Driving forces of population change following the Canterbury Earthquake Sequence, New Zealand: A multiscale geographically weighted regression approach

The Canterbury Earthquake Sequence (CES), which includes the 2010 and 2011 Christchurch earthquakes, is one of the deadliest disasters in New Zealand history. Following the CES, displacement of the affected population occurred, leading to an out ‐ migration from affected areas and changes to places of residence. This paper investigates the spatial changes in population following the CES, using a multiscale geographically weighted regression (MGWR) analysis approach to examine if there is a relationship between population change within the Canterbury region, and potential driving forces across two time periods: 2006 – 2013 and 2013 – 2018. The findings of this study could assist in informing future decision making and planning for earthquake events and to increase the effectiveness of land use policy decisions for post ‐ disaster recovery in New Zealand.


| INTRODUCTION
The Canterbury Earthquake Sequence (CES), which includes the devastating 2010 and 2011 Christchurch earthquakes, is considered one of the deadliest and disruptive disasters in New Zealand history.In September 2010, the Canterbury region of New Zealand was struck by a M7.1 earthquake 40 km west of the major city of Christchurch and 10 km deep, causing widespread moderate damage (Newell et al., 2012).This earthquake was followed by a M6.3 earthquake in February 2011, only 5 km deep and centred only 10 km away from the centre of Christchurch city (Ministry for Culture and Heritage, 2021).The 2011 Christchurch earthquake resulted in the deaths of 185 people and extensive damage to homes, properties and infrastructure, compounding on existing damage from the 2010 earthquake (Stats NZ Tatauranga Aotearoa, 2011).Roughly half the housing stock (~100,000 houses) in Christchurch was damaged following the 2011 earthquake, including ~7,000 houses damaged beyond repair (Paton et al., 2014).In addition, over half the road network required replacing, and up to 5,000 businesses in the CBD were displaced (Paton et al., 2014).Damage to housing in Christchurch and in the adjacent Waimakariri region led the central government to establish the Canterbury Earthquake Recovery Authority (CERA) 2011, which implemented a residential colour zone system for allocating resources for repair (Newell et al., 2012).Those residential properties with the most extensive and significant damage were designated 'red zone' areas and deemed uninhabitable, predominantly in flat land in areas susceptible to ongoing liquefaction, along rivers and coasts (such as the Avon River), and in the Port Hills where increased risk of cliff collapse and boulder roll exists (Saunders & Becker, 2015).Those properties with less extensive damage and lower ongoing risk in the greater Christchurch area were zoned green and divided into three technical categories, from most at risk TC1 to TC2 to least at risk TC3 (Saunders & Becker, 2015).Those properties outside land damage mapping were zoned white.
Widespread damage to housing stock and the displacement of people from their homes led to a large out-migration and movement of people from Christchurch city, representing a 17.5% loss (~70,000) of the overall population of 400,000 before the 2011 earthquake (King & Gurtner, 2021;Love, 2011;Newell et al., 2012).
Many people chose to relocate to less damaged and less at-risk smaller urban areas in the wider Canterbury region, and to other parts of New Zealand (King & Gurtner, 2021;Newell et al., 2012;Parker & Steenkamp, 2012).Population growth was recorded for the adjacent regions to Christchurch of the more rural Waimakariri and Selwyn districts for 2011 (Greater Christchurch Partnership, 2016;Stats NZ Tatauranga Aotearoa, 2018), while a western redistribution of the population was recorded for greater Christchurch as people moved away from the significantly damaged eastern suburbs of Christchurch city (Stats NZ Tatauranga Aotearoa, 2018).Concern that unconstrained rural residential development could lead to increased urban sprawl and dispersed population and settlement patterns (Environment Canterbury Regional Council, 2021) led to the central government amending the Christchurch district plan and Greater Christchurch Urban Development Strategy (UDS).In addition, the central government pushed through the statutory document Land Use Recovery Plan (LURP) in 2013 under the emergency earthquake response policy to assign undeveloped greenfield land to future residential and commercial development (Rivera-Muñoz & Howden-Chapman, 2020).These changes were enabled through the establishment of the CERA through the Canterbury Earthquake Recovery Act (CER Act) 2011, which granted powers needed to manage the earthquake recovery for the Christchurch area.The LURP allowed for an increase in the availability of greenfield sites for suburban development, assisting in the housing recovery but leading to rapid advancement of suburbanisation in the Greater Christchurch area and a slowing of redevelopment in Christchurch city.This was compounded by the red zoning of the Christchurch city CBD and closure for months following the 2011 earthquake, with many businesses choosing to relocate to other business hubs outside the CBD, drawing the workforce out of the city (King & Gurtner, 2021;Marsh Risk Management Research, 2014).The availability of single-use lower density housing in the outer suburbs and adjacent districts of Christchurch city, still within commuting distance of the city, may also have drawn property owners and workers out of the inner suburbs of the city (Kusumastuti & Nicholson, 2018).This study will investigate local changes in population for the Canterbury region following the CES, and assess the spatial scale at which potential driving forces of population change may have been operating at.There is little research on the long term effects of the CES on population movement within the wider Canterbury area, and the potential driving forces which influence that movement.An overall assessment of the out-migration of people from Christchurch city following the CES has been carried out by official bodies (Stats NZ Tatauranga Aotearoa, 2011) and consulting firms (i.e.Love, 2011).
The driving housing and economic forces behind population change have been briefly noted in reports (i.e.Wood et al., 2016), and other long term impacts of the earthquake on factors related to population change in the region (i.e.Bond & Dermisi, 2014) (Bond & Dermisi, 2014), crime (King, 2016), transportation network (Yonson et al., 2020), GDP related indices (Yonson et al., 2020), and the effect of land use planning on demographic change (King & Gurtner, 2021).In the wider GWR literature, existing studies of population change and movement have used variables such as population density, ethnicity, urban/rural population, age, education, and employment (Li et al., 2016), distance to nearest metropolitan area, population growth, distance to coast, and environment-related variables such as average rainfall (Gutiérrez-Posada et al., 2017), and variables related to a specific event such as the percentage of crop land under potatoes in the Irish Famine (Fotheringham et al., 2013).
MGWR can be used to investigate the potential drivers of population movement and change before, during and after the CES.MGWR can also be used to assess in the longer term whether these new earthquake-related drivers still influence population movement and people's choice on where to live in the wider Canterbury region, or whether these new drivers have decreased in relevance as the recovery process progresses.Many studies investigating the potential determinants of population change, including those under extreme situations such as disaster events, have used global regression analyses, such as ordinary least squares (OLS) regression (i.e.Fussell et al., 2017).However, these global models do not account for information about the spatial context of data, that is, that the relationship between variables may vary over space.This may result in inaccurate results at the local level, in particular where spatial heterogeneity in relationships is present.GWR (and MGWR) takes this spatial variation into account, allowing for the analysis of local relationships between population change and determinants.GWR, and MGWR, is increasingly used for understanding the processes that underpin changes in population (i.e.population dynamics), ranging from studies on population growth and forecasting (i.e.Chi & Wang, 2017;Gutiérrez-Posada et al., 2017) to understanding patterns of migration (Viñuela et al., 2019), specific case studies such as community resilience of locations in China following an earthquake (i.e.Li et al., 2016), and understanding the driving factors of historic changes in population (i.e.Fotheringham et al., 2013).
Recent advancements in GWR approaches have led to the development of MGWR (Fotheringham et al., 2017), which allows a different bandwidth for each covariate rather than a single bandwidth for all covariates as seen in standard GWR.We will employ MGWR to assess spatial heterogeneity in the population change for the Canterbury region following the CES.
The aim of this study is to investigate local changes in population for the Canterbury region following the CES, and how changes in space and time may be related to socioeconomic, demographic, land use and earthquake-related variables.Data obtained from New Zealand censuses alongside data on land use and housing policy (LURP 2013; CERAct 2011), and earthquake damage will be used in MGWR modelling for two time periods covering before and after the CES: 2006CES: -2013CES: and 2013CES: -2018. .The results of this study will assist in understanding the regional changes in population that occurred within the Canterbury area following a large disaster event, and can be used to assess the impact of land use and housing policy implemented following the CES, and to inform future regional policies for disaster management, housing, land use and land development.To the best of our knowledge, this study is the first to use a MGWR approach to assess spatially changing relationships between population and potential driving forces for the Canterbury area over the long term (12+ years).
The rest of the paper is organised as follows.The next section discusses the data set and variables chosen for this study.A brief explanation of the GWR analysis technique (MGWR) follows, including model specifics for this case study.The results of the MGWR analysis for both time periods and significant parameter estimates are presented in Section 3. The paper concludes with a section discussing the main results and conclusions, considering the wider implications of the research.

| Data and study area
The study area is located on the west coast of New Zealand's South Island, encompassing all of the district of Christchurch, most of the adjacent districts of Selwyn and Waimakariri, and parts of the Hurunui and Ashburton districts in the Canterbury region (Figure 1), covering an area of about 9,613.47 km 2 .The study area extent was determined using the 2013 census area units in which workers lived in and went to work in Christchurch city (Stats NZ Tatauranga Aotearoa, 2020).This gives an indication of likely areas to which workers may choose to move to and still be able to commute into the city for work.This area was chosen as it is expected to encompass most of the population which would have been affected by the CES.
The city of Christchurch and the greater Christchurch area is largely low-lying, flat land prone to liquefaction, with the exception of the higher elevation rocky cliffs of the Port Hills Peninsula (Figure 1).
The demographic and socioeconomic data used in this study were chosen from the 2006, 2013 and 2018 New Zealand population censuses (Stats NZ Tatauranga Aotearoa, 2020), with those initial variables considered to be related to internal population movement within the wider Christchurch city extent and the Canterbury region (Table 1).While the New Zealand censuses usually occur every 5 years, the planned 2011 census was delayed to 2013 due to the CES.
This provides an opportunity to assess changes in population before and after the CES using officially collected data, and to use recent 2018 data to assess long-term changes to population for the region.
Additional variables were created using land use and land cover information, earthquake damage and topographical GIS layers, and LURP policy GIS layers (see Table 1 for further details).
Following an exploratory analysis of correlation and collinearity between these variables, 23 final variables were chosen for use in MGWR modelling, as further described in Table 2.The R function StepAIC (using forward direction) was used for each time period to identify the best covariates for global OLS regression models.The set of best covariates for each model was combined to create a single set of covariates which could be used for both time periods in GWR modelling.This allowed for comparison of GWR model results between time periods, but as the same set of variables was needed for both time periods, the usual step-wise variable selection procedure commonly seen in GWR modelling work (i.e.Comber et al., 2020) was not used here.

| Model specification of MGWR methodology
MGWR was adopted as the main methodology in this study.OLS The GWR model can be defined as in Equation ( 1) (Fotheringham et al., 2017): (1) were u v ( , ) i i is the spatial location of the ith observation (ith SA1), and β j is the jth coefficient for the spatial location of u v ( , ) i i .For a unit area SA1 i, y i is the change in the proportion of total CURPop within a time period (calculated as, e.g.2006-2013, as the proportion of total CURPop in 2013 minus that in 2006), x ij is the jth covariate, and ε i is the random error.
In the above Formula (1), local parameter estimates for each variable in the model at each SA1 i are calculated using weighted least squares as follows, using matrix representation (Fotheringham et al., 2002) as in Equation (2): where X is a matrix of variables used in the model, W u v ( , ) i i is a diagonal spatial weighting matrix which weights each observation based on distance to location u v ( , ) i i , and y is a vector of observations of the dependent variable, change in population.W u v ( , ) i i indicates the weight of SA1 j in regard to SA1 i.
To calculate the weights matrix, a kernel function is applied to the distances (d) between observations, placing emphasis on observations closer in space.For this study, local GWR models are fitted for each SA1 i using a subset of SA1's (i's) weighted using an adaptive bi-square spatial kernel function, where the nearest K neighbours where d ij is the distance from the kernel centre between SA1s i and j, and b is the chosen bandwidth.The bandwidth, b, is used to determine the optimal number of nearest neighbours to each SA1 used in the kernel function.The optimal bandwidth used in the kernel function was chosen using the corrected version of Akaike information criterion (AICc; Fotheringham et al., 2002;following Akaike, 1973).
Unlike standard GWR, which uses a single bandwidth for all point observations and variables' relationship in the model, MGWR allows for a separate bandwidth to be chosen for each X variable.While mixed GWR (MX-GWR), another GWR approach, allows for both global and local scale relationships, MX-GWR only uses a single local bandwidth for all local variables, assuming that all relationships which vary locally operate at the same local scale.MGWR addresses this by allocating a separate bandwidth to each relationship in the model, allowing for variation in the spatial scale of relationships (Fotheringham et al., 2017;Lu et al., 2017).An iterative back-fitting procedure is used for fitting MGWR models, rather than the weighted least squares used to fit standard GWR models.In this study, MGWR is preferred over standard GWR or MX-GWR, as it is expected that some variables (such as binary) will tend to a global spatial scale, while other variables will tend towards local spatial scales, but the local scale may not be the same across all local variables.
The MGWR formula can be defined as in Equation ( 4) (Fotheringham et al., 2017): ∑ where u v ( , ) i i is the spatial location of the ith observation (ith SA1), and bwj indicates the bandwidth used to calibrate the jth spatial (conditional) relationship.Note that as MGWR uses a different bandwidth for each relationship in the model, each relationship at the same location uses a different spatial weighting matrix.
To address the multiple hypothesis testing problem in GWR, once local parameter estimates are obtained from the model, the statistical significance of local parameter estimates is determined using the adjusted critical t-value, as defined in Byrne et al. (2009).Specifically, the adjusted t-values are calculated based on the function gwr.t.adjust in the R package GWmodel (Lu et al., 2014), using the Fotheringham-Byrne procedure.Adjusted t-values are used to assess the significance of the regression coefficients.
Using the variable names in Table 2, the final MGWR model ( 23covariates) used in this study can be formulated as follows: where y i is the dependent variable -change in total proportion of CURPop at SA1 location i, β i0 is the intercept parameter at SA1 location i, β ix is the parameter for the xth regression variable at SA1 location i, and ε i is the random error associated with SA1 location i.
Two MGWR models were fitted, one for each time period: 2006-2013 and 2013-2018.The same covariates were included in models for both time periods, in order for comparisons to be made between time periods.OLS regression models using the same data set and variables were additionally implemented for comparison purposes.

| RESULTS
Coefficient estimates for global regression models are presented in Table 3. (negative significant for both), internet (positive significant for both), medweeklyrent (positive significant for both), TC3bin (negative significant for both), redzonebin (negative significant for both), and diffagri (negative significant for both) being both significant and having the same sign for both models.The statistics of local estimates for the MGWR models are given in Table 4, and the selected bandwidths for each covariate are given in Table 4.Note that the bandwidths for the same variables in the two MGWR models can vary.These differences could lead to different coefficient estimates, and therefore different results for the two time periods despite the same variables being used in the models for both years (Comber et al., 2020;Fotheringham et al., 2017;Oshan et al., 2019).The choice of bandwidth (GWR) or bandwidths (MGWR) is considered the most important decision when fitting these models, as the bandwidth determines the number of observations, as well as their weights, used in each local regression (Comber et al., 2020).When bandwidth is large and close to the total number of observations, for example, 3,172 for the variable of over65 in the

| LOCAL PARAMETER ESTIMATE RESULTS AND DISCUSSION
For those local variables with at least one significant local estimate in both time periods (as seen in Table 4), the variables of youth, over65, ownhome, medweeklyrent and medhouse were chosen for further description.Five of 24 maps of local parameter estimates are shown in Figure 4.  Christchurch city (Kusumastuti & Nicholson, 2018).Those areas with greenfield land and new housing developments have seen an increase in the working-age population and those with young children, leaving Christchurch city as an ageing population (King & Gurtner, 2021).
Those over 50 were more likely to stay in Christchurch city, despite earthquake damage, whereas those more likely to relocate following the CES were aged 15-54 (Wood et al., 2016).This change in demographic also led to an increase in those commuting to the city for work from neighbouring regions, and a decrease of workers in the CBD of Christchurch city (King & Gurtner, 2021).The decrease in workers in the CBD may reflect the significant damage that occurred to buildings in the CBD, which was closed completely for months after the CES, and many businesses had to find alternative premises outside of the CBD permanently, or while repairs were being carried . However, current studies are largely descriptive in nature and the spatial scales at which those factors might have affected population change remain unknown.Spatial census data available from before and after the CES, including the most recent 2018 census, allows the use of local spatial analysis approaches such as multiscale geographically weighted regression (MGWR).MGWR enables the investigation of possible influencing factors on population changes in the Canterbury region, such as demographic and socioeconomic factors, land use policy, and earthquake-related factors.MGWR provides a novel approach to assessing changes in population and the effects of different factors on those changes.MGWR enables the assessment of the spatial scale at which possible driving forces may have an effect on population change.This methodology may allow an assessment of the key determinants of population movement within Christchurch city and the wider Canterbury region, as well as the potential impacts of land use and housing policy implemented by the government following the 2011 earthquake on population movement.Population movement and change are usually assessed and forecasted using socioeconomic and demographic variables such as age, ethnicity and median income, for example, but following the CES new drivers of population movement became relevant, in particular those drivers related to earthquake damage and recovery such as land stability, liquefaction potential, land use and housing-related variables.Prior studies describing changes in Christchurch city and the wider Canterbury region following the CES have included variables such as change in house price two main time periods, used to assess the change in population and potential drivers over the three main census years.The change in population was considered over two time periods: 2006-2013 and 2013-2018.Due to changes in the spatial census units between 2013 and 2018, the smallest level of aggregation for the 2018 census, known as Statistical Area 1 (SA1), was used for all three census years.In total, 3,174 SA1 units were used (n = 3,174).The Currently Resident Population count (CURPop) from the censuses was used as the population count measure.To account for the natural birth and death rate, the CURPop was adjusted by subtracting the total count of CURPop under 15 years of age and over 65 years of age. Figure 2 shows the dependent variable (change in proportion of total adjusted CURPop between time periods) for the SA1 units for the study area for both time periods.

Figure 2
Figure2shows the change in the proportion of total CURPop in each SA1 for both time periods, the inset showing the full study area extent.For SA1s which were most damaged in the central red zones, there is a negative change in the proportion of the total CURPop living in those areas, which is seen in both time periods (i.e. higher proportion of total CURPop in 2006 than in 2013).Overall, for the

F
I G U R E 2 Dependent variable, change in proportion of total CURPop for (a) model 1 time period 2006-2013, (b) model 2 time period 2013-2018.Inset map for both (a) and (b) shows the full study site extent.Before standardisation for MGWR.MGWR, multiscale geographically weighted regression.
regression and standard GWR were also implemented for comparison purposes.OLS, GWR and MGWR were all implemented using the software MGWR 2.2(Oshan et al., 2019), and results were visualised in ArcGIS Pro(Version 2.7.1, ESRI).The open source software R (version 3.6.1)was used alongside ArcMap 10.7.1 (ESRI) for data management and processing.A MGWR modelling approach was used to investigate the spatial changes in population and potential determinants due to the advantages of the methodology over traditional OLS regression, and standard GWR.In comparison to global OLS regression, which assumes that relationships between variables in the regression model are the same everywhere (i.e.global), GWR takes into account the spatial context of data, in that relationships between variables may vary over space (i.e.local;Fotheringham et al., 2002Fotheringham et al., , 2013)).GWR can capture spatially varying relationships between changes in population and potential determinants.MGWR extends GWR by accounting for multiple scales, that is, each determinant (X) in the regression model may have a different spatial scale in its relationship with change in population (Y).

(
SA1s) are used in model calibration.A bi-square kernel function can be defined as in Equation (3): F I G U R E 3 Location of technical categories and Land Use Recovery Plan priority residential greenfield areas R 2 and AICc indicate that the model for 2013-2018 performed better than the model for 2006-2013, where covariates explain about 21% and 46% of the variations in the dependent variable, respectively.The significance of covariates varies between the two models, with only the variables over65 For these variables, such as over65 which is negative, this indicates that the change in proportion of total population and the change in proportion of people over 65 will vary in opposite directions.That is, if a SA1 had a greater change in proportion of total population between 2006 and 2013, then it would have a lesser change in proportion of people over 65 over the same time period (i.e. if an SA1 had an increase in the dependent variable over the time period, the proportion of people over 65 in the SA1 would decrease over the time period, and vice versa).As the sign of the estimate is the same between time periods, if a SA1 had a greater level of change in proportion of the over 65 population during 2006-2013, then it would also have a greater level of change in proportion of the over 65 population during 2013-2018.The covariates of level3, unemp, medhouse, whitezonebin and distgrn did not have a significant effect on the changes in population in either model.
Therefore, the bandwidth(s) chosen will directly affect the local coefficient estimates.In the context of this study, the different bandwidths of the same variable in different models could indicate a temporal change in the relationship between population change and the variable under concern.For example, the bandwidth of the variable medhouse changed from 381 in the first model to 44 in the second model.This could indicate higher spatial variations in the impact of the median house price on the change in population in the second time period (smaller bandwidth and more local relationship).
Figure 4a shows the local parameter estimate for the relationship between population change and the proportion of youth (CURPop < 15 years of age), for both time periods.The global parameter estimate is −0.077 (p < 0.05) for 2013-2018.There is a positive cluster in 2006-2013 for those SA1s located in the red zone, and negative clusters are seen in 2013-2018 for SA1s to the northeast, north-west and south of the city, and along the northern coastline.The location of these positive clusters in or near the red zone is to be expected, as following the CES and the establishment of the CERA 2011, all properties located in the red zone were designated to be demolished and all residents living in the red zone areas were required to shift elsewhere voluntarily (McDonagh, 2014).Any properties not bought by the government in these areas would have limited services and support from the council.This would have resulted in a decrease of population overall in these areas.

Figure
Figure 4b shows the local parameter estimates for the relationship between population change and the proportion of over65 (CURPop > 65 years of age), for both time periods.The global parameter estimate is −0.101 (p < 0.05) for 2006-2013, and −0.187 (p < 0.05) for 2013-2018.Only the time period of 2013-2018 exhibited a local scale relationship.A significant negative cluster is seen to the west of the Christchurch city covering the smaller western township of Rolleston, located in the Selwyn district.Following the CES, many people chose to move out of the more earthquake damaged areas in the city (including the inner suburbs and red zone), and move to the outer suburbs of Christchurch city, and to larger towns in the surrounding districts.While some people have chosen to move back into the city in 2013-2018 and more recently, policies implemented following the CES, such as the LURP (2013), opened up greenfield land in the outer suburbs of Christchurch city that had been assigned by the UDS before the CES for long term growth (Greater Christchurch Partnership, 2019).While this supported the recovery process, the LURP and subsequent housing developments on greenfield land encouraged urban sprawl and a rapid advancement of suburbanisation in the Greater out.From an insurance perspective, many landlords and affected properties in the CBD would have had a loss of access to their premises, and denial-of-access claims would have accumulated(Marsh Risk Management Service, 2014).As a result of the CBD closure in Christchurch, most policies in New Zealand have extended out the waiting periods before denial-of-access claims can be made.In the CBD, many landlords may have taken a negotiated settlement for property damage and denial-of-access rents claims and invested in alternative properties outside of the CBD (Marsh Risk Management Service, 2014).Therefore, both business premises and residential properties in the CBD may have decreased in number following the CES, and money from claims invested in buildings and properties outside of the CBD.The level of earthquake damage following the CES had a significant effect on housing-related variables in the greater Christchurch area, including the level of home ownership, the median weekly rent ($), and the median sale house price ($).Figure4c-eshows the local parameter estimates for the relationship between population change and the proportion of CURPop (over 15 years of age) who own or partly own their own home (home ownership), the change in median weekly rent ($), and the change in median house price ($), respectively, for both time periods.For home ownership (ownhome), this relationship can also be interpreted as the proportion of people who are not renting the home they live in.The global parameter estimate for this relationship is −0.039 (p < 0.05) for 2006-2013, but is not significant for 2013-2018.Local parameter estimates for this relationship have a significant negative cluster in the centre of the Christchurch city area in 2006-2013, covering the CBD and parts of the eastern suburbs and red zone.In 2013-2018, the significant negative cluster moves to the south-west of the Christchurch city CBD, and a positive cluster appears on the south western boundary of the district.The negative cluster in 2006-2013includes those houses in the red zone area and those apartments in the CBD which may have also been affected by earthquake damage.This is to be expected, as for these areas, many homes were rented or used for social housing, especially in the eastern suburbs(McDonagh, 2014).For those properties owned privately which were located in the red zone, the government offered a voluntary buy-out, using property valuations from 2007(McDonagh, 2014).Many of those homes affected in the red zone were also government and local authority social housing or affordable privately owned properties, and these houses would likely be replaced by new homes in a different area within Christchurch with higher house price and rent costs(McDonagh, 2014).In the CBD, many landlords and property owners may have chosen to take a negotiated settlement for claims and re-invest in alternative properties outside of the CBD (Marsh Risk Management Service, 2014), therefore decreasing the availability of rental apartments or higher density housing in the CBD.For the change in median weekly rent (medweeklyrent), the global parameter estimate for this relationship is 0.117 (p < 0.05) for F I G U R E 4 Significant local estimates for (a) youth, (b) over65, (c) ownhome (home ownership), (d) medweeklyrent (median weekly rent) and (e) medhouse (median house price) 2006-2013, and 0.127 (p < 0.05) for 2013-2018.A positive cluster of local parameter estimates is seen in 2006-2013 located in the CBD and in the eastern red zone areas near the coastline, where significant earthquake damage occurred.From 2013-2018, positive clusters are seen in and around Kaiapoi, including the northern coastal red zone area, and to the south-west of the city in the Selwyn district.For the change in the median house price (medhouse), the global parameter estimates for both time periods are not significant.Local parameter estimates have a number of significant positive clusters in both time periods, in 2006-2013 to the north of Christchurch city near the northern red zones near Kaiapoi, and in 2013-2018 to the west of Christchurch city and the northern edges of the city.Negative clusters are also seen in 2006-2013 in the CBD of the city, F I G U R E 4 Continued variables used in MGWR modelling and description T A B L E 3 Global regression parameter estimates and goodnessof-fit measures for time periods2006-2013 and 2013-2018 T A B L E 4 Final model local parameter estimates (range, median, SD and bandwidth) Bandwidths chosen from initial MGWR model runs (global bandwidths in bold).Note that different bandwidths can be chosen for the same variables in different MGWR models.Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/psp.2583by University Of Glasgow, Wiley Online Library on [25/11/2022].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License first model, this could indicate that the relationship between over65 and the change in population is global (same relationship for the entire study area).