## 3 Results
### Negative Binomial Generalized Linear Regression Analysis
From the estimated incidence rate ratios, which can be interpreted as the estimated coefficients from the regression model, dwarf shrubs have the highest contribution while pine forest has the lowest, with mixed hardwood and grassland in between. The alternative model, which is not as good as the calibrated model according to the AICc and pseudo-R\({}^{2}\), sheds some light on the influences of seasonality and vegetation. When the season is added as a predictor, it is statistically significant, indicating there are more question black-legged ticks in the fall season than in the spring. Unsurprisingly, the inclusion of season reduces the significance of temperature. In fact, the combination of season and elevation performs better than temperature in terms of increasing the model fitness. The coefficient of the humidity is lower with the presence of season, although its \(p\) value is still less than 0.05 and has the same signs as in the calibrated model. One major contribution of the alternative model is to illustrate the importance of NDVI, which has a statistically significant positive coefficient, although it is less superior than using the percentages of the specific land cover of vegetation. Unlike what we expected, the ecotone boundary length, an indicator of landscape fragmentation, has no significant impacts on the number of question ticks, although the predictor does have a positive coefficient. Overall, the generalized linear regression based on negative binomial distribution gave results that are consistent with the existing theories. Higher ambient temperature and relative humidity, when in the normal ranges, lead to more tick question activities. Vegetation, characterized by NDVI, also has a positive effect on the number of question ticks. More specifically, dwarf shrubs and mixed hardwoods have the highest positive impacts on ticks' question activities, while grassland and pine trees have much lower, yet still positive, impacts with residential land and paved roads being the baseline, which is also the consensus from a recent literature review [33]. \begin{table}
\begin{tabular}{l l c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Specification**} & **AICc** & \multirow{2}{*}{\(\overset{\text{\tiny{\textbullet}}}{\text{\tiny{\text@bullet}}}\)**(se)**} & \multirow{2}{*}{\(\overset{\text{\tiny{\textbullet}}}{\text{\tiny{\text@bullet}}}\)**(normalized)**} & \multirow{2}{*}{**Nagelkerke**} & **Adjusted** \\  & & & & & & **McFadden** \\ \hline
**Null** & Tick count \(\sim\) 1 & 490.25 (0.00) & 0.94 (0.17) & 6.04 (0.086) & 0.00 & 0.00 \\
**Full** & Tick count \(\sim\) temperature + & & & & & \\ relative humidity + season + & & & & & \\ solar + elevation + ndvi + & 455.22 (35.03) & 2.67 (0.62) & 5.86 (0.084) & 0.57 & 0.10 \\  & ecotone length + land cover * & & & & \\  & Tick count \(\sim\) elevation + relative & & & & \\ humidity + season + ndvi + & 449.15 (41.10) & 2.01 (0.43) & 5.57 (0.080) & 0.47 & 0.10 \\  & ecotone length & & & & \\
**Calibrated** & Tick count \(\sim\) temperature + & & & & \\ relative humidity + land cover * & 440.90 (49.35) & 2.69 (0.70) & 5.12 (0.073) & 0.55 & 0.11 \\ \hline \hline \end{tabular}  
N = 80 (after excluding the records with incomplete items). * Land cover includes percentages of four land-cover types: mixed hardwoods, dwarf shrubs, grasslands, and pine forest. \(\overset{\text{\tiny{\textbullet}}}{\text{\tiny{\text@bullet}}}\)**(se)** is the estimated dispersion parameter and standard error. When the dispersion is zero, the distribution becomes a Poisson. CVc is the corrected prediction error (RMSE) from a leave-one-out cross validation. It is normalized by Y\({}_{\text{max}}\) \(-\) Y\({}_{\text{min}}\). The mean and standard deviation of Y are 7.19 and 9.91, respectively.  
\end{table} 
Table 3: Negative Binomial Regression Modeling Results.