*2.3. Analysis*

The definition of NORC varies in different places and different periods. In the place of origin, the US Federal Government, through Title IV of the Older Americans Act, recognised NORCs as 'communities in which at least 40% of the heads of households are older individuals' [25]. According to prior studies, 'resident', 'head of household', 'old adult' and 'house owners and renters' are the most frequently used concepts (and their datasets) in identifying NORCs [13,14,26]. The most widely cited definition of NORCs is 'communities in which at least 40% of the heads of households are older individuals'. In Australian statistical data, older people are defined as people aged 65 years or more [27]; however, the concept of 'head of household' was not applied in the 2006, 2011 and 2016 ABS Census data. Alternatively, this research employed the concept and dataset of all household members who usually reside in the private dwellings rather than the head of household to define NORCs. It also excluded older residents living in nursing homes or aged care facilities. Therefore, this study adopted the combined circumscription of NORC as the community with 40% or more members of households aged 65 years and older, which has excluded holiday visitors and persons who have moved to nursing homes.

Four approaches of spatial analyses were conducted to identify the formation and development of NORCs. These were: (i) geovisualisation, (ii) spatial autocorrelation (global Moran's I), (iii) cluster and outlier analysis (local Moran's I), and (iv) hotspot and coldspot analysis (Getis-Ord Gi \*). These are among the frequently applied spatial analysis techniques in the age and healthcare studies [28]. The software of ESRI ArcMap Version 10.8.1 was applied for data analysis.

A geovisualisation was conducted to identify the distribution of NORCs in 2006, 2011 and 2016. When working with spatially referenced data, geovisualisation is helpful to recognise patterns across large geographical regions [29,30]. Choropleth maps, in this study, are used to display different classes of proportion of older people in each census unit and recognise the possible NORCs that meet the criteria.

Global Moran's I was used to measure the spatial autocorrelation of NORCs based on both locations and the proportion of older population simultaneously. Given a set of features such as location, areas and population, it evaluated whether the distribution pattern of NORCs was clustered, dispersed or random. Global Moran's I supports geovisualisation by statistically distinguishing the level of the spatial structure, which qualitatively improves the reliability of the interpreted geovisualised information [31]. In this research, global Moran's I statistic for the proportion of household members in the greater Brisbane region aged 65 years and over in each census unit has value ranges from −1 to 1. A negative value reveals that farther census units are more related than closer ones, a positive value of I reveals that the closer census units are more connected than farther ones, and 0 informs no spatial autocorrelation between them. [32]. A *Z*-score and *p*-value were used for the statistical significance test to verify the result: when *z*-score < −1.65 or >+1.65 associated with *p*-value < 0.10, the confidence level is 90%; when z-score < −1.96 or >+1.96 associated with *p*-value < 0.05, the confidence level is 95%; when z-score < −2.58 or >+2.58 associated with *p*-value < 0.01, the confidence level is 99%.

Local Moran's I, 'a local spatial autocorrelation statistic' [33], was employed to identify local clusters or outliers of NORCs to understand their contribution to the 'global' cluster statistic. It assesses each feature of census units within the context of neighbouring features and compares the local circumstance to the overall situation. Local Moran's I could be utilised to detect the clusters of census units with 40% or more of the members of a household aged 65 years and over among nearby census units in the greater Brisbane region.

Getis-Ord Gi \* (Gi \*) was used to verify a statistically significant spatial cluster of high values (hotspots) or low values (coldspots) of proportion of older household members within a distance [34]. A Gi \* analysis was employed to reveal whether a high or low proportion of older household members is concentrated over the greater Brisbane region at the different statistically significant levels, which means that to be a statistically significant hotspot, a census unit will have a high value and be surrounded by other census units with

high values as well. The visualisation of hotspots and coldspots of older population is the enhanced tool of cluster statistic in Local Moran's I, where hotspot identification not only describes the state of aggregation of older population at the moment but also predicts a trend of cluster for some neighbourhoods with low proportions of older population located in the contexts of high values. Meanwhile, coldspot areas are indicated as the aggregation of suburbs with a low proportion of older population, with the neighbours co-locating with low values as well. This research focused on finding hotspots of highly proportioned older household members including NORCs. icant hotspot, a census unit will have a high value and be surrounded by other census units with high values as well. The visualisation of hotspots and coldspots of older population is the enhanced tool of cluster statistic in Local Moran's I, where hotspot identification not only describes the state of aggregation of older population at the moment but also predicts a trend of cluster for some neighbourhoods with low proportions of older population located in the contexts of high values. Meanwhile, coldspot areas are indicated as the aggregation of suburbs with a low proportion of older population, with the neighbours co-locating with low values as well. This research focused on finding hotspots of highly proportioned older household members including NORCs.

Getis-Ord Gi \* (Gi \*) was used to verify a statistically significant spatial cluster of high values (hotspots) or low values (coldspots) of proportion of older household members within a distance [34]. A Gi \* analysis was employed to reveal whether a high or low proportion of older household members is concentrated over the greater Brisbane region at the different statistically significant levels, which means that to be a statistically signif-

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 5 of 13

### **3. Results 3. Results**

As shown in Figure 1, the proportion of older Australians increased obviously across the census units in the greater Brisbane region from 2006 to 2011 to 2016. The total number of household members aged 65 and over in the greater Brisbane region were 185,490, 215,149 and 267,281 in 2006, 2011 and 2016, respectively. Meanwhile, the proportion of older household members (aged 65+) increased from 10.68% in 2006 to 11.15% in 2011 to 12.76% in 2016 in the greater Brisbane region. This indicated a significant growth rate (44.1%) of older household members (65+), much higher than the growth rate of the total household members (20.6%) in the greater Brisbane region from 2006 to 2016. In addition, in 2006, 57.9% of the census units had less than 10% of older household members (those with 65+ years old), while in 2016 it dropped to 48.9%. By contrast, in 2006, only 7.6% of the census units had an older population of more than 20%, and this number increased to 10.7% in 2016. As shown in Figure 1, the proportion of older Australians increased obviously across the census units in the greater Brisbane region from 2006 to 2011 to 2016. The total number of household members aged 65 and over in the greater Brisbane region were 185,490, 215,149 and 267,281 in 2006, 2011 and 2016, respectively. Meanwhile, the proportion of older household members (aged 65+) increased from 10.68% in 2006 to 11.15% in 2011 to 12.76% in 2016 in the greater Brisbane region. This indicated a significant growth rate (44.1%) of older household members (65+), much higher than the growth rate of the total household members (20.6%) in the greater Brisbane region from 2006 to 2016. In addition, in 2006, 57.9% of the census units had less than 10% of older household members (those with 65+ years old), while in 2016 it dropped to 48.9%. By contrast, in 2006, only 7.6% of the census units had an older population of more than 20%, and this number increased to 10.7% in 2016.

**Figure 1.** Map of census units with the percentage of older household members (age 65+) in the Greater Brisbane Region in 2006, 2011 and 2016. The colours are classified by N/A, 0–9.9%, 10–19.9%, 20–29.9%, 30–39.9%, 40% and higher. **Figure 1.** Map of census units with the percentage of older household members (age 65+) in the Greater Brisbane Region in 2006, 2011 and 2016. The colours are classified by N/A, 0–9.9%, 10–19.9%, 20–29.9%, 30–39.9%, 40% and higher.

Figure 2 shows the locations of NORCs in 2006, 2011 and 2016. In 2006, 25 (0.8%) out of 3236 census units were identified as NORCs (with the proportion of 65+ years old more than 40%) in the greater Brisbane region. These numbers increased to 65 (1.3%) out of 5164 census units in 2011 and 92 (1.7%) out of 5373 census units in 2016, which indicated a rapid Figure 2 shows the locations of NORCs in 2006, 2011 and 2016. In 2006, 25 (0.8%) out of 3236 census units were identified as NORCs (with the proportion of 65+ years old more than 40%) in the greater Brisbane region. These numbers increased to 65 (1.3%) out of 5164 census units in 2011 and 92 (1.7%) out of 5373 census units in 2016, which indicated a rapid growth of NORCs over the 10-year span. In addition, the older household members (65+) living in NORCs accounted for 3.4% of the total older household members in 2006, and it increased to 6.1% in 2011 and 7.2% in 2016. According to Figure 2, NORCs were distributed mostly along the coastline and Brisbane River. Especially on the Bribie Island, there already existed four NORCs accommodating 886 older household members (65+) in 2006, and this number increased rapidly to 10 NORCs with 1961 older household members (65+) in 2011 and 15 NORCs with 2963 older household members (65+) in 2011. Currently, the Bribie Island has the oldest median ages (60.6 years) in Queensland.

Bribie Island has the oldest median ages (60.6 years) in Queensland.

growth of NORCs over the 10-year span. In addition, the older household members (65+) living in NORCs accounted for 3.4% of the total older household members in 2006, and it increased to 6.1% in 2011 and 7.2% in 2016. According to Figure 2, NORCs were distributed mostly along the coastline and Brisbane River. Especially on the Bribie Island, there already existed four NORCs accommodating 886 older household members (65+) in 2006, and this number increased rapidly to 10 NORCs with 1961 older household members (65+) in 2011 and 15 NORCs with 2963 older household members (65+) in 2011. Currently, the

**Figure 2.** Map of naturally occurring retirement communities (NORCs) with suburb boundaries in the Greater Brisbane Region in 2006, 2011 and 2016. The distributions along the Brisbane River and coastal areas are marked out. Bribie Island has the greatest number of NORCs and oldest median ages. **Figure 2.** Map of naturally occurring retirement communities (NORCs) with suburb boundaries in the Greater Brisbane Region in 2006, 2011 and 2016. The distributions along the Brisbane River and coastal areas are marked out. Bribie Island has the greatest number of NORCs and oldest median ages.

As indicated by the NORCs' distribution pattern, Global Moran's I was 0.352423 (z = 33.740511) in 2006, 0.252765 (z = 30.630196) in 2011 and 0.282963 (z = 35.100097) in 2016. For the Global Moran's I statistic, the null hypothesis states that the NORCs are randomly distributed in the study area. This result indicated that the distributions of NORCs were spatially autocorrelated or considered as not randomly distributed (rejecting the null hypothesis), which means that the NORCs or census units with a high proportion of older household members (65+) tended to get close to similar ones. Similarly, census units with low proportions of older household members were close to similar ones as well. Given the z-score of 33.74, 30.63 and 35.10, there was less than 1% likelihood that this clustered pattern could be the result of random chance. As indicated by the NORCs' distribution pattern, Global Moran's I was 0.352423 (z = 33.740511) in 2006, 0.252765 (z = 30.630196) in 2011 and 0.282963 (z = 35.100097) in 2016. For the Global Moran's I statistic, the null hypothesis states that the NORCs are randomly distributed in the study area. This result indicated that the distributions of NORCs were spatially autocorrelated or considered as not randomly distributed (rejecting the null hypothesis), which means that the NORCs or census units with a high proportion of older household members (65+) tended to get close to similar ones. Similarly, census units with low proportions of older household members were close to similar ones as well. Given the z-score of 33.74, 30.63 and 35.10, there was less than 1% likelihood that this clustered pattern could be the result of random chance.

Local Moran's I was used to detect the clusters, outliers and hotspots of NORCs. Figure 3 shows that the high-high clusters of census units (i.e., the census units with high proportions of older household members were co-located or clustered together, with a red colour in the red dot-line circle in Figure 3) were located in some specific areas, such as the Bribie Island, Cleveland and Victoria Point, most of which were distributed along the coastal line and expanded their cluster areas rapidly from 2006 to 2011 and 2016. By contrast, the low-low cluster (where census units with a low proportion of older household members (65+) were co-located together) were mainly located in the mountainous areas. Especially those blue areas in the black dot-line circle were disappearing from 2006 to 2011 and 2016 primarily due to the increase of the older population. For high-low and low-high outliers, no obvious patterns exist in this study. Local Moran's I was used to detect the clusters, outliers and hotspots of NORCs. Figure 3 shows that the high-high clusters of census units (i.e., the census units with high proportions of older household members were co-located or clustered together, with a red colour in the red dot-line circle in Figure 3) were located in some specific areas, such as the Bribie Island, Cleveland and Victoria Point, most of which were distributed along the coastal line and expanded their cluster areas rapidly from 2006 to 2011 and 2016. By contrast, the low-low cluster (where census units with a low proportion of older household members (65+) were co-located together) were mainly located in the mountainous areas. Especially those blue areas in the black dot-line circle were disappearing from 2006 to 2011 and 2016 primarily due to the increase of the older population. For high-low and low-high outliers, no obvious patterns exist in this study.

Figure 4 shows the optimised hotspot and coldspot living areas of older household members in 2006, 2011 and 2016. The optimised hotspot map shows that the statistically significant hotspot suburbs (with high proportions of older household members) are distributed along the coastline, and these areas were expanding rapidly from 2006 to 2016. The total number of older household members (65+) living in those optimised hotspot areas were 69,326, 60,341 and 69,595 in 2006, 2011 and 2016, respectively, accounting for 37.4%, 28.0% and 26.0% of the total older household members (65+). Meanwhile, some of the inland regions became hotspots as well, although the number of older household members (65+) was small. Take the Laidley, for example. Only 493 (18.9% of its total household members), 516 (16.1% of its total household members) and 619 (18.9% of its Total household members) older household members (65+) were living there in 2006, 2011 and 2016, respectively. By contrast, the coldspots (with low proportions of older

household members) in the inner-city areas and urban suburbs were increasing along with the decrease of the hotspots in these areas during the 10-year period. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 7 of 13

**Figure 3.** Cluster and outlier analysis of census units with a proportion of older household members (age 65+) in the Greater Brisbane Region in 2006, 2011 and 2016. Different colours indicate different meanings, including not significant, high-high cluster, low-low cluster, high-low outlier and lowhigh outlier. Significant high-high clusters and low-low clusters are marked out. **Figure 3.** Cluster and outlier analysis of census units with a proportion of older household members (age 65+) in the Greater Brisbane Region in 2006, 2011 and 2016. Different colours indicate different meanings, including not significant, high-high cluster, low-low cluster, high-low outlier and low-high outlier. Significant high-high clusters and low-low clusters are marked out. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 8 of 13

**Figure 4.** Optimised hotspot analysis of census units with the proportion of older household members (age 65+) in the Greater Brisbane Region in 2006, 2011 and 2016. Different colours indicate 90%, 95% and 99% confidence of hotspots and coldspots. The red circles mark out the increased hotspot areas from 2006 to 2011 to 2016, and the black circles in-**Figure 4.** Optimised hotspot analysis of census units with the proportion of older household members (age 65+) in the Greater Brisbane Region in 2006, 2011 and 2016. Different colours indicate 90%, 95% and 99% confidence of hotspots and coldspots. The red circles mark out the increased hotspot areas from 2006 to 2011 to 2016, and the black circles indicate the increased coldspot and decreased hotspot areas from 2006 to 2011 to 2016.

dicate the increased coldspot and decreased hotspot areas from 2006 to 2011 to 2016.

multilevel collaborations may serve the older people more efficiently because of the spa-

opportunity for the government to provide home and community care in NORCs where the older people can enjoy professional care with comparatively low cost due to the econ-

According to the Queensland Department of Communities, Housing and Digital Economy [35], the distribution of retirement villages in the greater Brisbane area is highly consistent with the distribution of older people, where the areas with high density of older residents have one or more retirement villages located around them. This implies that the retirement village developers have realised the advantage of the economic scales brought by the concentration of the older population. Similarly, one or more nursing homes can also be found in these popular areas with older people. NORC supportive service programmes as the solution of ageing-in-place provide the older people with another choice of ageing, which is different from the retirement village or nursing home, and the NORC participants can enjoy some of the services that the institutional care system could not provide, such as exercise and dance classes, trips and cultural events [36]. For the government, NORC programmes play a positive role in reducing the pressure of resource scarcity in the healthcare system [37]. However, it must be clarified that NORCs are different from NORC Service Support Programmes where multilevel collaborations, services and supports are provided to those NORCs with a high proportion of older people. Governments should provide NORC service support programmes to existing NORCs, with the
