Interpretability of Models with Discrete Dependent Variables in Natural Resource Valuation: A Case Study of Recreational Values of Avidar Lake in Nowshahr County of Iran

Designing hypothetical markets and utilizing stated preference models, such as the Contingent Valuation Method (CVM), to assess the value of non-market services provided by natural and environmental resources is accompanied by various problems. These problems can be broadly categorized into two groups according to Williams (2016). Firstly, there are challenges related to the initial stage of study design, which occurs before estimating the econometric model. Secondly, there are problems related to selecting, estimating, and interpreting the results derived from the models. These challenges include selecting the appropriate model type, conducting estimations and ultimately, interpreting the results correctly (Williams, 2016).

In natural resource valuation research, logistic models are commonly employed in various forms including ordinary logistic regression, conditional logistic regression, ordered logistic regression, multinomial logistic regression, as well as other forms like mixed logit and nested logit (Baker and Ruting, 2014; Greene, 2018). This study thoroughly analyzed the interpretability of logistic regression in the normal logistic mode and it was preferred using the risk ratio index over the odd ratio index, because it was found to be more practical. However, the study mainly aimed at calculating the extent of changes in the probability of an event occurring, rather than representing its multiplication. This notion was quantified and articulated through the concept of marginal effect. In the studies conducted in Iran, the values of marginal effect were typically measured and expressed based on the average level of the considered independent input and the average of other independent inputs in the model. In addition, however, the marginal effect concept for each independent variable can be measured and expressed in three different ways (Williams, 2020): 1) Marginal Effect at the Means (the means of independent variables) (MEMs), 2) Average Marginal Effects (AMEs), and 3) Marginal Effects at Representative Values of independent variable (MERs). To calculate the marginal effect in each case, the Adjusted Prediction (AP) index should be calculated. This index is measured in three different ways, depending on the type of marginal effects used in the calculation (Williams, 2020): 1) Adjusted Predictions at the Means (APMs) (Means of Independent Variables), 2) Average Adjusted Predictions, and 3) Adjusted Predictions at Representative Values of Independent Variables. To assess the recreational value of Avidar Lake in Nowshahr County of Iran, the Contingent Valuation Method (CVM) and the One-and-One-Half Bound (OOHB) model were used. During the summer season of 2019, a total of 270 questionnaires were filled out. The odds ratio, risk ratio and marginal effects Indexes were estimated by Eviews software. 

The study findings indicated slight variations in the calculations of Marginal Effects of Means (MEMs) and Average Marginal Effects (AMEs). Furthermore, the results of Marginal Effects at Representative Levels (MERs) calculations demonstrated changes in the marginal effect values of independent variables across different levels of these variables. The average amount that the users were willing to pay for each leisure visit to Avidar Lake was determined as 334900 IRI rials by integrating the area under the curve of visitors' demand. Additionally, the annual recreational value of the lake was calculated to be 8650 million IRI rials. This value would reflect the economic potential of Avidar Lake in terms of creating recreational opportunities. 

Based on the study findings and to enhance its applicability in real-world scenarios and improve its effectiveness in practical policies, it is recommended that studies focusing on the assessment of natural resources and the environment prioritize the calculation of comprehensive outcome indicators using the specific details outlined in this study. More specifically, the study results demonstrate that evaluating the average result across various levels of variable values (rather than solely considering the average value) can effectively capture and illustrate the diverse impacts resulting from policy implementation at these different levels (in terms of the intensity of change impact).