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The parallel application of two probability models, logit and probit, for the accurate analysis of spruce timber damage due to thinning operations

Bakinowska E., Mederski P. S., Szczepańska-Alvarez A., Karaszewski Z., Bembenek M.

Drewno : prace naukowe, doniesienia, komunikaty

2016

vol. 59, nr 197

49--59

Logit and probit models belong to the class of generalised linear models. A few applications of both models have been documented in the field of forestry. The objective of this paper was to test the parallel use of these models to discover the differences in damage to a spruce stand after thinning using the full tree system, the long wood system and the short wood system. In particular the aim was to ascertain the general damage probability caused by the harvesting systems (HS) and the particular damage class probability in each HS. When the general damage probability was calculated the logit model was used. When nine damage classes were taken into account, however, the probit model was found to fit the data better. In this case, the results obtained gave accurate information on the probability of the appearance of a particular damage class for each HS. It was concluded that the probit and logit models should be considered in parallel in order to obtain the best possible goodness of fit and to get accurate information on the distribution of damage classes.

Comparison of linear interpolation and arctan approximation of one-dimensional monotonic utility functions based on experimental data

Nikolova N., Tenekedjiev K., Dong F., Hirota K.

Control and Cybernetics

2009

Vol. 38, no 3

835-861

Elicitation of utilities is among the most time consuming tasks in decision analysis. We search for ways to shorten this phase without compromising the quality of results. We use the results from an empirical experiment with 104 participants. They elicited 9 inner nodes from their one-dimensional utility function over monetary gains and losses using three elicitation techniques. A specific feature of the results is their interval character, as the elicitators are fuzzy rational individuals. The data is used to construct arctan-approximated and linearly interpolated utilities and to compare the results. We form partial samples with 3, 4 and 5 nodes for each participant and each elicitation method, and again interpolate/approximate the utilities. We introduce goodness-of-fit and deterioration measures to analyze the decrease in quality of the utility function due to reduced data nodes. The analysis, using paired-sample tests, leads to the following conclusions: 1) arctan-approximation is more adequate than linear interpolation over the whole samples; 2) 5 inner nodes are sufficient to construct a satisfactory arctan-approximation; 3) arctan-approximation and linear interpolation are almost equal in quality over the partial samples, but the local risk aversion of the linearly interpolated utility function is of poor quality unlike that of the arctan-approximated utility function.