In a linear model, say
$$\hat{y}_i = \beta_0 + \beta_1 x_{1i}$$
the effect of $\mathbf{x}_1$ on the response is constant. If we add $\mathbf{x}_2$ to the model and an interaction between both covariates
$$\hat{y}_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + \beta_3 (x_{1i}\times x_{2i})$$
the magnitude of the linear effect of $\mathbf{x}_1$ depends linearly on the effect of $\mathbf{x}_2$.
The same intuition guides the interpretation of a varying coefficient model such as the one you fitted. The key difference is that now we are thinking about how the magnitude of linear effect of $\mathbf{x}_1$ depends smoothly on $\mathbf{x}_2$.
The way to read the plot you show is to think in terms of $\hat{\beta} \times \text{ses}$, and the value of $\hat{\beta}$ for any value of $\text{acc}$ is indicated by the smooth line. The effect of $\text{ses}$ on the response is estimated to be positive, but only for values of $\text{acc}$ between ~6 and ~11, with the strongest effect of $\text{ses}$ on the response found at $\text{acc} \approx$ 8.
As this is a Negative Binomial model, all of the above effects are on the log scale. You would need to exponentiate the values on the y-axis to see the (now multiplicative) effect of $\text{ses}$ on the response. To guide this however, $\exp(0) = 1$, so the zero line in the plot indicates no effect or change in response on the log scale and on the response scale it also means no effect because the interpretation there is that we multiply values by $\exp(0) = 1$.
If you want to really dig into this visually, do as @AndrewM suggests, and create a new data frame with all the covariates except acc
held at their mean or median values and vary acc
over it's range. If you predict from the model passing this new data set as newdata
you can explore the predicted values on the response scale (using type = "response"
) as you vary acc
. I would do this for a few values of sec
so you can see how the two variables interact.
predict
method. $\endgroup$