Linear regression in INLA
NADIA LOPEZ
Hello. I am a beginner using INLA. I would greatly appreciate your help.
I am studying the relationship between "fish larvae count" and water temperature (°C). The larvae count in the samples was collected from various filtered volumes (m3). Instead of using relative abundance (larvae count/filtered volume), I am using the larvae count as the dependent variable to utilize known distributions like the Negative binomial or Poisson. The filtered volume was included as an "E".
1.- Is it correct to utilize the argument "E" in this case? Additionally, does "E" function effectively in a negative binomial distribution?
I am sharing with you the structure of my data and the model:
df <- data.frame(count_larvae = c(3,3,2,2,1,1,3,1,3,8,3,11,16,26,1,1,15),
filtrate_volume = c(237.0,256.0,259.2,232.3,262.2,189.6,210.3,
245.9,145.3,260.6,158.2,148.3,258.0,266.8,
237.5,192.8,116.0),
temperature = c(30.2,30.2,30.3,30.3,30.2,30.3,30.0,30.1,29.9,
29.6,29.8,29.6,29.7,29.3,29.9,29.9,29.7))
model <- inla(data = df,
E = filtrate_volume,
formula = count_larvae ~ temperature,
family = "nbinomial",
control.predictor = list(compute = TRUE,
link = 1),
quantiles = c(0.025, 0.5, 0.975),
control.compute = list(
return.marginals.predictor = TRUE,
mlik = TRUE,
config = TRUE))
2.- What units does the model output employ? The output is not in the form of larvae count, as they are continuous quantities even though link=1 is utilized. Consequently, I am unable to incorporate the observations (larvae count, discrete quantities) in the plot.
names(model$summary.fitted.values) <- paste("fit_",
names(model$summary.fitted.values),
sep = "")
df_output <- cbind(df, model$summary.fitted.values)
str(df_output)
'data.frame': 17 obs. of 9 variables:
$ count_larvae : num 3 3 2 2 1 1 3 1 3 8 ...$ filtrate_volume: num 237 256 259 232 262 ...
$ temperature : num 30.2 30.2 30.3 30.3 30.2 30.3 30 30.1 29.9 29.6 ...
$ fit_mean : num 0.00847 0.00847 0.00622 0.00622 0.00847 ...
$ fit_sd : num 0.00234 0.00234 0.00204 0.00204 0.00234 ...
$ fit_0.025quant : num 0.00475 0.00475 0.00312 0.00312 0.00475 ...
$ fit_0.5quant : num 0.00818 0.00818 0.00593 0.00593 0.00818 ...
$ fit_0.975quant : num 0.0139 0.0139 0.011 0.011 0.0139 ...
$ fit_mode : num 0.00765 0.00765 0.00541 0.00541 0.00765 ...
Thanks in advance for your support.
Best regards,
Nadia L.
Finn Lindgren
As you noted, this is not a count, and that's because it is the the value of the expectation _parameter_ of the Negative Binomial distribution, and _not_ a value generated from that distribution.
To do data-level prediction, you need to post-process the results to incorporate the observation-level model variability.
Precisely how to do that depends on precisely what you wish to compute and/or estimate.
A common approach is to do posterior sampling of the predictor/expectation values, and combine that with a data-level simulation step.
Finn
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Helpdesk (Haavard Rue)
also note that the 'E' in the Poisson and nbinomial, is _not_ part of the fitted
values. if you want it to be, use
formula= .. ~ .. + offset(log(E.values))
instead, where 'E.values' are the values of 'E' you would 'normally' use
he...@r-inla.org
NADIA LOPEZ
Thank you both for your support!
All the best!
Nadia L.