  Fractal dimension is an effective scaling exponent of characterizing
scale-free phenomena such as cities. Urban growth can be described with time
series of fractal dimension of urban form. However, how to explain the factors
behind fractal dimension sequences that affect fractal urban growth remains a
problem. This paper is devoted to developing a method of logistic regression
modeling, which can be employed to find the influencing factors of urban growth
and rank them in terms of importance. The logistic regression model comprises
three components. The first is a linear function indicating the relationship
between time dummy and influencing variables. The second is a logistic function
linking fractal dimension and time dummy. The third is a ratio function
representing normalized fractal dimension. The core composition is the logistic
function that implies the dynamics of spatial replacement. The logistic
regression modeling can be extended to other spatial replacement phenomena such
as urbanization, traffic network development, and technology innovation
diffusion. This study contributes to the development of quantitative analysis
tools based on the combination of fractal geometry and conventional
mathematical methods.
