Estimating tree resin dose effect on termites

The aim of this study is to determine the effectiveness of a natural tropical tree resin in controlling termites thus providing protection from their destruction. Tree resin from the bark of tropical trees offers the potential for this protection. Termites were fed by filter paper soaked in tropical tree resin dissolved in a solvent at different concentrations for 15 days. The number of termites still alive on each day was observed and recorded. In this paper, we use four types of statistical models: Partially linear model, piecewise linear model, cubic smooth spline and mixed effect model to analyze the termite data. The results show that tropical tree resin, particularly at a higher concentration of 10mg is significantly more effective in killing termites. We show that two dishes under 10mg of tree resin were mistaken since the data for these two dishes are shown insignificantly different from data under 5mg. The partially linear model shows that there is non-linear (piecewise linear) time effect. Both piecewise linear model and cubic spline smoothing show that the most effective period is the first week. The nonparametric smoothing, cubic spline, and piecewise linear model are not significantly different. Mixed effect model is consistent with partial linear model and piecewise linear model. The estimated treatment effect is time varying with a change point at day 7. Therefore, we suggest the piecewise linear model as the final simplest one for prediction. This model fits the data with adjusted R1⁄4 93.7 per cent and shows that on average, 10mg is 68.9 per cent more efficient than 5mg in killing termites during the first week. Copyright # 2005 John Wiley & Sons, Ltd.