# Brms - non-linear model estimate parameter used within another model

**URL:** <https://discourse.mc-stan.org/t/brms-non-linear-model-estimate-parameter-used-within-another-model/38762>\
**Category:** brms\
**Tags:** fitting-issues, brms\
**Created:** [February 12, 2025, 3:16pm UTC](https://discourse.mc-stan.org/t/brms-non-linear-model-estimate-parameter-used-within-another-model/38762 "2025-02-12T15:16:56Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![benjamin\_hlina](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/benjamin_hlina/32/17511_2.png) [@benjamin\_hlina](https://discourse.mc-stan.org/u/benjamin_hlina)\
**Post date:** [February 12, 2025, 3:16pm UTC](https://discourse.mc-stan.org/t/brms-non-linear-model-estimate-parameter-used-within-another-model/38762/1 "2025-02-12T15:16:56Z")

</div>

Hi everyone,

I am trying to create a non-linear model to estimate trophic position based on [Post 2002](https://www.researchgate.net/publication/221959341_Using_Stable_Isotopes_to_Estimate_Trophic_Position_Models_Methods_and_Assumptions) and [Heuvel et al. 2024](https://aslopubs.onlinelibrary.wiley.com/doi/full/10.1002/lno.12466). I can write this model in JAGS and use {rjags} to estimate `ac` and `tp` but would like to move over to stan and use {brms}. However, I consistently run into the following error message `Error: The parameter 'd15n' is not a valid distributional or non-linear parameter. Did you forget to set 'nl = TRUE'? `. From what I can understand {brms} has issues with circular phased estimates considering I’m first estimating `ac` which is then to be used in the formula for `tp`. Is that correct? If so how can I get around this? I’ve thought of just inserting the formula for `ac` into the `tp` but this doesn’t seem to doing what I expect. Would it be best to write this in {rstan} instead?

If this question has been asked and answered before, sorry for taking up your time. Thanks

```r
suppressPackageStartupMessages(
  library(brms)
)

```

```r
test <- structure(list(common_name = c("Lake Trout", "Lake Trout", "Lake Trout", 
"Lake Trout", "Lake Trout", "Lake Trout", "Lake Trout", "Lake Trout", 
"Lake Trout", "Lake Trout", "Lake Trout", "Lake Trout", "Lake Trout", 
"Lake Trout", "Lake Trout"), d13c = c(-22.24432219, -22.19363157, 
-23.12710892, -21.94797704, -22.09868526, -23.15772812, -22.46564577, 
-22.06822162, -22.58020397, -22.78587869, -23.2490471, -22.09275059, 
-22.27354166, -21.77119478, -22.02081495), d15n = c(18.0137765, 
17.9057604, 17.04653059, 18.08178664, 17.44761289, 17.20065531, 
17.98916764, 17.602950331349, 16.84128291, 17.14235167, 16.65215117, 
17.7093308, 16.77823155, 18.284430048708, 17.12016153), n1 = c(8.823124606, 
8.823124606, 8.823124606, 8.823124606, 8.823124606, 8.823124606, 
8.823124606, 8.823124606, 8.823124606, 8.823124606, 8.823124606, 
8.823124606, 8.823124606, 8.823124606, 8.823124606), n2 = c(12.629882536375, 
12.629882536375, 12.629882536375, 12.629882536375, 12.629882536375, 
12.629882536375, 12.629882536375, 12.629882536375, 12.629882536375, 
12.629882536375, 12.629882536375, 12.629882536375, 12.629882536375, 
12.629882536375, 12.629882536375), lambda = c(2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2), alpha = c(1.23643632363876, 1.24970560263278, 
1.00534932149529, 1.31401056664222, 1.27455968957911, 0.99733413629192, 
1.17850047020125, 1.28253415385541, 1.14851258059064, 1.0946731278142, 
0.973429575190285, 1.27611320760606, 1.22878754563037, 1.36028684278827, 
1.29494379355616), amin = c(0.885791396936097, 0.885791396936097, 
0.885791396936097, 0.885791396936097, 0.885791396936097, 0.885791396936097, 
0.885791396936097, 0.885791396936097, 0.885791396936097, 0.885791396936097, 
0.885791396936097, 0.885791396936097, 0.885791396936097, 0.885791396936097, 
0.885791396936097), amax = c(1.53574192008444, 1.53574192008444, 
1.53574192008444, 1.53574192008444, 1.53574192008444, 1.53574192008444, 
1.53574192008444, 1.53574192008444, 1.53574192008444, 1.53574192008444, 
1.53574192008444, 1.53574192008444, 1.53574192008444, 1.53574192008444, 
1.53574192008444)), row.names = c(NA, -15L), spec = structure(list(
    cols = list(common_name = structure(list(), class = c("collector_character", 
    "collector")), d13c = structure(list(), class = c("collector_double", 
    "collector")), d15n = structure(list(), class = c("collector_double", 
    "collector")), n1 = structure(list(), class = c("collector_double", 
    "collector")), n2 = structure(list(), class = c("collector_double", 
    "collector")), lambda = structure(list(), class = c("collector_double", 
    "collector")), alpha = structure(list(), class = c("collector_double", 
    "collector")), amin = structure(list(), class = c("collector_double", 
    "collector")), amax = structure(list(), class = c("collector_double", 
    "collector"))), default = structure(list(), class = c("collector_guess", 
    "collector")), delim = ","), class = "col_spec"), class = c("spec_tbl_df", 
"tbl_df", "tbl", "data.frame"))

```

```r
tp_formula <- bf(
  alpha ~ ac * (amax - amin) + amin,
  d15n ~ dn * (tp - (lambda + n1 * ac + n2 * (1 - ac))),
  ac ~ 1,
  n1 ~ 1,
  n2 ~ 1,
  tp ~ 1,
  dn ~ 1,
  nl = TRUE
)

```

```r
tp_priors <- c(
  # Beta prior for 'ac'
  brms::prior(beta(1, 1), class = "b", lb = 0, ub = 1, nlpar = "ac"),
  # Baseline (n1)
  brms::prior(normal(8, 1), class = "b", coef = "Intercept", nlpar = "n1"),
  # Baseline (n2)
  brms::prior(normal(10, 1), class = "b", coef = "Intercept", nlpar = "n2"),
  # Trophic enrichment factor (ΔN)
  brms::prior(normal(3.4, 0.5), class = "b", lb = 3, ub = 4, nlpar = "dn"),
  # Trophic Position (tp)
  brms::prior(uniform(2, 10), class = "b", nlpar = "tp", lb = 2, ub = 10),
  # Standard deviation prior
  brms::prior(uniform(0, 10), class = "sigma")
)

```

```r

tp_fit <- brm(
  formula = tp_formula,
  data = test,
  family = gaussian(),
  prior = tp_priors,
  iter = 4000,
  warmup = 1000,
  chains = 2,
  cores = 4,
  control = list(adapt_delta = 0.95)
)
#> Error: The parameter 'd15n' is not a valid distributional or non-linear parameter. Did you forget to set 'nl = TRUE'?

```

Created on 2025-02-12 with [reprex v2.1.1](https://reprex.tidyverse.org)

---

<div class="post-metadata">

**Author:** ![amynang](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/amynang/32/19114_2.png) [@amynang](https://discourse.mc-stan.org/u/amynang)\
**Post date:** [February 12, 2025, 6:46pm UTC](https://discourse.mc-stan.org/t/brms-non-linear-model-estimate-parameter-used-within-another-model/38762/2 "2025-02-12T18:46:29Z")

</div>

Hey @benjamin_hlina , welcome!

**EDIT: the following approach is incomplete because it does not handle `ac` as a _shared parameter_, as was intended. See the followup discussion [here](https://discourse.mc-stan.org/t/what-is-rescor-in-brms-doing-for-this-non-linear-multivariate-model/40677/2).**

This worked: I separated your formula into two distinct formulas and specified the response in the priors. (I also upped the iterations to 40000.)

```no-highlight
tp_formula <- bf(
  alpha ~ ac * (amax - amin) + amin,
  ac ~ 1,
  nl = TRUE
) + 
  bf(
    d15n ~ dn * (tp - (lambda + n1 * ac + n2 * (1 - ac))),
    ac ~ 1,
    n1 ~ 1,
    n2 ~ 1,
    tp ~ 1,
    dn ~ 1,
    nl = TRUE
  )

tp_priors <- c(
  # Beta prior for 'ac'
  brms::prior(beta(1, 1), lb = 0, ub = 1, resp = "alpha", nlpar = "ac"),
  brms::prior(beta(1, 1), lb = 0, ub = 1, resp = "d15n", nlpar = "ac"),
  # Baseline (n1)
  brms::prior(normal(8, 1), resp = "d15n", coef = "Intercept", nlpar = "n1"),
  # Baseline (n2)
  brms::prior(normal(10, 1), resp = "d15n", coef = "Intercept", nlpar = "n2"),
  # Trophic enrichment factor (ΔN)
  brms::prior(normal(3.4, 0.5), resp = "d15n", lb = 3, ub = 4, nlpar = "dn"),
  # Trophic Position (tp)
  brms::prior(uniform(2, 10), resp = "d15n", nlpar = "tp", lb = 2, ub = 10),
  # Standard deviation prior
  brms::prior(uniform(0, 10), resp = "alpha", class = "sigma"),
  brms::prior(uniform(0, 10), resp = "d15n", class = "sigma")
)

```

(I had to comment out `problems = < pointer:0x120723a80 > ,` for your test data to work)

---

<div class="post-metadata">

**Author:** ![benjamin\_hlina](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/benjamin_hlina/32/17511_2.png) [@benjamin\_hlina](https://discourse.mc-stan.org/u/benjamin_hlina)\
**Post date:** [February 12, 2025, 6:53pm UTC](https://discourse.mc-stan.org/t/brms-non-linear-model-estimate-parameter-used-within-another-model/38762/3 "2025-02-12T18:53:48Z")

</div>

Thank you so so much! This makes a lot of sense, I just kept getting stuck in having it make it all in one.