I am having troubles fitting a four-parameter log-logistic (LL4) model with partial pooling to dose-response data. The four-parameter log-logistic function is a function of the dose x, and is given by f(x) = c + \dfrac{d-c}{1+\exp(b(\log(x)-\hat{e}))} where the response is measured in counts (hen…

[image] arya: I wonder if there’s an issue going on with using normal priors on positive parameters without truncating the distribution. I was under the impression that I had already used truncated distributions; e.g. for c I have vector<lower=0>[J] c; real<lower=0> mu_c; real<lower=0> sigma…

Following @arya ’s suggestion, I changed model_code to implement non-centred parametrisation (as discussed in the Stan user guide ). model_code <- " functions { real LL4(real x, real b, real c, real d, real ehat) { return c + (d - c) / (1 + exp(b * (log(x) - ehat))); } } data { int<lower=1>…

Blockquote [image] mevers: Since c has a lower bound of 0, normal(mu_c, sigma_c) should correspond to a truncated normal, no? Do you think it might make more sense to have a Poisson prior on c and d , since they correspond to asymptotic counts and y ~ poisson(mu_y) ? That would reduce the …

[image] arya: Usually for parameters that are constrained to be positive I would go for a log-normal, a chi-square, a gamma, or an inverse-gamma. Ok, I will look into this. I’m not convinced that this will make a significant difference though. On that note I also realised that I cannot use Po…

An update Log-normal densities for 0-bounded (count-like) parameters Having lognormal densities for c and d significantly improved the runtime (thanks @arya for the suggestion). The model now looks like this functions { real LL4(real x, real b, real c, real d, real ehat) { return c + (d - c)…

Glad to hear the lognormal worked out. I wonder if it could’ve been the problem with normalizing the truncated normal. Yeah that’s definitely a funnel but if you’re not getting divergences and otherwise good sampler diagnostics, you should be ok.

I notice that using the original pooled model with normal priors, sigma_d is estimated to be 985 but its prior is cauchy(0, 2.5). If you shift that prior to have more amplitude near the estimated value, does the performance improve?

Thanks @FJCC for pointing that out. In fact, I had a closer look at the d estimates (including hyperparameters), and here are the results summary(fit, pars = c("d", "mu_d", "sigma_d"))$summary # mean se_mean sd 2.5% 25% 50% 75% #d[1] 3489.865 0.5093660 …

First, a disclaimer - I am just a novice Stan user trying to learn by participating in this forum. Don’t take anything I say as authoritative. I am unsure which model produced your last results but in any case, I think of mu_d as being estimated from only three values. d is the upper asymptote of …

[image] FJCC: If you do have the tight prior on mu_d, try making it much broader and not pinned to the global maximum and see how the result changes. I think you hit the nail on the head @FJCC ! Good spot. The prior on mu_d was way too tight, which meant that the posterior density was entirely…

Dose-response model with partial pooling

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Dose-response model with partial pooling

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