I found this chunk a little unintuitive...I'm wondering if it might be better to phrase it something like:

Link functions $g(\cdot)$ transform the response onto the unbounded scale of the linear predictor $\nu_i = X_i \cdot \beta$, allowing regression coefficients to operate without constraint. Inverse link functions $g^{-1}(\cdot)$ map the linear predictor back onto the scale of the response. This ensures that predictions respect their distributional constraints (e.g., non-negative for count data, bounded between 0 and 1 for binary data).

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Try something like this maybe:

In this chapter, we will consider models where the variance also depends on covariates. This leads to the following model specification:

\begin{gather} Y_i \sim N(\mu_i, \sigma_i^2) \nonumber \ \mu_i = \beta_0 + X_{1i}\beta_1 + X_{2i}\beta_2 + \ldots X_{pi}\beta_p \nonumber \ \sigma^2_i = f(Z_i; \delta) \nonumber \end{gather}

where \sigma_i^2 is written as a function, f(Z_i; \delta), of predictor variables (Z) and additional variance parameters \delta. The set of predictor variables (Z) may overlap with or be distinct from the predictors used in the mean model (X).

If you don't go with this version, I think splitting up that long sentence into a few distinct sentences and removing the appositive expressions separated by "," in favor of something more readable that doesn't break up the flow as much.

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