changed quantities of interest and model components explanation

docs/notebooks/plot_cap.ipynb

@@ -29,7 +29,7 @@
     "Due to the link function, there are typically three quantities of interest to interpret in a GLM:\n",
     "1. the linear predictor $\\eta$\n",
     "2. the mean $\\mu = g^{-1}(\\eta)$\n",
-    "3. the response variable $\\mathbb{E}(y|X) = \\mu$\n",
+    "3. the response variable $Y \\sim \\mathcal{D}(\\mu, \\theta)$ where $\\mu$ is the mean parameter and $\\theta$ is (possibly) a vector that contains all the other \"nuissance\" parameters of the distribution.\n",
     "\n",
     "As modelers, we are usually more interested in interpreting (2) and (3). However, $\\mu$ is not always on the same scale of the response variable and can be more difficult to interpret. Rather, the response scale is a more interpretable scale. Additionally, it is often the case that modelers would like to analyze how a model parameter varies across a range of explanatory variable values. To achieve such an analysis, Bambi has taken inspiration from the R package marginaleffects, and implemented a `plot_cap` function that plots the conditional adjusted predictions to aid in the interpretation of GLMs. Below, it is briefly discussed what are conditionally adjusted predictions, how they are computed, and ultimately how to use the `plot_cap` function."
    ]
@@ -133,7 +133,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We can print the Bambi model object to obtain the model components. Below, we see that the Gaussian linear model uses an identity link function, i.e., the response and link are on the same scale, and the distribution of the likelihood is Gaussian."
+    "We can print the Bambi model object to obtain the model components. Below, we see that the Gaussian linear model uses an identity link function that results in no transformation of the linear predictor to the mean of the outcome variable, and the distrbution of the likelihood is Gaussian."
    ]
   },
   {