GLMMで対応する生態毒性データのばらつき

抄録

The generalized linear model (GLM) is a useful tool to evaluate the relationship between the response variable and explanatory variables. However, the GLM analysis cannot consider the variation between experimental groups when the data shows over-dispersion of ecotoxicity testing data due to experimental replication. Alternatively, the generalized linear mixed model (GLMM) contains random effects which show a probability density distribution (in many cases, the Gaussian distribution is applied) attributed to the data variation. The GLMM can make a large variation by mixing the assumed probability density distribution with the fixed effects. To show the difference between GLM and GLMM analysis, we introduced two toxicity tests (Chironomus acute toxicity test in and mesocosm test) using dummy count data. The GLMM shows larger errors in the slope and intercept values than those in the GLM.

For the Chironomus acute toxicity test, the GLMM estimated large 95% confidence intervals for the EC₅₀ (median effective concentration) values, which could show the toxicity variations between the replications. Our findings suggested that the GLM analysis is likely to increase frequency of Type I error in estimating the relationship between variables if there is a large variation between the data.