Application of Logistic Regression in Landscape Aesthetic Quality Modelling (Case study: Ziarat watershed of Golestan Province)

Introduction
Main trend of ecotourism is nature and its beauties; so finding the beautiful landscapes and evaluating aesthetic values of the area would be considered as one of the principles of recreational planning. Scenic beauty is a major component of every encounter with the natural environment in tourism and recreation activities. Visual elements of landscape not only present aesthetical values but also verify the mutual relationships of these values in cultural, economic and biological dimensions. The perceived aesthetic value of landscape is beyond identifying processes of physical and biological signs on the landscape and virtually is a perceptional process originated from visual aesthetic exchanges between the observer and geographic space. This perception is a process through which sensory information can be detected and classified into meaningful structures. The aesthetic appreciation of a landscape as it is perceived by humans has been a subject of theory development in various disciplines. With the development of land use planning, and its requirement for environmental data on which to base land use decisions, came an increased desire to elaborate valid means to quantify the scenic characteristics of landscapes. Due to the fact that visual sense has the highest amount of influence on the quality of individuals’ recreational experience, visual quality assessment seems to be essential. Integration of GIS beside field surveys has provided more sophisticated decision support tools for solving complex management problems such as evaluating the scenic value considered as a non-quantifiable source in the recent past. Most studies have been conducted to assess the landscape visual quality in Iran is based on subjective approach and there is no references about objective assessment. Accordingly, the purpose of this research is to evaluate the visual quality of landscapes to single out more valuable landscapes.
Materials and method
Since the main trend of ecotourism is nature and its beauties so finding beautiful landscapes and evaluating aesthetic values of the area would be considered as one of the principles of recreational planning. Special geographic position, climate diversity, special topographic and geomorphologic statuses are considered as unique potentials of ecotourism. Given that, Ziarat watershed which is one of the tourism poles of the Golestan province in Iran and comprises the above mentioned characteristics was selected as the study area to assess and model the aesthetic value of its walking tracks using an objective approach as it named logistic regression method.
Regression model is a statistical model which explained the relationship between a phenomenon (the dependent variable) and some of its elements (independent variables) based on a defined set of observed data. Logistic regression model is a special type of regression model which independent variable in it is Boolean and attaches only zero or one. The main assumption of regression logistic is that the possibility of which the dependent variable attaches the one score (a positive response) is followed by a logistic curve and this amount would be calculated using the equation (1):
Equation (1): p(Y=1/X)=(exp∑▒BX)/(1+exp∑▒BX)
According to the above equation:
P: Is the probability in which the dependent variable attaches One score.
X: Is the independent variables
B: Is the coefficients of the independent variables
This logarithmic change caused that the predicted possibility was in the range of 0 to 1.
Accuracy assessment of regression model:
Accuracy assessment of regression model will be calculated using Pseudo-R2 and ROC indices. Pseudo-R2 will be examined the fitness of the model based up on the rate of the possibility as it followed (equation 2):
Equation (2): Pseudo- R2 =1-( log(likelihood)/ log(Lo))
If Pseudo- R2 were higher than 0.2 , it would be regarded as a good fitness of model in spatial studies.

In summary, the main steps of this research are as it follows:
Identifying effective criteria on scenic values of the study area (independent variables)
Marking the most beautiful points of the study area (dependent variable)
Mapping independent variables
Standardization of independent variables
Running the regression model
Accuracy assessment of regression model

Discussion of results:
After data collection and mapping the factors affecting the aesthetic value of the study area, these criteria were standardized between 0-255. Finally eight criteria including tree type, vegetation density, diversity of vegetation density, ecotone of tree type, viewshed layer for waterfalls, peaks and rivers along the walking tracks and visibility of points with higher diversity were inserted in the model as independent variables. As mentioned in previous part, dependent variable is a Boolean layer including beautiful and non-beautiful point of the study area. Finally, after the implementation of the model, each variable with respect to their impact on the aesthetic value, has allocated separated regression weight as it shown in table 1.
Table 1. Regression coefficient assigned to each criterion
Independent variable Regression coefficient
Tree type 0.00113912
Vegetation density 0.01807187
Diversity of vegetation density 0.01763468
Ecotone of tree type
Waterfall viewshed -0.00324110
0.08655779
Peak’s viewshed 0.00562768
River’s viewshed 0.00970483
High diversity point viewshed 0.01256638
Intercept -7.2442
The results of regression model (coefficients) shows that the ecoton of tree type has an inverse relationship with aesthetic value and by increasing the ecotone value, the aesthetic value will be decreased While other parameters have a direct relationship with aesthetic value.
The model was validated using Pseudo-R2 and ROC indices. The estimated value of Pseudo- R2 for this model was equal to 0.4129, and this amount was higher than 0.2 which represented the good fitness of model. Validating by ROC confirmed the results of the model too, ROC index was equal to 0.875.
Fig (1) shows the prediction map of the model. This map has predicted aesthetic value of the study area using the independent variables.

Fig (1): Prediction map of the aesthetic value using logistic regression model
In order to determine the importance of each independent variable, we tried to remove each of variables from the regression equation and examined its impact of each criterion (fig 2). The indices of river and the visibility of high diverse point were the most effective criteria.

Fig (2): The elimination effect of each independent variable on model’s validity

Conclusion:
The development of measuring aesthetic/environmental quality has made progress over the last years. In addition, it is possible to create statistically reliable maps to predict visual quality of environment. The process is relatively efficient and effective. Planners, designers, and citizens can measure the perceived effects of spatial treatments and can assess the perceived impact of various proposals and plans. The represented approach in this research is one more tool in a toolbox of expert and statistical measures to understand the impacts proposals and plans may have upon the environment. The proposed approach (not with the same criteria as each region can differ in terms of their biophysical characteristics) can be conducted in other similar geographic regions to evaluate and rank the scenic beauty of landscapes.
The results showed that the zones which have had more aesthetic value often has been located in central region, eastern and western ridge and south part of the study area. Validating the regression model by Pseudo-R2 and ROC indexes showed the high capability of model to determine the areas which have the high aesthetic quality. The results of this research can