10 recognition of categories of real-world objects and labeling of the classified
entities normally pixels. In the context of remote sensing of the land surface these categories could include, for example, woodlands, water bodies, grassland
and other land cover types, depending on the geographical scale and nature of the study. In digital image classification the labels are numerical, so that group of
pixels that are recognized as belonging to the class ‘water’ may be given the label ‘1’, ‘woodland’ may be labeled ‘2’, and so on Mather 2004.
There are several methods used in image classification, but generally those methods can be categorized as unsupervised classification and supervised
classification. Unsupervised classification is an analytical procedure based on clustering using some algorithms. Application of clustering partitions the image
data in multispectral space into a number of spectral classes, and then labels all pixels of interest as belonging to one of those spectral classes. The process
followed segmentation of the multispectral space to cluster pixels into ground cover types, by the analyst Richards and Jia 2006.
Supervised classification methods are based on external knowledge of the area shown in the image. Unlike some of the unsupervised methods, supervised
methods require some input from the user before the chosen algorithm is applied. This input maybe derived from fieldwork, air photo analysis, reports, or from the
study of appropriate maps of the area of interest. In the main, supervised methods are implemented by using either statistical or neural algorithms. Statistical
algorithms use parameters derived from sample data in the form of training classes, such as the minimum and maximum values on the features, or the mean
values of the individual clusters, or the mean and variance–covariance matrices for each of the classes. Neural methods do not rely on statistical information
derived from the sample data but are trained on the sample data directly. This is an important characteristic of neural methods of pattern recognition, for these
methods make no assumptions concerning the frequency distribution of the data. In contrast, statistical methods such as the maximum likelihood procedure are
based on the assumption that the frequency distribution for each class is multivariate normal in form. Thus, statistical methods are said to be parametric
11 because they use statistical parameters derived from training data whereas neural
methods are non-parametric Mather 2004.
2.3 Land Use Change Modeling
Model is a simplification of real-world system while a system is a mechanism in which various component interact in such a way as to perform a
function in a real world Handoko 2005; Shenk and Franklin eds 2001. The purpose of using a model is to easily understand the system’s behavior by
simplifying its process. There are three objectives for constructing a model, namely: 1 to understand the process, 2 to make prediction, and 3 to support
management Handoko 2005. Models can be categorized in three classes of models: theoretical,
empirical statistical, and decision-theoretical. The theoretical models are developed to suggest mechanisms and thus lead to predictions even before data
are collected. Theoretical models are used to investigate systems responses and trajectories that are possible under specific hypotheses. These uses do not include
comparison of model predictions with data or observation. Statistical models, by contrast, are used to make inferences from data. Statistical models may also be
used to test hypotheses which may require the complementary skills of theoreticians and empiricists. Decision-theoretical models can be used to indicate
which decisions are likely to meet management objectives in line of uncertainty and dynamics systems. In decision-theoretical models, scientific models are used
to project the consequences of hypotheses about how a system behaves in order to derive wise, or even optimal, management actions. Models are used to project
system’s responses to the various management actions that could be employed in order to assist in deciding which action is most appropriate Shenk and Franklin
eds 2001. Models can be used to address specific issues in natural resource
management, and it has led to development of various disciplines. Population viability analysis and wildlife resource selection are some of modeling disciplines
Shenk and Franklin eds 2001. The strength of a modeling technique lies in its ability to model many variables, some of which may be on different measurement
12 scales Hosmer and Lemeshow 2000. Modeling land use change is another
modeling discipline that has attracted many scientists in the world in order to study the causal relationship of land management to changes of land use.
Modeling land use change studies the changes of land use in consequences of the response of land management that has been done by human in order to fulfill their
need. Hopefully, land use change model, which has been developed, may facilitate the understanding of the process of land use change and its driving factors
Verburg et al. 2004; Koomen et al. 2007.
2.4 Multinomial Logistic Regression Model
Land use change and its driving factors can be categorized as binary, continuous, or categorical variables. There are several ways to model binary,
continuous and categorical variables, and the most important model for categorical response data is logistic regression model Agresti 2002. The
dependent variables of logistic regression could be binary or categorical variables, whereas its independent variables could be a mixture of continuous and
categorical variables Xie et al. 2005. The logistic regression model is used increasingly in a wide variety, and it is also commonly used in modeling land use
change Agresti 2002; Verburg et al. 2004; Fang et al. 2006; Dewantara 2006; Koomen et al. 2007.
The goal of an analysis by using logistic regression method is the same as that any model-building technique in statistics: to find the best fitting and most
parsimonious, yet biologically reasonable model to describe the relationship between an outcome dependent or response variable and a set of independent
predictor or explanatory variables. The outcome variable in logistic regression is binary or dichotomous. However, the model can be easily modified to handle the
case where the outcome variable is nominal with more than two levels Hosmer and Lemeshow 2000.
Modeling land use change may consider many factors or variables in the model which will be referred as the multivariable case. In this case, McFadden
1974 in Hosmer and Lemeshow 2000 proposed a modification of the logistic regression model and called it a discrete choice model. As a result the model is
