Simultaneous Inequity of Elderly Residents in Melbourne Metropolitan

Abstract

The importance of proper access to urban amenities for elderly residents is evidenced in the literature. Among them, mobility infrastructure, particularly public transport (PT), is of pivotal significance due to its intermediary role in access to other amenities such as healthcare or urban green space (UGS). Given this, the inequity in access to PT could lead to more adverse impacts on society, especially if it coincides with inequities in other amenities. In response, we calculate local indicators of spatial association (LISA) between the elderly population and urban amenities of PT, healthcare, and UGS at the suburban level of Melbourne Metropolitan. We, then, introduce and develop a LISA-on-LISA model to analyze and reveal the coexistence of inequities at the suburban level. The results evidence the existence of inequity in access to PT for elderly cohorts. We further reveal the clusters of PT inequity which are, at the same time, experiencing healthcare and UGS inequities. The implications of the study for resource allocation and distribution in areas suffering from simultaneous inequity are discussed.

1. Introduction

Rapid population and urbanization are accompanied by inequities [1], especially in peripheral growth forms where urban amenities provision is lagging behind population and dwelling growth [2,3]. Public transport (PT), as one of the main elements of urban infrastructure, forms arteries of the city which provide group mobility. Other than its main purpose, PT also improves or has benefits for the environment [4], social and financial equity [5], health [6], access to employment [7,8], alleviating social exclusion and mobility [9,10]. Hence, access to PT is considered a method by which public infrastructure can eliminate the impact of various inequities [11]. However, PT itself could be subject to inequitable distribution.

Several studies highlight the inequity in access to PT for disadvantaged communities (e.g., low-income, minority, children, and the elderly) [11,12,13,14,15]. Inequity in access to PT manifests itself in children’s access to school, labor’s access to the central business district, and the elderly’s access to mental or physical health infrastructure. However, housing with good access to PT carry a premium price [16], and, as a result, poorer access to PT for disadvantaged cohorts could arise out of their lower purchasing power. This issue raises concerns about spatial inequity in access to PT and potential simultaneous disadvantages.

Access to PT is particularly important for elderly cohorts. Although some studies indicate the use of PT decreases for people older than sixty, these did not consider the socioeconomic characteristics of the observation [17]. People with lower incomes and at a retirement age may not have access to a personal vehicle [18], or at some point, due to health problems and their mental condition, they may not able to drive. They often prefer shorter trips utilizing barrier-free infrastructure to healthcare facilities [19] or social infrastructure, including urban green space (UGS) [20]. However, there are also several studies highlighting existing inequity in these amenities, as well.

To study the inequity in access to PT, it is required to go beyond its distribution. First, and in line with conventional wisdom, one needs to consider the factors that impact the use of PT. For instance, crowding has been found to negatively impact the perception of high-quality PT service, particularly for senior cohorts [21], and the experience of both quality and quantity is reduced when space becomes congested [22]. In addition, other close-by facilities also impact the experience of PT proximity, but are somehow ignored in many studies. Consequently, standard measures of access to PT only partially capture these important access dimensions which, as a result, affect our understanding of access to PT and its social-justice outcomes. Second, the coexistence of PT inequity with inequities in other urban amenities for which PT could play an access mediator has not attracted enough attention in the literature.

Given this, PT access for the elderly population is of paramount significance, especially for Australia in the 21st century, where its population aged 65 or over constitutes approximately 16% of the total population and it has been projected that, over the next 20 years, this figure will increase to more than 18.4%, and then to around 23% by 2066 [23]. Furthermore, despite the Metropolitan’s reputation for its liveability which indicates its high ranking in multiple qualitative and quantitative factors including infrastructure, healthcare, and environment in global comparisons, reviewing the Metropolitan amenities distribution reveals a number of quite strong regional disparities in some of them. In the case of PT, Melbourne’s tram network, which is the largest in the world and is one of the major transport modes, is concentrated in the central business district and toward the inner and middle suburbs, with the outer ones being not well provided for [24]. The high concentration of healthcare facilities around the inner suburbs is another examples of imbalance. The skewed distribution of UGS toward the eastern suburbs is also evidenced in myriad studies. These pieces of evidence raise concerns about spatial inequity in Metropolitan Melbourne.

Hence, this study is concerned with “how does access to PT for elderly cohorts vary across Melbourne Metropolitan, Australia?” and then “how does PT inequity potentially coincide with inequities in healthcare and UGS?”. We answer these questions by, first, building gravity indices of access to these amenities, considering the network distance as well as other factors that could positively or negatively impact their potential use. We, then, run a local indicator of spatial association (LISA) model on the variable of the elderly population and PT index and continue with the same analysis for the other urban amenities of healthcare and UGS. Finally, all the obtained results are put together in a LISA-on-LISA analysis to reveal the patterns of simultaneous inequity. Unlike previous studies, we utilize a measure of PT which incorporates all alternative PT locations weighted by distance and congestion (users), rather than proximity or share of the locality. Next, in a methodological and empirical contribution, we use LISA-on-LISA analysis to highlight areas suffering from simultaneous inequity. Following [25] and others, we argue that the study of inequities must go beyond the distribution of only PT to the need to consider it as a cause and solution for simultaneous inequity.

The results show that the distribution of PT in Melbourne Metropolitan is skewed towards areas with a lower proportion of the elderly cohort. Local clusters of significant PT inequity are revealed, which have implications for municipal decision making in service and resource allocation and distribution. In addition, the elderly cohort in Melbourne suffers from simultaneous inequity in access to PT and healthcare and also PT and UGS. There is a significant correlation between inequity in access to PT and inequity in access to healthcare and UGS. This study sheds light on how policy-making can intervene in the redistribution process.

The remainder of the paper is structured as follows. Section 2 reviews key concepts and the existing literature. Section 3 briefly introduces the study area and model variables. Furthermore, in this section, we set out the LISA model to analyze the inequities and how to combine different LISA models, a method we call LISA-on-LISA, to reveal the patterns of simultaneous inequity. Results are presented and discussed in Section 4. Finally, we conclude and extrapolate policy implications in Section 5.

2. Inequitable Access to PT

Coinciding with advances in globalization, urbanization, and social change, the issue of spatial inequity in cities has become a concern for researchers and policymakers. The issue of urban spatial inequity is well-documented and includes inequity in access to the urban amenities of housing [26], UGS [27], education [28], PT [12], and healthcare [29,30], to name a few. The forms and causes of these existing inequities are varied and impacted by multiple factors, such as the history of urban growth, human-capital developments, levels of economic development, and fiscal and political decentralization [31].

Among different urban inequities, PT is considered a solution to decreasing spatial inequity’s negative impact, particularly on health and well-being [32]. In particular for the elderly cohort, demographic changes and the formation of an aging society can cause increased demand for PT as a mobility vehicle to access healthcare [25]. As a result, PT disparity is related to social disadvantage, poverty, social exclusion, and health and well-being inequity.

Healthcare and UGS infrastructure are seen as urban resources to reduce residents’ health and well-being inequity; however, due to rapid land development, land scarcity, and budget limitations, these amenities themselves are inequitably distributed [33,34]. Equity in access to healthcare is essential for creating healthy cities. There are several studies indicating the importance of access to healthcare. For instance, poorer access to healthcare is related to the risk of late diagnosis of breast cancer [35] and higher distance to healthcare is related to avoidable hospitalization in older adults [36]. Given the importance of access to healthcare and existing inequity, PT can, to some extent, mediate the impact of healthcare inequity by providing mobility facilities for access to healthcare. In terms of physical health, for instance, access to transportation is considered beneficial for managing chronic kidney disease (CKD) in older adults [37]. In addition, in terms of mental health, the study of Fortney et al. [38] reveals that travel barriers may prevent rural patients from making a sufficient number of visits to receive depression treatment services. Healthcare is seen as a cure infrastructure; however, it is important to prevent diseases. Several studies show that UGS can promote physical activity and health, and well-being. The provision of UGS can, therefore, potentially counteract some of the health-related manifestations of inequality [39,40]. According to Ravulaparthy et al. [41], elderly people who participate in outside-the-home activities experience higher levels of well-being. The high importance of access to UGS among Australians is, furthermore, acknowledged by [42]; however, several studies evidence the inequity in access to UGSs within Australian cities, including Melbourne [27].

Given this, access to PT is of significant importance, not only as a form of mobility service but also as a vehicle which helps reduce other forms of spatial inequity. The study of Chen et al. [43] suggests combining PT to improve accessibility to facilities for elderly cohorts. Of particular relation to this research, Yoon and Park [25] suggest PT as an efficient way to access healthcare for elderly cohorts and the study of Dang et al. [44] finds poor allocation of PT resources is related to inequity in access to UGS. Elderly people have limited options when they cannot drive, highlighting PT’s role as an essential means to meet their needs. As a result, efficient and well-designed PT facilitates the accommodation of different ways of meeting their needs. From this perspective, PT improves equal access to opportunity [45,46].

Considering the co-importance of these urban amenities, there is a need to analyze access to them in an integrated study. However, the existing literature, considering the cross-section of urban-amenities inequities, usually focuses on the intermediary role that one plays for another (i.e., the role of PT in access to healthcare) and the issue of revealing simultaneous inequity is not a focus and, hence, underdeveloped (see [47,48], for instance). Therefore, building upon this literature, we, first, analyze potential inequity in access to PT, healthcare, and UGS for the elderly population; and, further, we analyze the coexistence of these inequities in Melbourne Metropolitan.

3. Data and Methodology

3.1. Study Area and Data Source

Our area of study is Melbourne Metropolitan, which is projected to be the fastest growing capital city from 2023–2024 onwards, overtaking Sydney to become Australia’s largest city in 2029–2030 [49]. Fast-growing populous cities often struggle to provide the infrastructure required to achieve social inclusion, health, and well-being [2,50]. As in most developed countries, Australia’s population is aging. Australia’s elderly generation (those aged 65 and over) continues to grow in number and as a share of the population. The aging of the population creates both pressures and opportunities for Australia’s health and welfare sectors [51].

This population is distributed across more than 350 different suburbs of the metropolitan where, as discussed, there are quite significant regional disparities among them. This uneven distribution of urban amenities across regions increases the potential for spatial-inequity issues for the vulnerable cohorts of society who have chosen to live in the under-served regions due to economic issues. To analyze the potential spatial inequity in access to urban amenities, we focus on regional disparities in the distribution of these amenities. The regional level in our study is Statistical Area Level 2 (SA2). SA2s are almost the size of a locality or suburb and represent a community which interacts socially and economically. At Australia’s level, “SA2s generally have a population between 3000 and 25,000 with an average of about 10,000 people” [52].

Our main study variable, the population of elderly people at the SA2 level, comes from the recent, 2021, census of population and housing. The number of elderly people was obtained as the population of those aged 65 or above. These variables were then combined with spatial data on PT, healthcare, and UGS, to analyze the inequities. In this study, PT facilities include train, tram, and bus stations; healthcare facilities include hospitals, either public or private (public hospitals are Victoria’s government health services providers, including large public healthcare providers, “rural and regional health services, specialist mother and child hospitals and small specialist rehabilitation and psychiatric hospitals” and private hospitals are “health service establishments where persons are provided with health services of a prescribed kind for which a charge is made and includes a privately-operated hospital.” [53]); and UGS facilities consist of all public open spaces, which are mainly green spaces, and are used as UGS in many studies. The spatial maps for these urban amenities were obtained from the Victorian Government’s open data platform and the point in time for each was chosen to be the closest to the census night date, August 2021. In what follows, we explain how we translate these spatial data to access indices needed for our study.

3.2. Gravity Model of Access to Urban Amenities

An initial step in analyzing access to urban amenities is gauging or quantifying the access. Several methods are used in the literature to quantify spatial accessibility. The conventional and most used approaches are the nearest distance and buffer approach (AKA container approach, i.e., residing within x meters of amenity). Both these approaches could be based on either the direct (Euclidean) or network distance. The direct distance has the limitation of not being realistic in practice [54], but the network distance uses GIS technology and takes the routes that are likely to be used by residents to reach destinations [55,56]. However, all these approaches are limited in the sense that they assume residents effectively ignore longer journeys to other urban amenities [57].

To quantify access to urban amenities in this research, we use a “gravity” model. The gravity model provides a potential accessibility measure and has been used in spatial and urban studies since late 1940 (see, e.g., [55,58,59]). Our gravity-based access measures consider all the urban amenities within urban environments while weighting them using the factors which positively or negatively impact the potential use of those amenities.

3.2.1. PT Index

Accordingly, we build access indices of different PT modes of the train, tram, and bus as

$$PTModeInde{x}_i=\sum _{t=1}^n\frac{1}{D_{it}*P_t}$$

(1)

where each $PTModeIndex$ (e.g., train index) for $SA{2}_i$ is obtained from summing access to all stations of that mode weighted negatively by network distance between $SA{2}_i$ and train station t, $D_{it}$, and population density in the vicinity of station t, $P_t$.

We are incorporating a couple of innovations here. First, we are not restricting the accessible PT to a certain distance; rather, all the PT facilities are considered and weighted based on their network distance. This is based on the statement that “the provision of public goods and services, in practice, is not limited to specific geographic boundaries” [54,60] but their attractiveness decreases based on the separation or distance from them [61,62]. Second, we are considering population density as a negative factor. This is according to the work of Geurs and Van Wee [63], who suggests congestion or competition as a useful factor when analyzing access to urban amenities for which competition impacts destination locations (There are mixed pieces of evidence on the impact of population density and crowding on PT. While inter-city analyses reveal that there is a positive correlation between population density and PT access due to economic and sustainability feasibility [64,65], intra-city studies tend to show a negative impact of population density on PT quality perception and use [66,67]. We are building our model based on the latter, which implies that between two urban regions with the same level of PT services, the region with lower population density has higher PT satisfaction and use. We also acknowledge that there could be a non-linearity or threshold for the population-density impact which is not captured in our study).

The same formula was used for train, tram, and bus indices, and then all of them were combined to obtain the PT index as

$$P{T}_{i,Equal-Weighted}=TrainInde{x}_i+TramInde{x}_i+BusInde{x}_i$$

(2)

Here, we are assuming an equal weight or importance for different PT modes, which may not be true in practice. Therefore, we used principal component analysis (PCA) to obtain weights for them. We ran a PCA on the three PT modes’ indices and took the first principal-component rotations to obtain the weights. Therefore, the weighted PT index was calculated as

$$P{T}_{i,PCA-Weighted}=w_{train}\times TrainInde{x}_i+w_{tram}\times TramInde{x}_i+w_{bus}\times BusInde{x}_i$$

(3)

This PCA-Weighted PT index is our main PT index and also the basis of some of our other calculations, to be explained later.

3.2.2. Healthcare Index

The same approach as PT was followed for healthcare, where we obtained healthcare for each suburb as

$$HealthcareInde{x}_i=\sum _{h=1}^n\frac{1}{D_{ih}*P_h}$$

(4)

where $D_{ih}$ is the network distance between SA2 i and hospital h and $P_h$ is the population density in the neighborhood of hospital h.

3.2.3. UGS Index

We, similarly, built the UGS access index; however, here, we incorporated the impact of area (km${}^2$) as a positive factor. Thus, we built our gravity index as

$$UGSInde{x}_i=\sum _{g=1}^n\frac{A_g}{D_{ig}*P_g}$$

(5)

where $A_g$ is the area of UGS g, $D_{ig}$ is the network distance between SA2 i, and UGS g and $P_g$ is the population density in around the UGS g.

3.3. Measuring Access Inequity: LISA Clusters

We used the bivariate LISA [68] clustering method to determine the regions or suburbs with statistically significant patterns of lack or excess. As [69] states, the bivariate LISA is the most suitable model for analyzing accessibility for different social groups and revealing clusters or hotspots.

The bivariate LISA model calculates local Moran’s I index for each SA2 as

$$I_i=Z_i\sum _j{W}_{ij}{Z}_j$$

(6)

where $Z_i$ and $Z_j$ are standardized formats of the two variables of interest, “elderly population” and “PT index” in our case, and $W_{ij}$ is the row-normalized neighborhood weight matrix. Moran’s I index is a scale variable and is interpreted similarly to a correlation coefficient, where positive and negative values indicate the direction and strength of the spatial association.

This step yields statistically significant spatial clusters of low or high values of variables. These clusters can be directly used for revealing the areas with inequitable distribution of urban amenities and potentially needing decision-makers’ intervention. However, there are indirect uses of these clusters as well.

First, it is common in the literature to use LISA clusters in a Mann–Whitney U test [70] to further discern the inequitable distribution at the aggregated level, in contrast to local insights that LISA provides. The use of the Mann–Whitney U test is encouraged as it does not rely on normality assumption for the data and also works with small samples and even semi-quantitative or ordinal data [71].

The calculation of Mann–Whitney U statistic is as follows

$$U=n_1{n}_2+\frac{n_1\left(n_1+1\right)}{2}-R_1,$$

(7)

where $n_1$ and $n_2$ are the sample sizes of the two groups obtained from LISA clustering—group 1 includes the regions with high elderly populations and group 2 includes the regions with low elderly populations. $R_1$ is the sum of the ranks of regions in group 1 when we sort and rank all the regions in groups 1 and 2 based on their PT index. We test the U statistic against the alternative hypothesis that the first group has a lower PT index than the second group.

It should also be noted that as PT inequity is the focus of this study and our main aim is to analyze simultaneous inequity, we kept our LISA clusters fixed (obtained from LISA on the elderly population and PCA-Weighted PT) when running the Mann–Whitney U test for healthcare and UGS. This is discussed further in Section 4.

Next, as a further innovation, we aim to use the LISA clusters to reveal the patterns of simultaneous inequity in our study area. This is explained in the next subsection.

3.4. Analyzing Simultaneous Inequity: LISA-on-LISA

The existence of simultaneous inequity could cause additional pressure on already disadvantaged communities. Thus, revealing the patterns of simultaneous inequity could provide policy-makers with new insights and tools to manage and possibly reduce urban inequities and, as a result, prevent their negative consequences. Here, we are suggesting and employing an innovative and effective use of LISA clusters to analyze simultaneous inequity.

Suppose we have two sets of LISA clusters, the first one on variable 1 and variable 2, e.g., elderly population and PT, and the second one on variable 1 and variable 3, e.g., elderly population and healthcare. From each set, we take the clusters that indicate unfavorable inequities, e.g., “high elderly and low PT” and “low elderly and low PT”, and their local Moran’s I indices. These indices are then used as the degree of inequity, where negative values (for high elderly and low PT) indicate high inequity and positive values (for low elderly and low PT) indicate low inequity. The degree of inequity for other regions is effectively put to zero. This provides us with two new spatial variables which designate the degree of inequity in two urban amenities for the same disadvantaged cohort. The next step is to run the third LISA analysis on these new variables. The results reveal the clusters of simultaneous inequity in the variables of interest. This process is illustrated in Figure 1.

One major difference between “LISA” and “LISA-on-LISA” analyses is that LISA clusters contain both favorable and unfavorable inequities; however, all 4 clusters of LISA-on-LISA are unfavorable and the analysis helps to reveal the degree of importance or significance of the inequity in question. Further discussion on this difference is provided in Section 4.3.

4. Results

4.1. Descriptive Statistics

The main variables used in our analysis are summarized in

Table 1. Summary statistics.

	Mean	Std.Dev.	Min	Q1	Median	Q3	Max
Total population (×1000)	$13.622$	$5.418$	$0.000$	$9.851$	$13.205$	$17.363$	$28.119$
Population density (×1000 per km${}^2$)	$2.402$	$2.575$	$0.000$	$0.965$	$2.080$	$2.967$	$30.041$
Eldery (×1000)	$2.049$	$1.220$	$0.000$	$1.170$	$1.831$	$2.818$	$7.665$
Train distance (km)	$3.573$	$4.962$	$0.080$	$0.883$	$2.037$	$3.649$	$33.603$
Tram distance (km)	$11.555$	$12.337$	$0.022$	$1.391$	$7.401$	$17.844$	$55.168$
Bus distance (km)	$0.893$	$2.431$	$0.010$	$0.127$	$0.239$	$0.563$	$21.604$
PT index (equal weight)	$16.115$	$4.718$	$6.127$	$12.984$	$16.269$	$18.890$	$41.255$
PT index (PCA weight)	$3.757$	$1.172$	$1.272$	$2.912$	$3.678$	$4.471$	$8.305$
Healthcare index	$1.893$	$0.400$	$0.827$	$1.671$	$1.900$	$2.136$	$3.677$
UGS index	$3.003$	$0.462$	$1.850$	$2.748$	$2.987$	$3.289$	$5.081$

. On average, Melbourne suburbs (SA2) have a population of around 13,600 people, of whom about 2000 are aged 65 or older, and this population is distributed at a density of 2400 people per km${}^2$. However, the Metropolitan is pretty diverse, where some areas have almost no population and some central suburbs have populations of around 28,000 or elderly populations of close to 7700, or quite densely distributed at 30,000 per km${}^2$.

Melbourne has three main modes of PT: train, tram, and bus. The train is the most used mode, followed by tram and then bus. As expected, among different PT modes, the bus network has the best coverage across the Metropolitan, where the median distance to a bus station is around 239 m. The median distance to a train station is about 2 km; however, the tram network has the lowest coverage across the Metropolitan which was not unexpected, due to the geotechnical requirements it needs. The median distance to a tram station is around 7.5 km.

These study variables were combined in a gravity model to give a summarized overview of the distribution of PT and other urban amenities, including healthcare and UGS. The summary of the obtained indices is presented in Table 1 and their spatial distributions are visualized in Figure 2. Focusing on PT, the central suburbs, those closer to the central business district (CBD), have better PT accessibility, as expected. The equal-weighted and PCA-weighted methods do not show significant differences at the overall level but for the southeastern suburbs, the latter is lower in comparison to the former, which seems more realistic. The summary of the PCA analysis that yields the latter index is presented in the Appendix A,

Table A1. PCA Analysis of PT modes.

	PC1	PC2	PC3
Standard deviation	$1.322$	$1.017$	$0.468$
Proportion of Variance	$0.583$	$0.345$	$0.073$
Cumulative Proportion	$0.583$	$0.927$	$1.000$

. The distribution of healthcare facilities shows a similar pattern to PT, and possibly to other urban amenities, in terms of its concentration around the CBD. However, UGS has a distinct distribution, with its accessibility diminishing from east to west.

4.2. Analyzing Spatial Inequities

Urban-accessibility indices for these urban amenities and the elderly population at the suburban level were fed into a LISA model to reveal the patterns of equity or inequity clusters. The results of the LISA analyses are illustrated in Figure 3. In all four obtained maps, the distribution of urban amenities follows the gravity-indices maps, discussed above. The addition here is the elderly distribution as well as the significance indicator. Each model yields five clusters of “high–high”, “high–low”, “low–high”, “low–low”, and “not significant”. The interesting point is that the clusters with high and low elderly are scattered across the metropolitan as well as the clusters of high and low urban amenities. These clusters are visualized in four colors for ease of use. The clusters in green indicate higher access to urban amenities and the clusters in red indicate lower access. The latter group is the clusters we used for the simultaneous-inequity analysis, LISA-on-LISA, and its results are discussed further in this section.

The LISA clusters were then subjected to an inequity analysis using the Mann–Whitney U test. The results are summarized in

Table 2. Analyzing Lisa Clusters.

	Low Elderly	High Elderly	Mann–Withney
	Suburbs	Suburbs	Test Stat.
N	110	42	-
Train index	$2.937$	$2.691$	$0.068$ *
Tram index	$3.921$	$3.139$	$0.003$ **
Bus index	$8.336$	$8.088$	$0.276$
PT index (equal weight)	$15.193$	$13.918$	$0.058$ *
PT index (PCA weight)	$3.894$	$3.410$	$0.020$ **
Healthcare index	$1.880$	$1.709$	$0.050$ *
UGS index	$2.878$	$2.917$	$0.143$

Note: * and ** indicate statistical significance at 10% and 5% levels, respectively.

. It should be noted that, as discussed in Section 3, the basis of this section and determining the regions with low and high elderly populations was the LISA model with the PCA-weighted PT index. These include 110 suburbs with relatively low elderly populations and 42 suburbs with relatively high elderly populations. The second and third columns present the average accessibility index for different urban amenities and the last, and fourth, column presents the statistics from the Mann–Whitney U test, where the alternative hypothesis is that the high elderly suburbs have lower PT indices than the low elderly suburbs.

The results confirm an overall inequity in train, tram, PT index, and healthcare, at different significance levels. However, the test did not confirm an inequity in bus or UGS. A couple of things should be noted about these results. First, the obtained statistics evaluate the overall accessibility, while we observed that there are local inequities in the studied amenities. Second, as in this research we are focusing on simultaneous inequity between PT and other urban amenities, the clusters are based on LISA on PT; hence, the results should only be interpreted in the context of the existence or non-existence of healthcare and UGS inequity in regions with significant PT inequity.

4.3. Analyzing Simultaneous Inequity

In the last step, to shed light on the areas suffering from multiple inequities and, hence, needing the most attention, we performed a LISA-on-LISA analysis. The results are illustrated in Figure 4. Section (a) is on the simultaneous inequity between PT and healthcare. As visualized, the outer northern suburbs and some in the far south are suffering from inequity in both the studied variables, although to different degrees. All four clusters obtained here are unfavorable and probably need intervention—this is one major contrast to the LISA analysis, in which we have both favorable and unfavorable clusters. In section (b), the focus is on PT and UGS. In line with the Mann–Whitney U test results, which can be seen in Table 2, there are fewer regions with this type of simultaneous inequity. Some regions in the outer west and some in the far south are suffering from simultaneous inequity.

The obtained clusters of simultaneous inequity were then subject to a population analysis. We compared the share of the elderly population living in different clusters with the same figures for the rest of the population. The results are tabulated in

Table 3. Share of elderly living in different simultaneous inequity clusters.

	PT and Healthcare		PT and UGS
Cluster	Elderly (%)	Rest of Pop. (%)	Elderly (%)	Rest of Pop. (%)
High simultaneous inequity	5.22	2.40	1.42	0.54
Moderate simultaneous inequity	2.12	2.73	2.94	4.73
Low simultaneous inequity	3.31	6.27	1.37	2.67
Not significant	89.35	88.60	94.27	92.06

Notes: Moderate cluster consists of clusters with one high and one low inequity.

. On PT and healthcare, more than 5.2% of the elderly population are living in high simultaneous (high PT and high healthcare) inequity. This compares to only 2.4% for the rest of the population. On the other hand, low simultaneous inequity is 3.3% for the elderly, while being 6.2% for the rest of the population. These yield a total of more than 10% of the elderly population living in simultaneous inequity. Regarding PT and UGS, the situation is much better, as expected. About 1.4% of elders live in high simultaneous inequity in comparison to 0.5% for the rest of the population. In addition, at the overall level, around 6% of the elderly population are living in simultaneous inequity.

5. Discussion and Conclusions

In 2015, for the first time since the establishment of the federation, the number of Australians aged 45 and over surpassed those aged under 30 [72], and it has been projected that the number of Australians aged 65 or over will increase significantly over the next 20 years. In addition, an ever-increasing share of urban residents and also modern lifestyles have raised concerns about chronic diseases while, already, half of Australians are struggling with at least one common chronic condition (e.g., cancer, cardiovascular disease, diabetes, mental-health conditions, lung diseases, asthma, arthritis or back pain) [73]. This foreshadowing puts pressure on governments at different levels to consider the needs of one of the most vulnerable social cohorts, elderly people.

Designing age-sensitive neighborhoods is important for generating positive experiences among older adults [74]. In this regard, providing physical and social infrastructure is of critical significance. This includes healthcare, UGS, and, most importantly, PT which, other than being a mobility infrastructure, is a mediator for access to other urban amenities. However, the question remains of to what extent urban governance has succeeded in achieving this aim. More specifically, is the current distribution of PT in Melbourne Metropolitan of benefit to the elderly population? In addition, is the potential inequitable distribution of PT coinciding with inequity in other urban amenities?

To analyze the possible patterns of inequities, we first calculated the accessibility indices using the gravity model, considering the factors that positively or negatively impact the use of these urban amenities, PT, healthcare, and UGS. These indices were then subject to bivariate LISA analysis with the elderly population. This yielded the patterns or clusters of inequity for each of these urban amenities for the studied population, which were then tested using the Mann–Whitney U test for revealing the overall inequities. In the last step, we ran a LISA-on-LISA analysis to reveal the patterns of simultaneous inequity.

The gravity-model results show how PT and healthcare facilities access is concentrated toward the CBD, while UGS access is higher for the eastern suburbs and the least for western areas, as expected from the skewed UGS distribution in Melbourne Metropolitan. Employing the obtained accessibility indices reveals the patterns of inequity in access to PT, healthcare, and UGS for the elderly population. For PT and healthcare, the favorable inequity suburbs, those with high elderly and high PT, are those in central regions and unfavorable inequities are in outer regions. However, for UGS, a decreasing distribution from east to west is evidenced. The obtained clusters were then tested using the Mann–Whitney U test to reveal the significance of overall inequities. Finally, in an innovative contribution, a LISA-on-LISA analysis was used to shed light on the clusters with simultaneous inequity. The population analysis of the PT and healthcare simultaneous-inequity regions shows that 5.5% of the elderly population are living in regions with high simultaneous inequity, which compares to 2.4% for the rest of the population. The similar figures for PT and UGS are 1.4% and 0.5% for the elderly population and the rest of the population, respectively.

There is no direct study on the simultaneous inequity in Melbourne Metropolitan with which to compare our results; however, our findings on the inequitable distribution of some urban amenities echo those of other studies, to some extent. PT inequity in, mainly the outer suburbs of, Melbourne Metropolitan for the general population [75] and for socio-economically disadvantaged groups [76] is stated in the literature. The role that this inequity plays in the access of vulnerable cohorts to healthcare facilities is also documented by [77], which indirectly indicates the existence of simultaneous inequity for diabetic citizens caused by inequitable PT for some outer suburbs. Given the well-documented inequity in these urban amenities and for mainly the outer suburbs of the metropolitan, there is the potential for other forms of simultaneous inequity to emerge and for other vulnerable cohorts of the society to be affected. New urban development projects are mainly formed in these suburbs and, additionally, economic drivers could potentially direct vulnerable cohorts toward these regions. These could exacerbate existing inequities over time, as [33] evidence that UGS inequity for families with children is worsening over time.

PT is of paramount significance in the process of urban planning due to the mobility infrastructure it provides. In addition, it provides a mediator for access to other urban amenities, including healthcare and UGS. Therefore, PT inequities are stated to be related to other social disadvantages. Given this, PT is not an isolated urban amenity which impacts only the mobility of residents. Rather, it is the underlying substructure to facilitate access to a diverse range of vital facilities. However, we evidence that some elderly residents of Melbourne Metropolitan are suffering from simultaneous inequity of not only healthcare and UGS but also PT, which is the mobility facilitator to access them.

Therefore, following [25], we emphasize that it is important to scrutinize PT with healthcare and UGS in urban-planning strategies aiming to create a just, healthy, green city for an aging society. In addressing this issue, we suggest considering all the factors that possibly impact the use of urban amenities. In the case of PT, these include factors such as crowding, waiting times, costs, and uncertainty over routes and timetables [78]. Moreover, there is a need for a specific focus on the elderly population as, in extreme situations, some people might not be able to access basic services such as hospitals, stores, and pharmacies, which are not normally accessible by walking. Older people’s needs in terms of PT affordability include concessionary fares, simplicity, transferable or flexible tickets, and a flat fare structure.

This research provides an original contribution by revealing the patterns of simultaneous inequity for the elderly population in Melbourne Metropolitan. However, future research analyzing the impacts of the observed multiple inequities could be instrumental in revealing the possible detrimental physical- and mental-health impacts this has had on the disadvantaged community. This could help researchers define new research priorities and policymakers prioritize suffering regions in planning agendas.