Poisson log-normal model in rstanarm

[malai...@gmail.com]

Hi All,

I have currently fitted a negative binomial model in rstanarm, but i would like to fit the same data using poisson-lognormal model. Is there a way I can achieve that in rstanarm?

Thanks.

[Ben Goodrich]

On Sunday, November 13, 2016 at 8:25:21 PM UTC-5, malai...@gmail.com wrote:

I have currently fitted a negative binomial model in rstanarm, but i would like to fit the same data using poisson-lognormal model. Is there a way I can achieve that in rstanarm?

No, but what is a Poisson-lognormal model?

[Bob Carpenter]

Presumably,

lambda[n] ~ lognormal(mu, sigma);

y[n] ~ poisson(lambda[n]);

- Bob

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[malai...@gmail.com]

following is the description of the two models; negative binomial (poisson-gamma) and poisson-lognormal model.

 y_(i,t)  ~ Poisson(ε_i λ_(i,t)) 

Where:

y_(i,t) =    Observed number of crashes at site i in year t

λ_(i,t) =    Expected number of crashes at intersection I in year t

ε_i =    Multiplicative random effect at site i

The main difference between the Poisson-Lognormal and Poisson-Gamma model in estimating the expected crashes is on estimating the multiplicative random effect for site i. the following equations describe the estimation of ε_i for the two models.

For the Poisson-Lognormal model, ε_i  ~ LogN(0,σ^2)

For the Poisson-Gamma model, ε_i  ~ Gamma(φ,(1/φ)

 

[Ben Goodrich]

In that case, I guess you can do a Poisson-lognormal model with

stan_glmer(y ~ ... + (1 | site), data = dataset, family = poisson(link = "log"), QR = TRUE)

Ben

[malai...@gmail.com]

Hi Ben,

Thank you for the response. I followed the option you proposed and its working fine. I am just wondering what is the site variable?

On Sunday, November 13, 2016 at 8:25:21 PM UTC-5, malai...@gmail.com wrote:

[Ben Goodrich]

On Monday, November 21, 2016 at 12:00:26 PM UTC-5, malai...@gmail.com wrote:

Thank you for the response. I followed the option you proposed and its working fine. I am just wondering what is the site variable?

I don't know,, but you said