AddObs - Details

In ctsmTMB: Continuous Time Stochastic Modelling using Template Model Builder

library(ctsmTMB)

In this document we show how to apply functions to the left-hand side of an observation equation.

# Create model object
obj = ctsmTMB$new()

# Add system equations
obj$addSystem(
  dx ~ theta * (mu-x) * dt + sigma_x*dw
)

Adding observation equations

---

Let's assume that our observations $y_{t}$ are log-normally distributed conditioned on $x_{t}$ i.e. $$ \log y_{t_{i}} \sim N(x_{t_{i}},\sigma_{y}^{2}) $$ It is sufficient for the user to provide the data column y in the provided data.frame to e.g. estimate or predict by adding the following observation equation

obj$addObs(
  log(y) ~ x, obsnames = "log_y"
)

Note that these kind of observation equations, where the left-hand side is a function of one (or more) observed variables must be explicitly named using the obsnames argument.

Adding observation variances

---

The names given with obsnames are important because they are needed to specify the observation variance. As an example the code below does not work, because the observation was named log_y

obj$setVariance(
  y ~ sigma_y^2
)

So the correct way to add the observation variance is this:

obj$setVariance(
  log_y ~ sigma_y^2
)

Multiple observation equations

---

You must supply multiple obsnames if you are supplying multiple observation equations, although the name will only be used if the left-hand side is not just a single variable i.e.

obj$addObs(
  log(y) ~ x,
  y ~ x,
  y^2+z^3 ~ x,
  obsnames = c("log_y", NA, "y2_plus_z3")
)

ctsmTMB documentation built on April 12, 2025, 1:45 a.m.