diff --git a/test/test_emission.py b/test/test_emission.py
index 34a28b2..40c9770 100644
--- a/test/test_emission.py
+++ b/test/test_emission.py
@@ -320,50 +320,3 @@ def test_categorical_less_categories_in_test():
     preds = model.predict(test)
 
 
-@pytest.mark.filterwarnings(
-    "ignore::sklearn.exceptions.ConvergenceWarning"
-)  # Ignore convergence warnings
-def test_categorical_n_parameters():
-    """Test number of parameters of a simple categorical mixture."""
-    rng = np.random.default_rng(42)
-    data = rng.choice(a=[0, 1, 2], size=200).reshape(-1, 1)
-
-    model = StepMix(
-        n_components=3,
-        measurement="categorical",
-        random_state=42,
-        verbose=0,
-        max_iter=5000,
-        n_init=1,
-    )
-
-    model.fit(data)
-
-    assert model.n_parameters == 8
-
-
-@pytest.mark.filterwarnings(
-    "ignore::sklearn.exceptions.ConvergenceWarning"
-)  # Ignore convergence warnings
-def test_categorical_n_parameters_max():
-    """Test number of parameters of a categorical mixture where some categorical features have fewer outcomes."""
-    rng = np.random.default_rng(42)
-    data_1 = rng.choice(a=[0, 1, 2, 3], size=300).reshape(-1, 1)
-    data_2 = rng.choice(a=[0, 1, 2], size=300).reshape(-1, 1)
-    data_3 = rng.choice(a=[0, 1], size=300).reshape(-1, 1)
-    data = np.hstack((data_1, data_2, data_3))
-
-    model = StepMix(
-        n_components=4,
-        measurement="categorical",
-        random_state=42,
-        verbose=0,
-        max_iter=5000,
-        n_init=1,
-    )
-
-    model.fit(data)
-
-    n_parameters = (4 - 1) + 4 * (1 + 2 + 3)
-
-    assert model.n_parameters == n_parameters
diff --git a/test/test_n_parameters.py b/test/test_n_parameters.py
new file mode 100644
index 0000000..aa2ad28
--- /dev/null
+++ b/test/test_n_parameters.py
@@ -0,0 +1,128 @@
+import numpy as np
+import pytest
+
+from stepmix import StepMix
+
+
+@pytest.mark.filterwarnings(
+    "ignore::sklearn.exceptions.ConvergenceWarning"
+)  # Ignore convergence warnings
+@pytest.mark.parametrize("model", ["binary", "binary_nan"])
+def test_binary_n_parameters(model):
+    """Test number of parameters of a simple categorical mixture."""
+    rng = np.random.default_rng(42)
+    data = rng.choice(a=[0, 1], size=(100, 7))
+
+    model = StepMix(
+        n_components=3,
+        measurement=model,
+        random_state=42,
+        verbose=0,
+        max_iter=1,
+        n_init=1,
+    )
+
+    model.fit(data)
+
+    assert model.n_parameters == 23
+
+@pytest.mark.filterwarnings(
+    "ignore::sklearn.exceptions.ConvergenceWarning"
+)  # Ignore convergence warnings
+@pytest.mark.parametrize("model", ["categorical", "categorical_nan"])
+def test_categorical_n_parameters(model):
+    """Test number of parameters of a simple categorical mixture."""
+    rng = np.random.default_rng(42)
+    data = rng.choice(a=[0, 1, 2], size=(200, )).reshape(-1, 1)
+
+    model = StepMix(
+        n_components=3,
+        measurement=model,
+        random_state=42,
+        verbose=0,
+        max_iter=1,
+        n_init=1,
+    )
+
+    model.fit(data)
+
+    assert model.n_parameters == 8
+@pytest.mark.filterwarnings(
+    "ignore::sklearn.exceptions.ConvergenceWarning"
+)  # Ignore convergence warnings
+@pytest.mark.parametrize("model", ["categorical", "categorical_nan"])
+def test_categorical_n_parameters_max(model):
+    """Test number of parameters of a categorical mixture where some categorical features have fewer outcomes."""
+    rng = np.random.default_rng(42)
+    data_1 = rng.choice(a=[0, 1, 2, 3], size=300).reshape(-1, 1)
+    data_2 = rng.choice(a=[0, 1, 2], size=300).reshape(-1, 1)
+    data_3 = rng.choice(a=[0, 1], size=300).reshape(-1, 1)
+    data = np.hstack((data_1, data_2, data_3))
+
+    model = StepMix(
+        n_components=4,
+        measurement=model,
+        random_state=42,
+        verbose=0,
+        max_iter=1,
+        n_init=1,
+    )
+
+    model.fit(data)
+
+    n_parameters = (4 - 1) + 4 * (1 + 2 + 3)
+
+    assert model.n_parameters == n_parameters
+
+
+@pytest.mark.filterwarnings(
+    "ignore::sklearn.exceptions.ConvergenceWarning"
+)  # Ignore convergence warnings
+@pytest.mark.parametrize("model,n_parameters", [("gaussian_unit", 19), ("gaussian_diag", 35), ("gaussian_unit_nan", 19), ("gaussian_diag_nan", 35),("gaussian_spherical", 23), ("gaussian_spherical_nan", 23), ("gaussian_tied", 29), ("gaussian_full", 59)])
+def test_gaussian_n_parameters(model, n_parameters):
+    """Test number of parameters of a simple categorical mixture."""
+    rng = np.random.default_rng(42)
+    data = rng.normal(size=(100, 4))
+
+    model = StepMix(
+        n_components=4,
+        measurement=model,
+        random_state=42,
+        verbose=0,
+        max_iter=1,
+        n_init=1,
+    )
+
+    model.fit(data)
+
+    assert model.n_parameters == n_parameters
+
+@pytest.mark.filterwarnings(
+    "ignore::sklearn.exceptions.ConvergenceWarning"
+)  # Ignore convergence warnings
+@pytest.mark.parametrize("intercept,n_parameters", [(False, 10), (True, 12)])
+def test_covariate_n_parameters(intercept, n_parameters):
+    """Test number of parameters of a simple categorical mixture."""
+    rng = np.random.default_rng(42)
+    data = rng.normal(size=(100, 2))
+
+    opt_params = {
+        'method': 'newton-raphson',  # Can also be "gradient",
+        'intercept': intercept,
+        'max_iter': 1,  # Number of opt. step each time we update the covariate model
+    }
+
+    model = StepMix(
+        n_components=3,
+        measurement="gaussian_unit",
+        structural="covariate",
+        structural_params=opt_params,
+        random_state=42,
+        verbose=0,
+        max_iter=1,
+        n_init=1,
+    )
+
+    model.fit(data, data)
+
+    assert model.n_parameters == n_parameters