Hello,

I’m hoping to build a model (ideally via `brms`

) which is able to use both linear (with smoothing splines) and nonlinear components but I am having some isues with specifying the model. The model I am hoping to make is:

r_{t,i} \sim Normal(\mu_i, \sigma)

\mu_i = f(\rho_i)

\rho_i = T_i + \frac{1}{\phi}D_i

D_i = sin(\theta)X_i + cos(\theta)Y_i

where I want to estimate parameters \theta and \phi and variables D and \rho, with \rho eventually being fed into a smoothing spline.

Simulated dataset:

```
phi <- 2
theta <- 90 * pi/180
x <- 1:10
y <- 1:10
t <- 1:10
map <- expand.grid(x, y, t)
df <- data.frame(
x = map$Var1, # x coord
y = map$Var2, # y coord
t = map$Var3 # time
)
df$D <- sin(theta) * df$x+ cos(theta) * df$y
df$rho <- df$t+ (1/phi) * D
df$rt <- sin(df$rho)
```

Based on a reply to another ~similar question about having a model with both linear and nonlinear components, I think it’s possible to have both together in `brms`

, but I may be misunderstanding the context (most questions I’ve seen are related to non-linear models with linear random/varying effects).

The syntax I have tried is:

```
linear <- bf(
rt ~ s(rho, k = 12, bs = "tp"),
)
nonlinear <- bf(
rho ~ t + 1/phi * D,
D ~ sin(theta) * x + cos(theta) * y,
phi ~ 1,
theta ~ 1,
nl = TRUE
)
priorz <- c(
prior(normal(5, 10), nlpar = "phi"),
prior(uniform(0, 2*pi), nlpar = "theta")
)
fit <- brms(linear + nonlinear,
prior = priorz,
family = gaussian(),
...
)
```

When I try this I get a warning that e.g. theta is not recognised as a distribution and a suggestion that I forgot to include `nl = TURE`

. Based on another post, I tried separating each component into its own `bf()`

:

```
linear <- bf(
rt ~ s(rho, k = 12, bs = "tp")
)
nonlinear <- bf(
rho ~ t + 1/phi * D,
phi ~ 1,
nl = TRUE
)
nonlinear2 <- bf(
D ~ sin(theta) * x + cos(theta) * y,
theta ~ 1,
nl = TRUE
)
```

But I get an error stating that ` The following variables are missing in 'data': 'rho', 'D'`

.

I’m not really sure where the problem is. Is it possible to mix linear and nonlinear together in this way? I’d really appreciate it if someone could give some advice.

Thanks,

- Operating System: Windows 10
- brms Version: brms_2.13.5