How to interpret threshold value not intersecting with smooth in ordered GAM? My model consists of an ordered factor with four levels as the response variable and a continuous predictor.
mod <- gam(lev ~ s(pred), family = ocat(R = 4))

The smooth of the predictor looks like this:

The estimated threshold values are:
> mod$family$getTheta(TRUE)
[1] -1.00000000  0.09669527  1.27291819

However, the last value (1.27) does not intersect with the smooth. How can that be interpreted?
Edit to include reproducible example:
(taken from https://github.com/eric-pedersen/mgcv-esa-workshop/blob/master/example-forest-health.Rmd)
library(mgcv)

forest <- read.table(url("https://raw.githubusercontent.com/eric-pedersen/mgcv-esa-workshop/master/data/forest-health/beech.raw"),
                     header = TRUE)

forest <- transform(forest, id = factor(formatC(id, width = 2, flag = "0")))

## Aggregate defoliation & convert categorical vars to factors
levs <- c("low","med","high")
forest <- transform(forest,
                    aggDefol = as.numeric(cut(defol, breaks = c(-1,10,45,101),
                                              labels = levs)),
                    watermoisture = factor(watermoisture),
                    alkali = factor(alkali),
                    humus = cut(humus, breaks = c(-0.5, 0.5, 1.5, 2.5, 3.5),
                                labels = 1:4),
                    type = factor(type),
                    fert = factor(fert))
forest <- droplevels(na.omit(forest))

ctrl <- gam.control(nthreads = 3)
forest.m1 <- gam(aggDefol ~ s(age),
                 data = forest, 
                 family = ocat(R = 3), 
                 method = "REML",
                 control = ctrl)
summary(forest.m1)

plot.gam(forest.m1, shift = coef(forest.m1)[1])


 A: It doesn't have to intersect with the smooth - you're not including the model constant term when trying to interpret the result.
There is an underlying latent variable stretching from $-\infty$ to $+\infty$ and the cut points $\theta_r$ ($r \in {1,\dots,R}$) mark the transitions from one category to the next where there are $R+1$ categories. The value of the linear predictor $\hat{\eta}_i$ for an observation, yields a value (point) on this latent variable. Together, the $\hat{\eta}_i$ and $\theta_r$ determine the estimated probability that the $i$th observation falls in each category.
The linear predictor in this model is of the form
$$
\eta_i = \alpha + f(x_i)
$$
where $\alpha$ is the model constant term (the thing labelled (Intercept) in the output from summary() coef() etc.)
To reconcile your observation that the partial effect of the smooth term $f(x_i)$ never gets above +1, we might conclude that the constant term $\alpha$ is a positive value sufficient to produce values of the linear predictor that are greater than 1.27 to allow the model to predict the $R+1$th category.
The y axis here is not the latent variable or the value of the linear predictor; it's the partial effect of the smooth $f(\mathbf{x)}$, which has been subjected to an sum-to-zero identifiable constraint, which has the effect of centring the smooth about the model constant term. All you can really conclude from the plot of the partial effect of $f(\mathbf{x})$ is that as you increase the value of $x_i$, the probability that you'll fall into one of the higher categories increases, for $x_i \approx 50$, and between  $50 \lessapprox x_i \lessapprox 100$ the effect of increasing $x_i$ is also to increase this probability but the effect on $Y$ for a unit change in $x_i$ is lessened and for $x_i \gtrapprox 100$ there is little effect of $x$ on the response. But this all needs to be recentred about the estimated value for $\alpha$ if you want to show the linear predictor (and that is only possible visually here as your model has a single smooth).
