Table 3.

Generalized Linear Mixed Effect Models of Sudden Oak Death (SOD) on Observed Nymphal Infection Prevalence

Model component	Parameter	Nymphal infection prevalence (z value)
Intercept	α	−2.50 (−20.95)***
SOD (PC 1)	β1	−0.11 (−2.09)*
Site	β2	0.36 (2.27)*

p Value: ^*0.05; ^***0.001.

SOD was summarized previously using principal components analysis (Swei et al. 2011a). Interpretations of principal components are provided in the table based on the parameters that were significantly loaded on each component (Swei et al. 2011a). The model for nymphal infection prevalence is: Y_i=NIP_i ∼ Binomial(nymphs_i, π_i) for i=1…n, where n=(number of plots) ^* (number of years)=42, nymphs_i is the number of nymphal ticks screened for Bb on survey i, and π_i is the probability of infection with Bb. E(Y_i)=π_i×nymphs_i, var(Y_i)=nymphs_i×π_i×(1–π_i); logit(π_i)=α+β₁×PC1+β₂×PC2+β₃×PC3+β₄×PC4+β₅×Site+γ_j[i]+ψ_k[i], where γ_j and ψ_k are random effects. The random effect of Plot is γ_j[i] ∼ N(0,σ_plot) for j=1…J, where J=number of plots=14. The random effect of Year is ψ_k[i] ∼ N(0,σ_year) for k=1…K, where=number of years=3. The final model included PC 1, and Site as a fixed effect. Model selection was determined by Akaike information criterion score values. The z value is the Wald statistic.