engleski

Analysis of defoliation using logistic regression model with ordinal response

We analyzed defoliation of beech-fir forests on two permanent plots (locations) "Brloško" (BRO) N=81 and "Bitoraj" (BIT) N=194. The emphasised vulnerability of fir and beech-fir forest on the edge of their areal stimulated us to conduct the research in these forests. Site BRO is Dinaric beech-fir forest on calcocambisol upon limestone, and BIT is fir forest with hard fern located on a dystric cambisol upon silicate bedrock. Visual assessment of defoliation was done in 2007 and estimates were classified in three levels as following: 1 (≤ 25%) healthy (BRO: 0.259 ; BIT: 0.134), 2 (25-60%) damaged (BRO: 0.148 ; BIT: 0.247), 3 (> 60%) severely damaged (BRO: 0.593 ; BIT: 0.619). The main goal was to estimate probability and odds ratio of transition from one level of defoliation to another and compare it between two observed locations. In order to assess odds ratio of transition from one level of defoliation to another we first wanted to use a cumulative logit model, but unfortunately Proportional Odds Assumption (chi2=7.84 ; df=1 ; p=0.0051) was not satisfied. We estimated model in a way that we do separate binary logit analyses for each phase comparison of dependent variable. The first phase is modelling the second level of defoliation to the first. The second phase is modelling the third level of defoliation to the second. For that we use dummy indicator variable. For each phase comparison we construct a data set that excludes all trees that did not make it to that phase. Finally we estimate a single model (binary logistic) on combined data set. In the first model we tested the difference between the phases, locations and interaction of phase and location. The results show that there is a statistically significant difference between phases (2/1 ; 3/2)(chi2=15.6327 ; df=1 ; p<0.001), between locations (chi2=8.8634 ; df=1 ; p=0.0029) and the interaction between the phase and location are also statistically significant (chi2=8.3396 ; df=1 ; p=0.0039) what indicates that the defoliation in 2007 behave differently at the analysed locations. For sake of better analysis of the observed defoliation at analysed locations and the relationship between the diameter at breast height (DBH), as a measure of physiological maturity, and defoliation, we modelled each phase separately, and the independent variables were location and DBH, and also their interaction if it significantly contributed to the model. In the model without interaction for the first phase (2/1) odds ratio for the transition to the second level of defoliation for BRO is 6.004 (95% CI 1.838-19.607), and DBH (cm) OR = 1.022 OR (95% CI 0.995-1.050). The interaction between location and DBH in 2007 is a statistically significant and left in the mode. The final model for the analysis of the first phase (2/1): Logit (p2/1)=0.575 - 3.137 location - 0.017 DBH + 0.119 locationxDBHThe results of the second phase, for modelling the third level of defoliation regard to the second (3/2) in the model without interaction OR for BIT = 0.427 (95% CI 0.147-1.244), and for DBH was OR = 0.99 (95% CI 0.970-1.010). When we put the interaction in, interaction significantly improves the model (-2logL = 19.9898, df = 1, p <0.001), and the location and DBH are becoming statistically significant. So the final model for the second phase (third level to the second level) is:Logit (p3/2)=-0.807+ 3.774 location + 0.035 DBH - 0.095 locationxDBH

forest damage; defoliation; beech-fir forests; logistic model

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