چكيده لاتين :
Environment has a general sense and the term "urban and urbanism" brings a narrow image of environment to minds. Development of cities and population growth is normally associated with an increase in the environmental pollutions created by human activities, which in turn affects land use and land cover of the area under urban growth. Changes in land use are results of complex interaction of many factors including policy, management, economics, culture and human behavior
Modeling is widely used by decision-makers for controlling land use changes and their trends. It is a suitable tool for exploring the interactions within the land use dynamics and the driving factors of change. Through linking data and theory using formal equations, models help to improve our understanding of the underlying processes of land use change. A land use model typically consists of three components: multi-temporal land use maps derived from remotely sensed data, a multivariate function of the hypothesized determinants of change, and the resulting prediction map of land use change. Land use models serve three main purposes. Firstly, they help to identify the set of variables that are most important in explaining land use change. Secondly, they reveal the relative importance of the significant variables. The magnitude of the effect of factors on land change is important because it may indicate areas where policy intervention is most urgently needed, and whether local action to mitigate adverse effect of land change will be sustainable. Lastly, land use models may be useful in predicting the location of land use change in the immediate future. The ability to locate vulnerable places to land use change helps to mitigate their adverse effects.
Theobald and Hobbs (1998) described two basic types of spatially explicit land use change models: regression-type models and spatial transition-based models. However, rule-based simulation models, such as Cellular Automata (CA), are most suitable for incorporating spatial interaction effects and handling temporal dynamics but most dynamic simulation models cannot incorporate enough socioeconomic variables. Logistic regression (LR) is a special case of multiple regression in which the dependent variable is discrete. The difference between the multiple linear and logistic regression is that logistic regression is applicable when the dependent variable is discrete and probability of taking positive values (e.g. pi) is a logistic curve of independent variables. If dependent variable is dichotomous, Y takes on only two values: 1 and 0, where Y=1 confirms the event is occurred and Y=0 shows the event isnʹt occurred. The logistic regression equation can be expressed as follows:
logit(p)=ln(p/(1 -p))= a+ {bixXi} +{b2xX2}+ {b3xX3}+ ...{bnxXn}
where p is the probability of the dependent variable Y being 1 given (Xb X2,. . Xn), i.e. the probability of a cell being urbanized, X], X2, and X3 are the independent variables; a is the intercept; and bi, b2, and b3 are the coefficients of the independent variables XI, X2, and X3, respectively.
The relationship between the dependent variable and independent variables follows a logistic curve. The logic transformation of the equation effectively linearizes the model so that the dependent variable of the regression is continuous in the range 0-1. In linear regression, the method used most often for estimating unknown parameters is least squares, but in logistic regression, the method used is maximum likelihood. The nature of the land use/cover change of a cell is dichotomous that presents land use change and land use no-change. If binary values 1 and 0 are used to represent urban growth and no urban growth respectively and if it is assumed that the probability of a cell changing to urban use follows the logistic curve as described by
the logistic function: /(*)= 1
1 + eʹz
Then the probability of a cell being urbanized can be estimated with the following logistic regression model:
1
P(Y = l/Xl,X2,..,XK) =
J
Three groups of variables including economic-social (based on expert information: distance to economic centers, distance to administrative centers, distance to sport-recreation centers, distance to medical centers and distance to education centers) and biophysical (based on SLEUTH model: Slope, Land use, Exclusion, Urban extent, Transportation, Hillshade) plus land use were used. To provide excluded layer, past urban areas, road network and land use for the study area, we used Landsat TM and ETM+ images dated 16 July 1987 and 30 July 2001. We applied a supervised classification approach for discerning different land use and land cover types in the area. The change in the urban area was detected using a post-classification comparison. We also identified changes in the forested areas, agricultural lands, bare lands, pastures, and thin forests and then converted these layers into a Boolean map containing 1 and 0. Using the information-based approach, we also prepared layers for economic-social variables as independent layers. Biophysical variables were provided based on the input of the SLEUTH modeling method to make the comparison between modeling approaches possible. The slope layer was derived from a digital elevation map interpolated from 1:25000 contour map of the area.
Covariation among the independent variables is possible. If linear relationship between variables is observed, thus multi-collinearity exists. Principal Component Analysis with the option of computing covariance between variables was used in Idrisi to survey the likely relationships. Covariance of two variables was shown to be greater than 0.9. Covariance range is 0-1 and when this value is closer to 1 then the relation of the two variables in explaining variance is deemed to be higher. As a result, distance to administrative and sporting centers plus distance to cities were deleted from the group of independent variables. After collating independent variables, the data were fed into the logistic regression in Idrisi software.
To assess the results, the predicted urban change layer was compared to that of the real one in 2001. The relative operating characteristics (ROC) curve is a useful method of representing the quality of deterministic and probabilistic detection of forecast systems. ROC predicts the occurrence of an event by comparing a probability image depicting the probability of that event occurring and a binary image showing where that class actually exists. When there is a perfect match between reality map and the modeled one, the ROC takes a value of 1. In the case where there is no spatial agreement between those maps the ROC value becomes 0.5. ROC value for LR model was 0.87; hence the success of modeling with LR was confirmed.
Beside, McFaddenʹs pseudo R-square was used to test the goodness-of-fit of the model. Pseudo R square values between 0.2 and 0.4 are considered a good fit. Logistic regression does not have an equivalent to the R-square that is found in ordinary least square (OLS) regression. Although some come up with pseudo R-square statistics, this statistic does not mean what R-square means in OLS regression. The pseudo R2 value of the full model is 0.2107, indicating a good fit.
The result of fitting the logistic regression model with the full 10 independent variables is given below:
Logit (87-2001) = -4.9629 - (0.00033xF) + (0.96794x1) + (0.00006xD) - (1.66448xL) + (1.92012xK) + (1.59072xJ) - (0.00020xB) + (0.00793xA) - (0.000099xH) + (0.56282xM)
One of the outputs of urban growth models is an image map of urban growth probability predicted for future, which can be used to create new urban location maps for future. Based on the probability map, we can answer the question: "where would urban growth occur if we knew growth size?" New urban location is selected from the cells with the highest likelihood of land use change and thus predicted urban location for LR model in 2010, 202, 2030 and 2040 was created.
The relative effect of the 10 predictor variables were evaluated through ROC method using 10 reduced-variable models and the full model. After models were run with complete data, models were again run 10 more times. At each run, one variable was removed and the model was run to see the effect of the reduced variable. Through this application, it was possible to assess the sensitivity of the models and to discover the relative effect of the variables. The results show that land use type in the study area has the highest effect on urban growth in the logistic regression method. Cultivated and pasture land uses have also high effect on the predicted urban growth map.
This study has shown that a logistic regression model has strengths relative to a CA model in that the logistic regression model not only can include such biophysical variables as SLEUTH (slope, land use, exclusion, urban extent, transportation, hillshade) in the CA model, but it is a better approach for incorporation of human drivers. The modelʹs ability to include more demographic and econometric variables allows us to better understand human forces in shaping urban patterns.
Although the logistic regression model can incorporate demographic data, it suffers from some limitations such as personal or household preferences for locations, urban or regional development policies, and globalization of economy. Unlike the CA models, the logistic regression model is not temporally explicit.
