Threshold moderation effects: how body length modifies the effect of temperature on parasite abundance

The moderation effect is one of many useful research strategies to modelparasitological data. Researchers typically compute an interaction term and focus on whether this variable is statistically significant. However, the marginal effect plots allow for capturing the situations where the effects of changing the explanatory variable are significantly different from zero only at specific values of the moderator. For illustration, the empirical data from 535 individuals of pacific so-iuy mullet, Planiliza haematocheila, sampled from localities in the Sea of Azov during 1998–2014, were used (doi.org/10.1016/j.ijpara.2020.06.008). The parasite abundance of Ligophorus llewellyni was as dependent variable, the temperature and the month wereexplanatory covariates, and the body length of the fish was amoderator. We applied a generalized linear model with negative binomial distribution: abundance ~ temperature * body length + month * body length. The interaction effects were statistically significant (p<0.01). The marginal effect plot showed that the temperature affects the abundance of values of body length in the range 34-71.5 cm, and this effect becomes stronger with increasing body length. According to the data, approximately 74% of the observations have values of body length higher than 34 cm. For interaction models, the marginal effect plots provides valuable insights into changes in the interaction across different ranges of the moderator.

S.S. is funded by the Ministry of Education, Research, Development and Youth of the SK (bilateral scholarship, letter of award No. 2025/10152:5-A9161), and V.S. is supported by the International Visegrad Fund, No. 52510298.