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Interpretation of model coefficients in a multivariate poisson GLM with spatial random effect #179

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cabuelow opened this issue Mar 31, 2024 · 0 comments

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@cabuelow
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cabuelow commented Mar 31, 2024

Hello,

I could use help interpreting model coefficients in a multivariate poisson GLM with a spatial random effect.

I've set up a reprex here with code and rds files to load fitted models.

The script provides code to simulate a spatial dataset of multivariate species abundances in response to an explanatory variable Fire severity and a spatially structured latent variable.

This script also contains code to fit two models to the simulated dataset: 1) a multivariate poisson GLM with a non-spatial, site-level random effect, and 2) a multivariate poisson GLM with a spatial random effect.

Here are the simulated 'known truths' for the slope beta coefficients representing the associations between 5 different species abundances and Fire severity.

spp b1
spp1 -0.69314718
spp2 -0.09531018
spp3 0.00000000
spp4 0.09531018
spp5 0.69314718

Both models provide coefficient estimates slightly biased from the simulated 'known truths'. And the mean value of the alpha parameter estimated by the spatial Model 2 is 0.18, but was simulated to be 0.35.

Model 1 summary of estimated b1 coefficients:

Mean
B[Fire_severity (C2), spp1 (S1)] -0.8731268
B[Fire_severity (C2), spp2 (S2)] -0.1009772
B[Fire_severity (C2), spp3 (S3)] -0.1928004
B[Fire_severity (C2), spp4 (S4)] 0.2030243
B[Fire_severity (C2), spp5 (S5)] 0.6712431

Model 2 summary of estimated b1 coefficients:

Mean
B[Fire_severity (C2), spp1 (S1)] -0.9392138
B[Fire_severity (C2), spp2 (S2)] -0.1949200
B[Fire_severity (C2), spp3 (S3)] -0.1580849
B[Fire_severity (C2), spp4 (S4)] 0.2176851
B[Fire_severity (C2), spp5 (S5)] 0.6902558

I wanted to check my interpretation is correct, but I assume that the b1 coefficients should interpreted as the expected change in mean species abundance given a one unit shift in Fire severity conditional on the random effect (rather than the change in mean species abundance expected with a one unit shift in X (Fire severity))?

I also wondered if there is anything I can do to improve estimation of the alpha parameter by the spatial model 2, to get closer to the known truth of 0.35 (instead of the estimated mean value of 0.18). I left the number of latent factors to the default setting (returning 5).

Many thanks for the help, I really appreciate it.

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