How does heterogeneity in dwelling type preferences relate to housing and built environment characteristics?

ABSTRACT Understanding housing preferences is critical for successful compact city development. However, there is limited research on understanding preference heterogeneity in dwelling type choices. Using the Household Income and Labour Dynamics in Australia survey, this paper identifies the key housing and built environment characteristics associated with changes in dwelling type choice from detached houses to high-density. A latent class choice model captures the heterogeneity of dwelling type preferences within a traditionally low-density city, Brisbane, Australia. Findings reveal six household classes with distinct dwelling preferences: Class 1 (senior households without children with other family members) and Class 2 (couple families with children) in inner-city areas, Class 3 (high-income young households) and Class 4 (low-income households without children) in middle-city areas, Class 5 (low-income families with children) and Class 6 (middle-income young families without children) in outer-city areas. Residential environments with better access to educational facilities encourage Classes 3 and 6 to change to high-density living. Greater land use diversity encourages Classes 2, 3, and 6 to move towards high-density living. The findings can be used to design and improve high-density housing for targeted population groups across inner-, middle- and outer-city areas.


Introduction
High-density housing has been promoted by governments worldwide to manage urban growth and achieve sustainable city goals (Howley 2009;Liao, Farber, and Ewing 2015;Myers and Gearin 2001).Inner-city 1 apartment living enhances community liveability, supports ethnic diversity, and addresses sustainability concerns through minimising automobile reliance (Howley 2009).However, inner-city apartment living also results in negative impacts, including increasing trafficinduced noise and air pollution (Aristodemou et al. 2018;Tang and Wang 2007).There are also constraints due to limited supplies of easily developable land, such as large former industrial or undeveloped sites available for high-rise apartment construction in inner-city areas (Gallagher, Liu, and Sigler 2019).This necessitates the exploration of alternatives to inner-city high-rise apartments, including middle housing, and high-density housing in outer urban areas.While scientific and policy attention has focused more on high-rise apartments in urban inner-city areas, less attention has been given to middle housing (MH), also called the 'missing middle housing' 2 , a housing type that is currently in short supply (Parolek 2012).This housing type is important in housing supply and compact city development (Parolek 2020;Maharaj 2020).High-density housing in outer-city areas is also infrequently investigated in the existing literature.Lower housing prices, better accessibility to green spaces, and spacious dwelling sizes in high-density housing in outer urban areas may have the potential to both attract residents and achieve high-density living (Lee, Beamish, and Goss 2008).Examining who chooses and why they choose high-density dwelling types (both middle housing and medium-to high-rise residential) not only in inner-city areas, but also in the middle-city and outer-city areas, can help planners and policymakers understand the public demand for high-density living, and plan for high-density housing provision across urban areas.
The term 'housing choice' in this paper refers to 'actual housing choice' (hereinafter termed as 'housing choice').The term 'housing preference' in this paper refers to certain features any consumer wants to have in choosing a house to live (e.g.housing price, dwelling size).Existing studies on housing choice have found that housing preferences for certain features, such as housing or built environment characteristics, are heterogeneous in nature.For example, some people are more concerned with housing prices (Olanrewaju and Woon 2017), while others pay more attention to dwelling size (McKinlay, Baldwin, and Stevens 2019) or land-use diversity in the surrounding area (Koster and Rouwendal 2012).
Previous studies have employed various segmentation approaches to identify population groups with homogeneous preferences in housing choices, including lifestyle orientation (Walker and Li 2007), household socioeconomic variables (Niedomysl 2008), and latent psychological factors derived from attitude indicators (Lee et al. 2019;Cockx and Canters 2020).Multiple studies have examined the role of preference heterogeneity in housing choice, including location choice (e.g.Walker and Li 2007;Cockx and Canters 2020) and tenure choice (e.g.Chen 2016), but in one of the subsets of housing choice studies-dwelling type choices, the role of preference heterogeneity has yet to be explored.Understanding preference heterogeneity in dwelling type choices is important because the failure to account for the variations adequately could lead to an inappropriate or inadequate housing supply, which may further lead to the housing mismatch between the supply and the demand for dwelling types (Kelly, Weidmann, and Walsh 2011).
To address these knowledge gaps, this paper aims to examine the heterogeneity of housing preferences in dwelling type choices.Specifically, we identify the key features that might invoke housing choice change from low-density residences (detached houses) to high-density dwellings (both middle housing and medium-to high-rise residential) for different household groups.We also examine the role of preference heterogeneity in dwelling type choices in not only inner-city areas, but also middle and outer-urban areas.Our findings can provide evidence for housing provision policy-making and implementation by helping decision-makers target specific population groups who are likely to be receptive to the change from detached houses to high-density dwellings, particularly in outer city areas.
The ensuing section introduces critical background information for understanding high-density housing choices and the modelling of housing preference heterogeneity.This is followed by the case study context, data, and methods.The results section presents and discusses the housing and built environment characteristics that determine the preference heterogeneity of different household groups across inner-, middle-and outer-city areas.Section 5 summarises the key findings and outlines policy implications for promoting high-density development, before reporting our conclusion and avenues of future research in the final section.

Who lives in high-density housing and why?
A large number of academic studies have investigated people from different socioeconomic and demographic backgrounds who live in high-density dwelling types and why they chose these types of dwellings.Questions of high-density dwelling type choice have largely been investigated through multi-dimensional factors, including household demographic, housing, and built environment characteristics (Habib and Miller 2009;Lee et al. 2010;Pinjari et al. 2011;Van Ham 2012).Previous literature has shown that those who are highly educated professionals, students, young single professionals, double income no kids (DINKs), young urban professionals (YUPPIES)are most likely to rent high-rise apartments in inner urban areas (Allen and Blandy 2004;Randolph 2006).As they grow older or start a family, these people often leave inner-city apartments (Andrew and Meen 2006).After children have left a household and family size decreases, some may return to inner-city apartments to enjoy low-maintenance, inner-city lifestyles (Kwon 2012).Housing characteristics such as monthly costs, tenure, and the number of bedrooms are often considered in conjunction with a range of other factors when residents make housing decisions (Schirmer, van Eggermond, and Axhausen 2014;Tong et al. 2020).Furthermore, a number of the built environment and socioeconomic characteristics have been shown to influence housing choices, including land-use mix, population density, employment density, neighbourhood socioeconomic status, distance to transport provisions, facilities, and education resources (Ghasri and Rashidi 2018;Tokunaga and Murota 2022;Kerr, Klocker, and Gibson 2021;Torres, Greene, and de D Ortúzar 2013).
Existing housing choice studies have tended to focus on residents and their reasons for choosing inner-city high-rise apartments.Middle housing (MH) has received less attention in housing choice studies.Housing choice studies show a high demand for MH, as this high-density housing type is recommended as an affordable housing tool to accommodate different income levels, lifestyles, and demographics (Parolek 2012;Parolek 2020;An et al. 2022).Existing high-density housing choice studies also give less attention to the suburban context, where housing and built environment characteristics may be substantially different from that of inner-city areas.High-density housing choices in outer suburbs have been largely overlooked (Larco 2010).Dwellings in outer suburbs tend to be more affordable and larger than those in inner-city suburbs.The built environment in outer-city suburbs tends to feature more abundant open space, less crowded transport, and lower density than in inner-city areas (Brody 2013;Williamson 2013).Today, more and more high-density dwellings in outer urban areas are alternatives to detached houses (Rosewall and Shoory 2017;Australian Bureau of Statistics 2022).In contrast, there is limited easily developable land (e.g.large former industrial or undeveloped sites) available for apartment construction in inner-city areas (Gallagher, Liu, and Sigler 2019).The high demand for MH, in combination with the limited available land for high-density development in inner-city areas, creates a situation that necessitates the exploration of high-density housing choices in outer urban areas.

Modelling the heterogeneity of housing preference
Studies have shown that households' preferences for housing choices are heterogeneous in nature.To account for this preference heterogeneity, segmentation approaches are often applied by studies to classify individuals or households into segments (or subgroups) that have the same preferences (Kamakura and Russell 1989).One of these segmentation approaches is to use observable sociodemographic and economic variables to determine a variable for segmentation and the number of segments.This approach is usually called the a-priori approach.For example, the population might be divided into two segments based on gender (Devlin 1994) or age (Jancz and Trojanek 2020).Though this approach is simple, the assumed homogeneity within each segment cannot be guaranteed (Fu and Juan 2017).
Another segmentation option is the a-posteriori approach, a multivariate statistical classification technique that contains richer information (e.g.unobservable latent psychological factors) in describing each segment.One of the most popular a-posteriori approaches is cluster analysis.This analysis is performed based on certain selected variables, such as socio-demographic characteristics and latent psychological factors derived from a large number of attitudinal indicators (Salomon, Waddell, and Wegener 2002).For example, Ge and Hokao (2006) used cluster analysis to obtain three residential lifestyles in two Japanese cities, Saga and Kitakyushu.However, Bhat (1997) noted that using cluster analysis might pose difficulties in estimating and interpreting parameters.Two other popular a-posteriori approaches are the mixed logit model (McFadden and Train 2000) and the latent class model (LCM) (McFadden 1986).The mixed logit model captures the random variation of individual tastes and takes into account unobserved covariates over time.Hoshino (2011) employed a mixed logit model to identify the heterogeneity of housing preferences in Tokyo, and the result revealed significant heterogeneity in some residential attributes, such as residential land use.Though the mixed logit model effectively identifies residential preference heterogeneity, it cannot capture the different preferences of different segments (Ma et al. 2015).
To capture the preferences of different segments of a population, the LCM probabilistically assigns each respondent to each segment, in which both the membership probability and choice probability are simultaneously estimated (Wedel and Kamakura 2000).On the basis of individual and household socio-demographic characteristics (e.g.household income and structure), Walker and Li (2007) identified three lifestyle groups, including suburban, auto, and school-oriented, transit and school-oriented but in a suburban setting, and urban and auto-oriented; Liao, Farber, and Ewing (2015) found that those most likely to choose compact and transit-oriented neighbourhoods included: families with fewer school-age children; low-income households and renters; and individuals who valued social heterogeneity with less desire for privacy.In Kitchener Waterloo, Canada, Huang, Parker, and Minaker (2021) found that seniors and smaller-sized households were more likely to choose a transit-oriented development neighbourhood due to the transit accessibility, walkability, and green open space in the neighbourhoods.Cockx and Canters (2020) found that tenure status, education level, nationality, and household type distinguish heterogeneous residential location preference profiles in Belgium.However, the mechanisms of the preference heterogeneity in dwelling type choice studies yet remain unexplored (Kelly, Weidmann, and Walsh 2011;Yeoman and Akehurst 2015).

Study context
The Brisbane local government area (hereon referred to as 'Brisbane') is the capital city of the State of Queensland (Figure 1).It is located in South East Queensland, one of the fastest-growing metropolitan regions in Australia.Brisbane has recently undertaken initiatives to increase the diversity and density of its residential dwellings (Queensland Government 2017).The traditional housing supply dominated by detached houses has resulted in adverse environmental impacts, and has been criticised as being unsustainable (Queensland Government 2017).Considering recent high population growth rates and net interstate migration (Australian Government 2021), there is a need to think about where and how to accommodate the increasing population in a sustainable way-for example, by having more population living in high-density housing rather than detached houses.However, until now, there has been little research in Brisbane that explores the feasibility of how housing preferences could be changed to favour high-density housing over detached houses.Therefore, this study seeks to identify who (potential household groups) and why (potential influencing factors) people choose high-density housing in Brisbane.
The study area was classified into three urban areas (Figure 1), in accordance with the latest definition provided by the Brisbane City Council (2021).Areas were excluded if they were non-residential (i.e. with less than 50 households) or predominately national parks, state forests, lakes, and other water bodies, or industrial areas (i.e. the airport) in the northeast of Brisbane.

Data collection and processing
Data used in this study include: (1) the HILDA survey, and (2) built environment data obtained from multiple resources.

HILDA survey
The HILDA survey is an ongoing longitudinal survey that has been running since 2001 (Summerfield et al. 2018).The survey records a wide range of detailed individual and household characteristics such as household composition, income, dwelling structure, and residential mobility, with the objective of representing as wide a range of the Australian population as possible.Brisbane HILDA data from 2006 to 2016 have been selected for this study to ensure the consistency of administrative boundaries 3 and an adequate number of observations.Referring to existing dwelling type choice studies (Liao, Farber, and Ewing 2015;Yeoman and Akehurst 2015), we extracted three household variables (household size, household type, and household income) and five dwelling variables (the dwelling structure, the number of bedrooms, tenure, rent, and mortgage) from the HILDA data.
We categorised dwelling structures into three types as per the classification by the Queensland Government (2017).As shown in Figure 2, the dwelling types in this study are (1) DH: detached houses, single-family homes, and single-detached units; (2) MH: middle housing types, including diverse low-to mid-rise housing types such as duplexes, triplexes, quadplexes, townhouses, and small apartment buildings; and (3) MHR: medium-to high-rise residential (four stories or above).
We reclassified the 26 categories of household type data into six types (one-person household under 40, couple under 40 without children, one-parent household, couple family with children under 15, couple family with children aged 15 years or over, and households over 40 without children), according to the lifecycle theory (Mulder 1993).We classified household income into three categories-low-, medium-, and high-income-according to Australian Bureau of Statistics ( 2017).Finally, we aggregated the monthly rent and mortgage data to create a new variable-monthly housing cost, by referencing a similar work by Yates and Mackay (2006).

Built environment data
Built environment data from multiple sources are used to quantify neighbourhood characteristics.We aggregated built environment data to Statistical Area Level 2 (SA2), a medium-sized statistical unit with a population size ranging from 3000 to 25,000 persons (Australian Bureau of Statistics 2016b).SA2s are often used to represent single suburbs or neighbourhoods, and they are suitable to serve as spatial units for analysing housing choices.
We estimated population and employment from 2007 to 2010, and from 2012 to 2015 using the population and employment data from the 2006, 2011, and 2016 censuses, using an annual growth rate (l and h) calculated as: where Pop i and Pop j are the number of populations at the initial year i and the end year j.We calculated the number of populations from 2007 to 2010 by assigning i = 2006 and j = 2011.Similarly, population and employment numbers from 2012 to 2015 were similarly estimated.Then we calculated the population density and employment density by calculating the number of residents and employment per square kilometre.We quantified the other built environment features using multiple variables as documented in Table 1.

Analytical methods
Our analytical process consists of two components (Figure 3).The first component uses a multinomial logistic regression model (MNL) to identify factors driving dwelling type choices.The dependent variable is the three dwelling type choices, and the reference is the detached house.The independent variables are the three housing variables and nine built environment variables in the Component 1 box.Based on the outputs of Component 1, Component 2 identifies (1) latent household classes, both the number and naming of the class, and (2) the probability of each household class choosing each dwelling type.The dependent variable is the same as that in the MNL.The independent variables are the combination of all the observable variables in Figure 3.This stage uses the latent class choice model (LCM).
The LCM model consists of two components: (1) the class membership module; and (2) the class specific module (Figure 3).
The class membership module is a multinomial logistic regression model, and it estimates the probability that household h belongs to class s, and the utility function for the estimation is defined as follows: where X h is a vector of the socio-demographic characteristics of the household h, d s is the class specific constant, g s is a vector of parameters that need to be estimated, and 1 h|s is the random error.
The class specific module is also a multinomial logistic regression model, and the utility function is defined as follows: The percentage of green space over the total area in one SA2 Land use mix b  An index varies from 0 to 1 to represent the mixed level of land use type, calculated as Land use mix = − k j=1 P j ln(P j ) ln(k) , where P j refers to the percentage of each land use type j (e.g.residential, commercial, etc. j= 1,2 … 8) in each SA2 area, and k is the number of land use types j Population density b The number of residents per square kilometre Employment density b The number of employees per square kilometre IRSD b Index of Relative Socioeconomic Disadvantage (IRSD) in each SA2.IRSD is a socioeconomic index that measures the socioeconomic status of areas.The lower the index, the greater the disadvantage, and the higher the index, the less the disadvantage.

Crime rate c
The average offence rates of each SA2.Offence rate is the number of reported offences per 100,000 persons by police divisions.

Access to public transportation d
The scale representing the accessibility to public transit stops ranges from 1 (low accessibility) to 5 (very high accessibility) Access to educational resources d The scale representing the accessibility to schools ranges from 1 (low accessibility) to 5 (very high accessibility) Road density e The density of road network (km) per SA2 Note: a HILDA survey (Summerfield et  where U hp|s denotes the utility of housing choice p for the household h belonging to Class s; X hp is a vector of observable attributes of housing choice p for household h; 1 hp|s is the random error of the utility specification; and b ps is a vector of taste parameters for housing choice p with decisions made by Class s, and this parameter will capture the housing choice heterogeneity; for example, some classes might be more sensitive to housing variables, such as monthly cost and the number of bedrooms, while others might make a decision based on their preference for other built environment variables, such as crime rate or access to educational facilities.The advantage of using LCM is, this model can simultaneously estimate (1) the probability of households belonging to latent classes and (2) the probability of each latent household class choosing each alternative.Therefore, we choose LCM as the analytical method to analyse who and why choose certain dwelling types.
We run this two-component analytical method using Apollo, an open-source R package (Hess and Palma 2019).We used three sets of metrics to measure the model's goodness-of-fit, including Bayesian Information Criteria (BIC), Akaike Information Criteria (AIC), and rho-bar squared.Higher rho-bar squared, lower BIC, and lower AIC indicate better model fit.In addition to these three metrics, we also measure the model's goodness-of-fit based on interpretability (Rid and Profeta 2011;Walker and Li 2007;Liao, Farber, and Ewing 2015).
All the dependent and independent variables were based on HILDA survey and built environment data (Table 1).The number of latent classes (household classes in this paper) is unobservable, so we experimented with three possible numbers of classes in each urban area to identify the best latent number of household classes.After identifying the number of household classes, we produced a map to illustrate the location probability of each class.The map used an equal interval classification method to maximise the visual difference between household classes.
Before conducting the regression, we examined the potential collinearity amongst different variables using variance inflation factor (VIF) (Table S1).All the VIFs were less than 10, indicating that there was no multicollinearity among the independent variables (Kennedy 2008).

Demographic, housing, and built environment profile
Table S2 presents the descriptive statistics for each of the variables used in this study.People tend to choose detached houses in each urban ring.Of all the dwelling choices in the study, only 26.61% of the housing choices are middle housing and medium-to high-rise residential, generally representing the low occupancy rate of residential choice by high-density dwellings in Brisbane.In terms of the three dwelling types, middle housing has the lowest choice proportion across the three urban rings.This dwelling choice pattern could be attributed to the availability of each dwelling type across different urban areas, as suggested by the Queensland Government (2017).

Identification of latent household classes
In determining the best specification, both the number and naming, for each latent household class in each of the three urban areas, various latent classes and model specifications have been tested.We ran nine models with different household class numbers (Table 2).For each urban area, the twoclass model was chosen based on its fit statistics and degree of interpretability.
Based on the selected two-class models in each urban area, we named each household class according to the coefficients of household demographic characteristics in the class membership module (Table 3).Overall, we have six household classes: Class 1 (senior households without children with other family members) constitutes 34.02% of the sample population in inner-city suburbs and mainly consists of elder households without children but with other related or unrelated people living in the same dwelling; Class 2 (couple families with children) constitutes 65.98% of the sample population in the inner-city suburbs; Class 3 (high-income young households) constitutes 54.82% of the sample population in middle suburbs and it consists largely of the young high-income couples without kids, and couple families with children under 15; Class 4 (low-income households without children) constitutes 45.18% of the sample population in middle suburbs, and it is likely to consists of lower-income young singles or older households without children; Class 5 (low-income families with children) constitutes 79.30% of the sample population in outer-city suburbs; and Class 6 (middle-income young families without children) constitutes 20.70% of the sample population in outer-city suburbs.The following analysis is based on the clarification of these six classes.

Determinants of dwelling type choices for each household class
Table 4 presents the extent to which each housing and built environment feature is associated with the dwelling type choices of each household class.The probability of households belonging to a certain household class is averaged over SA2s for identifying the spatial distribution of different household classes (Figure 4).
Model 1 (for inner-city areas) consists of two household-level dwelling preference classes.Class 1 (senior households without children with other family members) is likely to choose smaller-sized high-density dwellings with neighbourhoods that feature high green coverage, high crime rates, and less access to public transportation.They are likely to be concentrated in Brisbane CBD and the surrounding suburbs.Class 2 (couple families with children) is likely to choose smaller sized high-density dwellings with the neighbourhood featured by high green coverage, high land use mix, and high crime rates.These households tend to be concentrated in the suburbs such as East Brisbane and other suburbs along the Brisbane River (Figure 4).Model 2 (for middle-city areas) consists of two household-level dwelling preference classes.Class 3 (high-income young households) is likely to choose smaller-sized high-density dwellings in neighbourhoods featuring high population density, high green coverage, good access to educational facilities, lower road density, high mixed land use, and high crime rates.Class 4 (low-income households without children) tends to be unaffected by most built environment variables except for population density and Access to public transportation.These low-income young singles are largely young graduates or just entering employment.They tend to be concentrated in or around suburbs near universities, namely, Kelvin Grove (the Queensland University of Technology) and St Lucia (the University of Queensland).
Model 3 (for outer-city areas) consists of two household-level dwelling preference classes.Class 5 (low-income families with children) is likely to rent smaller-sized high-density dwellings in neighbourhoods with high population density, low road density, high mixed land use, low access to educational facilities, and low IRSD.Class 6 (middle-income young couple families without children) is likely to choose smaller-sized high-density dwellings in neighbourhoods featuring a high population density, high green coverage, high mixed land use, higher access to educational facilities, and lower IRSD.They tend to be concentrated in outer-south suburbs like Inala-Richlands and Rocklea-Acacia Ridge or outer-northern suburbs such as Bracken Ridge and Northgate-Virginia, with good accessibility to education and other amenities.
We further examined the dwelling type choice changes under hypothetical changes in housing and built environment characteristics.The results are presented in Table 5, where the percentage of dwelling type choice changes of each household class is listed in response to a 1% increase in each built environment characteristic and a 100% increase in bedroom numbers.Doubling the number of bedrooms in a dwelling will decrease the probability of residents choosing high-density dwellings, especially for Class 2 in the inner-city area (−136.66% in choosing MH and −118.59% in    ).This is reasonable as these three households are either small-sized families or low-income households, both of whom are unlikely to need additional bedrooms and may not be able to afford the housing costs associated with these increased dwelling sizes (Clinton 2018).The 1% increase in transport accessibility (e.g. higher road density, more bus stations) is unlikely to increase the probability of residents choosing high-density dwellings, except for those in Class 2 in the inner-city area, who may choose MHR due to increased road density.A plausible explanation is that most residents in high-density dwellings may be concerned with the negative impacts of increased transport accessibility (e.g.traffic congestion), despite Class 2 in the inner-city area may pay more attention to the positive impacts of high road density (e.g.slower traffic and more pedestrian crossing opportunities) (Mortezaei 2012).Access to educational facilities plays an active role in increasing the likelihood of choosing highdensity housing, arriving at growths of +90.95% for Class 3 in the middle-city area choosing MH and +98.99% for Class 6 households in the outer-city area choosing MHR.The only exception to this trend can be found in Class 5 in the outer-city area.Class 5 consists primarily of larger-size lowincome households that may not be able to afford the increase in housing prices that would result from increased educational accessibility (Guo et al. 2016).Similarly, an increase in land-use mix leads to a significant increase in the probability of residents choosing high-density dwelling types, from +2.74% to +254.92%.This is reasonable as more diverse urban land use usually indicates more convenient access to different types of activities in the neighbourhood, and apartment dwellers have been identified as placing a higher value on land-use mix than detached house dwellers (Koster and Rouwendal 2012).However, in the inner-city area, the increase in green coverage would increase the probability of choosing MH (+1777.87%for Class 1 households and +6.45% for Class 2 households) but decrease the likelihood of choosing MHR (−65.79% for Class 1 households and −52.47% for Class 2 households).One plausible explanation explanation is that the MH may have more direct access to green space than MHR, and as such, MH dwellers value green coverage more than MHR dwellers.In addition, the increase in crime will increase the probability of people choosing MHR dwellings which usually have better security characteristics, such as security cameras and key code entry systems (Australian Bureau of Statistics 2021).

Discussion
This study extends the existing literature (Kelly, Weidmann, and Walsh 2011;Yeoman and Akehurst 2015) by examining the role of preference heterogeneity in dwelling type choice across the inner-, middle-and outer-city areas of Brisbane.Our results show that in each of the three urban areas, two household classes are distinguished by their housing preferences: Class 1 (senior households without children with other family members) and Class 2 (couple families with children) in the inner-city area; Class 3 (high-income young households) and Class 4 (low-income households without children) in the middle-city area; Class 5 (low-income families with children) and Class 6 (middle-income young couple families without children) in the outer-city area.The dwelling choice change probability of each class to housing and built environment characteristics is analysed to discover how the changes in housing and the built environment could increase the probability of residents choosing high-density housing.
Our findings contribute to a more comprehensive understanding of households' dwelling type choices.Given that current research and housing provision policies for high-density housing have focussed on apartments in inner-city areas, our study analyses high-density dwelling choices across a broader range of dwelling types and urban spaces.The main similarity across the three urban areas is the negative impact of the number of bedrooms and the positive impact of the land-use mix.There are more differences than similarities across the three areas.First, tenure is only found to be associated with the high-density dwelling choices in outer-city suburbs, where most of the residents are low-income apartment renters.Second, Access to public transportation and green coverage is not related to high-density dwelling choices in outer-city suburbs, but it is relevant to high-density dwelling residents in the inner-and middle-urban areas.Specifically, a 1% increase in Access to public transportation will decrease high-density dwelling choice probability, ranging from −26.75% for Class 1 in the inner-city suburbs choosing middle housing to −570.41% for Class 4 in the middle-city suburbs choosing middle housing.This is reasonable as the increase in Access to public transportation will inevitably bring more commuters and, therefore, noise pollution (for example, see Fan, Teo, and Wan 2021).The noise pollution is undesirable for residents, especially Class 4 in the middle-city suburbs with older households who are more sensitive to noise than other household groups (Liu et al. 2002).An increase in green coverage is likely to increase the probability of high-density dwelling choices for Class 1 and Class 3. Similar results have also been found in previous studies where older adults and couple families with children attach a high level of importance to having access to green spaces (for example, see Aspinall et al. 2010;Mulliner, Riley, and Maliene 2020;Raynor 2018).However, this may not be the case for people living in outer-city areas where an increase in already-abundant green coverage may not sufficiently affect people's choices of dwelling types.Similarly, access to educational facilities is not related to dwelling type choices for residents in inner-city suburbs where a range of quality education facilities with easy access already exists.
In addition to the above factors, population density is a positive determinant for households in the middle-and outer-city areas choosing high-density dwellings (although this has not been observed to be associated with that of the inner-city area).This is due to the fact that higher residential density usually indicates better urban amenities and the presence of public services (Appold and Yuen 2007;Guo et al. 2016).This benefit may not sufficiently change people's housing choices in the inner-city area where sufficient urban amenities and public services already exist.Socioeconomic disadvantage measured as IRSD is likely to be negatively associated with high-density dwelling choices in the outer-city areas.
Our findings provide policy implications for urban planning, housing policy, and real estate development.First, we recommend the design of high-density dwellings be targeted at different household classes with distinguished preferences across all urban areas.For example, in the middle-city area, Class 3 is more likely to be responsive to the variations in education accessibility and mixed land use.Increasing education accessibility, land-use mix, and green coverage in the middle-city area will likely encourage those in Class 3 to switch their preferences to highdensity dwellings.Residential zoning policies can take advantage of the characteristics of Class 3 by providing more high-density dwelling types and improving education resource accessibility, mixed land use, and green coverage in the middle-city areas.Second, as there is a substantial share of low-income households (Class 4 and Class 5) that prefer high-density dwelling types, it is suggested that high-density housing developments should be designed to accommodate lower-income residents through reduced prices or mixing rentals with units that are purchasable outright, given that current policy interventions that specifically target low-income residents are limited (Easthope et al. 2020).Furthermore, due to the difference in the demographic feature of Class 4 (low-income households without children) and Class 5 (low-income families with children), population-targeted high-density housing construction strategies are recommended.For example, small units for Class 4 in the middle-city area and larger-sized housing for Class 5 in the outer-city area.
There are a number of limitations associated with the current study that can pave the avenue for future research.First, there are two limitations related to the HILDA survey data.One issue is the limited incorporation of dwelling characteristics (three variables, including monthly cost of dwelling, number of bedrooms, and tenure).As such, future analyses could be enriched by the involvement of lot and building architectural details, such as lot size and if the dwelling has a balcony, both of which have been observed to influence people's dwelling choices (Kelly, Weidmann, and Walsh 2011;Yeoman and Akehurst 2015).Another issue is that the HILDA survey data tell us less about the subjective attitudes, perceptions, and lifestyles on individual's self-selection that will influence people's housing decisions (Olaru, Smith, and Taplin 2011;Yang and O'Neill 2014).The class membership module presented in this study could be strengthened by incorporating psychometric indicators.An extension could involve a survey of such psychometric indicators such as lifestyle preferences (e.g. using a gym or not), feeling of place belonging, security concerns, etc.Second, the study is limited by the measure of some built environment indicators.We quantified the private transport accessibility using road network data at a one-time point-2013-without considering the dynamic nature of change of this factor over time.Given that this variable is not readily available, it presents opportunities for future research.

Conclusion
This study enriches the growing body of knowledge in housing choice studies by modelling residents' dwelling type choices that consider residents' preference heterogeneity, which is rarely considered in the current literature.The proposed analytical framework in this study can be readily applied to different geographic contexts, and a variety of urban areas with different urban morphologies (e.g.monocentric and polycentric urban structures).Our findings provide new insights for governments, planning authorities, and housing industries to design and improve high-density properties by enhancing the housing design and neighbourhood-built environment for different households.Catering to the demands of rapidly increasing populations, more efforts are needed to delineate areas for real estate development and/or urban densification and to provide affordable housing to households with different socioeconomic backgrounds.Due to the importance of highdensity and mixed housing in accommodating ethnocultural diverse urban populations (Fincher and Costello 2005;Liu et al. 2018), our analysis of high-density housing is beneficial to help Australia head toward a multicultural and liveable country.

Notes
1.This paper uses the notion of 'three urban areas' to explore the heterogeneity in dwelling type preferences across different urban areas.The term is adapted from (Latham 2003), who classified Sydney into three distinctive 'arcs': the 'global' arc, the 'middle' arc, and the 'outer' arc.Similarly, we classify Brisbane into three urban areas: inner-city areas, middle-city areas, and outer-city areas.Inner-city areas refer to the central areas near Central Business Districts (CBDs).These areas are featured by the high-density population and employment.Outer-city areas refer to suburbs located at the periphery of cities.These suburbs are usually featured by high rates of home purchase, car dependence, and single-family dwellings.Middle-city areas are the intermediate zone between the inner-city areas and outer-city areas.This paper uses the notion of 'three urban areas' in Brisbane, a monocentric city, as an example.This notion could also be applied in the polycentric city with multiple city centres.2. Missing middle housing is a high-density housing type, which usually consists of duplexes, triplexes, quadplexes, townhouses, and small apartment buildings.3.In December 2010, the Australian Statistical Geography Standard (ASGS) was released and replaced the previous Australian Standard Geographical Classification (ASGC) that has been used for the collection and dissemination of geographically classified statistics.Statistics have been based on the ASGS since August 2011.
01; MH = middle housing types, MHR = medium-to high-rise residential, G = Generic parameter of MH and MHR, IRSD = Index of Relative Socioeconomic Disadvantage; Class 1 = senior households without children with other family members, Class 2 = couple families with children, Class 3 = high-income young households, Class 4 = low-income households without children, Class 5 = low-income families with children, Class 6 = middle-income young couple families without children.choosing MHR), Class 4 in the middle-city area (−217.59% in choosing MH and −226.39% in choosing MHR), and Class 5 in the outer-city area (−232.43% in choosing MH and −235.28% in choosing MHR

Figure 4 .
Figure 4. Probability of belonging to household classes.

Table 1 .
Variables used in the latent class model.
al. 2018) b Australian Bureau of Statistics Censuses of Population and Housing in 2006, 2011, and 2016 (Australian Bureau of Statistics 2006, 2011, 2016a) c Monthly updated offence rates at police divisions (Queensland Government 2021) d The Metropolitan Accessibility/Remoteness Index of Australia in 2015 (Australian Government 2017) e Australia Statewide Road Network data in 2013 (Australian Government 2013)

Table 2 .
Estimated choice model performance.

Table 5 .
Dwelling type choice changes under hypothetical changes.MH = middle housing, MHR = medium-to high-rise residential, IRSD = Index of Relative Socioeconomic Disadvantage; Class 1 = senior households without children with other family members, Class 2 = couple families with children, Class 3 = highincome young households, Class 4 = low-income households without children, Class 5 = low-income families with children, Class 6 = middle-income young couple families without children.