  Research in examining the equity of service accessibility has emerged as
economic and social equity advocates recognized that where people live
influences their opportunities for economic development, access to quality
health care and political participation. In this research paper service
accessibility equity is concerned with where and when services have been and
are accessed by different groups of people, identified by location or
underlying socioeconomic variables. Using new statistical methods for modeling
spatial-temporal data, this paper estimates demographic association patterns to
financial service accessibility varying over a large geographic area (Georgia)
and over a period of 13 years. The underlying model is a space--time varying
coefficient model including both separable space and time varying coefficients
and space--time interaction terms. The model is extended to a multilevel
response where the varying coefficients account for both the within- and
between-variability. We introduce an inference procedure for assessing the
shape of the varying regression coefficients using confidence bands.
