# Articles containing the keyword 'log-log link'.

## Category: Research note

article id 1496, category Research note
(2016). Using a bivariate generalized linear mixed model to analyze the effect of feeding pressure on pine weevil damage. Silva Fennica vol. 50 no. 1 article id 1496. https://doi.org/10.14214/sf.1496
Highlights: Probability of damage of treated seedlings can be predicted from the probability of damage of control seedlings (feeding pressure).

The objective of the study is to derive a method by which one can analyze how the probability of damage made by pine weevils on seedlings treated with insecticides depends on the probability of damage on untreated control seedlings, called feeding pressure. Because the probabilities vary from stand to stand and from block to block, the analysis is done using a generalized linear mixed model. The dependency of probability of damage on the feeding pressure cannot be properly analyzed using observed relative frequency of damage of control seedlings as a covariate, but it can be analyzed using a bivariate model. One equation describes damage of control seedlings and another equation damage of treated seedlings. The random stand and block effects of different equations are correlated. For a given probability of stand level control seedling damage, the random stand effect for control seedlings can be computed using a link function, then random stand effects for treated seedlings can be predicted using the best linear predictor from the random effect for control seedlings. Using an inverse link the prediction can again be presented in the probability scale which is of interest to the user. Using these three steps the probability of damage of treated seedlings can be predicted from the control damage probability. The probability of damage of treated seedlings can also be predicted from the observed relative frequency of damaged control seedlings using simulation. The complementary log-log link was used for control seedlings and the log-log link for treated seedlings.

• Lappi, Natural Resources Institute Finland (Luke), Economics and society, Juntintie 154, FI-77600 Suonenjoki, Finland ORCID ID:E-mail: juha.lappi@luke.fi
• Luoranen, Natural Resources Institute Finland (Luke), Management and Production of Renewable Resources, Juntintie 154, FI-77600 Suonenjoki, Finland ORCID ID:E-mail: jaana.luoranen@luke.fi

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