Page 9 - IJPS-9-1

International Journal of
Population Studies Local population changes as a spatial varying multiscale process

(LAUs) based on the Eurostat definition, are the basic GWR/SGWR model, called MGWR, removes the single
spatial units adopted in this study. LAUs are defined with bandwidth assumption, and allows covariate-specific
the aim to dividing the territory of the European Union bandwidths to be optimized (Oshan et al., 2019).
for the purpose of providing statistics at local levels. They The scale of a spatial non-stationarity relationship may
are low-level administrative divisions of a country below vary for each predictor variable. The MGWR model has the
province, region, or state. LAUs may refer to a range of ability to differentiate local, regional, and global processes
different administrative units, including municipalities, by optimizing a different bandwidth for each covariate
communes, parishes, or wards. In Italy, they correspond to (Li & Fotheringham, 2020). The following equation gives
municipalities. the specification of MGWR:
For each municipality, we computed the rates following m
u ux
i
the approach proposed in Preston et al. (2001) and applied, y bwj , j ij i (1)
i
among others, by Strozza et al. (2016). In such approach, j0
the idea is that TOTPGR is the instantaneous growth rate Where β represents the coefficient of the bandwidth
(from one year to another) and can be expressed as the ratio with the spatial weighting kernel used for estimating the
bwj
between population change during time interval 0-t and j-th predictor variable x at local site (i.e., municipality)
the number of persons for that period t (P −P )/ln (P /P ) i, ε is the error term, and y is the response variable. As
ij
t
0
t
0
(Preston et al., 2001). We computed all the other rates in pointed out by Oshan (Oshan et al., 2019), MGWR provides
i
i
the same way. These rates, standardized to a Z distribution, an extension that allows each variable to be associated with
act as dependent (TOTPGR) and independent variables a distinct bandwidth by recasting GWR as a generalized
(NATPGR, MIGPGR, INTPGR, ITAPGR and FORPGR) additive model such that:
in a MGWR model. As known, scale is a fundamental
concept in spatial and regional demography (Howell k
i
et al., 2016; Lloyd, 2016). This is currently discussed in y j1 f i (2)
j
the considerable and diverse literature that investigates the
various roles that scale plays in different social processes Where f is a smoothing function applied to the j-th
j
(Fotheringham et al., 2017). It is generally accepted that explanatory variable at location i that may be characterized
different processes can operate at different spatial scales, by distinct bandwidth parameter and ε the error term
i
and we often make a distinction between micro and of the model. Hence, a key advantage of MGWR over
macro, or between local and global processes, but in real- GWR is that it can more accurately capture the spatial
world scenarios, data are often generated from spatial heterogeneity within and across spatial processes, minimize
processes operating at different spatial scales (Wolf et al., overfitting, mitigate concurvity (i.e., collinearity due to
2017). If we consider a less restrictive assumption that similar functional transformations), and reduce bias in
all spatially variable processes in a model operate at the the parameter estimates (Oshan et al., 2020). The MGWR
same spatial scale, we can think of a more flexible model. model is calibrated using a “back-fitting” algorithm which
Local models such as geographically weighted regression maximizes the expected log likelihood, and the criteria
(GWR) (Fotheringham et al., 2002) can capture process for selecting the bandwidths are derived from the same
heterogeneities but do not adequately incorporate the procedure used in the conventional GWR framework
multiscale properties of processes into modeling. Indeed, using the corrected Akaike information criteria corrected
the bandwidth of the latter is closely related to the spatial (AICc) for finite samples (Burnham & Anderson, 2004).
scale of the processes examined, and bandwidths for each The calibration process concerns the method and the
independent variable are assumed to be the same. In this criterion of choosing the bandwidth. In our empirical
respect, the semiparametric geographically weighted estimation, we used an adaptive (bi-square) kernel because
regression (SGWR) model (Nakaya, 2015; Nakaya et al., it is more favorable when dealing with non-uniform spatial
2005) provides, even if in a strictly rigid or extreme form, a distributions of observations (i.e., municipalities in our case)
first response to the multiscale problem by distinguishing and it is also able to better handle irregularly shaped study
between factors that play a role at a local and the global areas. We recall that, although the fixed kernel could be used
levels. Demographic research is often based on individual in the MGWR model, a limitation of this approach is that
and contextual level data over a wide range of spatial there may have calibration issues when there are sparsely
scales, and therefore, the corresponding variables, which populated regions of a study area (Oshan et al., 2019).
involve correlated social and economic aspects, require Furthermore, to compare each of the bandwidths obtained
a deep understanding of the spatial context (Mucciardi, from an MGWR model, it is necessary to standardize the
2021). To overcome this problem, the development of the dependent and independent variables so that they are

Volume 9 Issue 1 (2023) 3 https://doi.org/10.36922/ijps.393