---
title: "AddObs - Details"
author: ""
date: ""
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{AddObs - Details}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include=FALSE}
library(ctsmTMB)
```

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

```{r}
# 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

```{r}
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`

```{r, error=TRUE}
obj$setVariance(
  y ~ sigma_y^2
)
```

So the correct way to add the observation variance is this:
```{r}
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.
```{r, eval=FALSE}
obj$addObs(
  log(y) ~ x,
  y ~ x,
  y^2+z^3 ~ x,
  obsnames = c("log_y", NA, "y2_plus_z3")
)
```
