param(
+  formula = formula,
+  network = g,
+  block = z_memb
+)
 
+test_that("estimating between-block parameters by logit works", {
   # Check if between-block connections are all zero.
   g_logit <- est_between$network
   edgelist <- intergraph::asDF(g_logit)$edges
@@ -117,3 +117,14 @@ test_that("estimating between-block parameters by logit works", {
     method_second_step = "MPLE"
   ), NA)
 })
+
+test_that("estimating between-block parameters using a formula without externality terms works", {
+  # Check if within-block parameter estiamtion works
+  expect_error(
+    estimate_between_param(
+      formula = g ~ edges + nodematch("x1"),
+      network = g,
+      block = z_memb
+    ),
+    NA)
+})
diff --git a/lighthergm/tests/testthat/test-simulate_hergm.R b/lighthergm/tests/testthat/test-simulate_hergm.R
index 39c512b..8998603 100644
--- a/lighthergm/tests/testthat/test-simulate_hergm.R
+++ b/lighthergm/tests/testthat/test-simulate_hergm.R
@@ -412,3 +412,31 @@ test_that("Yielding the same between-block network using the cpp function when t
   expect_false(all(adj1 == adj3))
   expect_false(all(adj2 == adj3))
 })
+
+
+test_that("Simulating networks using formula without externality terms works", {
+  K <- 10
+  N <- 200
+  formula_1 <- g ~ edges + nodematch("x")
+  x <- sample(c(1, 2), size = N, replace = TRUE)
+  block <- sample(1:K, size = N, replace = TRUE)
+
+  nodes_data <-
+    tibble::tibble(x = x, node_id = as.character(1:N), block = block)
+
+  coef_between <- c(-6.5, 0)
+  coef_within <- c(-4.5, 5)
+
+  expect_error(
+    sim_net_1 <- lighthergm::simulate_hergm(
+      formula_for_simulation = formula_1,
+      data_for_simulation = nodes_data,
+      colname_vertex_id = 'node_id',
+      colname_block_membership = 'block',
+      coef_between_block = coef_between,
+      coef_within_block = coef_within,
+      n_sim = 1
+    ),
+    NA
+  )
+})
diff --git a/lighthergm/tests/testthat/test-start-from-given-cluster.R b/lighthergm/tests/testthat/test-start-from-given-cluster.R
index 078211b..f176480 100644
--- a/lighthergm/tests/testthat/test-start-from-given-cluster.R
+++ b/lighthergm/tests/testthat/test-start-from-given-cluster.R
@@ -70,7 +70,7 @@ test_that("starting EM iterations and parameter estimation from a given vector o
   # Check if starting from block memberships initialized Python's infomap works.
   expect_error(result2 <-
     lighthergm::hergm(g_sim ~ edges + nodematch("x") + nodematch("y") + triangles,
-      initialized_cluster_data = "initialized_cluster_data_by_infomap.clu",
+      initialized_cluster_data = system.file("extdata", "initialized_cluster_data_by_infomap.clu", package = "lighthergm"),
       n_em_step_max = 1,
       estimate_parameters = FALSE,
       verbose = 1