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
13 frequently referred to as the discrete choice model in business and econometric
literature. It is called the multinomial, polychotomous or polytomous logistic regression model in the health and life sciences Hosmer and Lemeshow 2000.
The term multinomial is used in this research. Multinomial Logistic Regression MLR uses an outcome variable with
any number of levels to illustrate the extension of the model and methods. However, the details are most easily illustrated with three categories. To develop
the model, assume we have p covariates and a constant term, denoted by the vector, x, of length p + 1 where x
= 1. The two logit functions for this model as
Equation 1. MLR Model Equation: Logit Functions It follows that the conditional probabilities of each outcome category given the
covariate vector are
Equation 2. MLR Model Equation: Conditional Probability of Each Outcome Category
Following the convention for the binary model, let π
j
x = PY = j|x for j = 0,1,2. Each probability is a function of the vector of 2p + l parameters
β = β
1
, β
2
Hosmer and Lemeshow 2000.
