Trajectories of Latent Vulnerability and Distress: Identifying Social and Spatial Fringes of the Swedish Population

It can be argued that a society is never better than how Individuals on its social and spatial fringes are faring. This motivates the purpose of this paper, which is to study how vulnerable groups can be identified, defined and explored in a spatial perspective using latent class analysis (LCA) on the whole Swedish population. We use space to refine meanings of vulnerability in individuals and groups, by contextualizing their vulnerability. This knowledge is fundamental for creating equal living conditions and for promoting the social cohesion needed for socially sustainable societies. Thus, equality and spatial integration are basic ideas in welfare policy but in recent years, the idea of integration has met various challenges with new population groups, rural–urban polarization, and disadvantaged housing areas. Using register data, we here identified life course trajectories associated with vulnerability, applying LCA to the total Swedish population aged 25 to 59 years. We identified latent classes of life courses, and detected and explored some classes with more vulnerability than others. The spatial patterns of vulnerable individuals were analysed using individualized neighbourhoods including the proportion of closest neighbours belonging to a latent class. A second LCA of vulnerable individuals refined the findings into different types of distress; extra distressed life courses were found in the metropolitan areas in Million program areas in urban outskirts, and other distressed life courses were more often found in unattractive (low housing price) rural areas, rural fringes.


Introduction
The purpose of this paper is to study how vulnerable groups can be identified, defined and explored in a spatial perspective, using latent class analysis (LCA) on the whole Swedish population.We will use the spatial perspective to contextualize and understand the circumstances of vulnerable individuals within life course trajectories.The approach is empirical and the analysis uses LCA on longitudinal, individual level, register data that includes geo-coordinates for every individual.In this study we will use the Swedish population cohorts born in the period 1945 to 1980 and follow them over the age range of 25 to 59 years divided into three life phases, whereof the oldest cohort, 45 to 59 will be further distillated into distressed latent classes.The three life phases we analyse are: Young adulthood, Early middle age and Late middle age, using labels of ageing similar to those by Slotkin (1954).To fulfil the aim, we have formulated the following research questions.
-What types of vulnerable life course trajectories can be identified in the Swedish working age population 1990 to 2019? -What spatial patterns are identified for the vulnerable life course trajectories across all working-age cohorts?-Which spatial patterns are found for the distilled distressed life course trajectories among the oldest ages 45 to 59?
Implicitly, many concepts related to vulnerability bear a meaning of spatiality, such as social polarization, exclusion and marginalization, but these concepts are seldom developed in recognition of their spatiality.Therefore, in this study, we will make use of thoughts developed by Wacquant to understand the spatial distribution of vulnerable and distressed life-courses.For example, Wacquant stresses that it is not the place and/or the individuals in a certain place that should be the focus of inquiry but rather the multiscalar processes leading to the what Wacquant calls "territories of relegation", which is the process of assigning an individual or population "to an obscure or inferior position, condition or location" (Wacquant, 2016(Wacquant, , 1077)).
Adding to the spatial approach, this study uses a life course framework.There have been important breakthroughs in using register data for the analysis of vulnerability of individuals over time, using a life-course framework (Almquist & Brännström, 2018;Bäckman & Nilsson, 2010;Ham et al., 2014;Ilmakunnas & Moisio, 2019;Virtanen et al., 2011).In sociology, economics and human geography the study of life courses (Browning et al., 2016;Elder Jr et al., 2003) has been central for a long time but we hope to develop the field further using latent class analysis (LCA), register based individual data and the spatial dimension to capture individual life course trajectories.By using longitudinal data in combination with LCA, we will explore whether vulnerability can be identified as an underlying condition, so called latent vulnerability, that manifests in life course outcomes, without relying on an explicit definition of vulnerability (Gruebner et al., 2016).In this way we also give room for different compositions of indicators that show vulnerability; indicator compositions that also may vary spatially.
A background to this study, is the still ongoing Swedish debates that started leading up to the most recent Swedish elections 1 in 2022.The debate concentrated on residential segregation and in particular vulnerable areas were discussed.The debates related all sorts of societal challenges to these vulnerable areas such as unemployment, challenges of integrating immigrants and children of immigrants, criminality and gang related criminality, dependence on social allowances and deteriorating living conditions for populations in vulnerable areas overall.In the general debate, the denoted vulnerable areas are suburban large housing estates built during the Swedish Million program 1965-74.In this paper we investigate empirical grounds for such debates by firstly, identifying parts of the working life population being vulnerable, and in a second step distilling distressed latent classes of life course trajectories.For both steps of analysis, we explore spatial distributions across all of Sweden based on municipality types and income contexts.We also create maps to represent the distribution of latent classes among the 200 nearest neighbours.

Vulnerability and Spatial Segregation
Earlier research on vulnerability suggests that vulnerability needs to be understood from a multidisciplinary life course framework.Such a framework calls for three important perspectives: 1) the life course perspective (multidirectional), 2) several domains in life (multidimensional) and 3) several levels of analysis, the individual, group and (in our case) neighbourhood/geography (Spini et al., 2017).They define vulnerability as "vulnerability in terms of the dynamics of stress and resources across the life course" (2017,5).In this paper we agree that vulnerability can be considered as a stage not already showing exclusion or despair but being vulnerable to entering/being in such a state; Spini et al. call it latent vulnerability or a period of fragilization (2017, 8) (Acconcia et al., 2020).Halleröd and Larsson (2008) investigate the relationship between poverty, and social exclusion with a large set of welfare problem indicators.They find that income poverty is not always related to social exclusion, but deprivation poverty is (poverty due to which a person must forgo consumption of goods and services).The results point to the importance of including welfare problems in the analysis of people living under poor conditions.Halleröd and Larsson interestingly use LCA for their large number of indicators on welfare problems.With the three latent classes (LCs) they obtained, they state that 71 percent of the population ended up in what they call a non-problematic group, and the rest, about 30 percent in two LCs with health problems and one with health, income, and economic problems and unemployment.
Furthermore, there is a body of literature combining life courses of vulnerability and spatial segregation, or rather concentration.This literature focuses on concentrations of poverty in certain residential areas (Andersson et al., 2021(Andersson et al., , 2023;;Lee et al., 2017).Note that this is not life course and neighbourhood effects research (e.g.Browning et al., 2016) but rather concerns geographical patterns of life course and vulnerability.
In Sweden, areas with high concentrations of poverty and social problems as well as criminality are called vulnerable areas in assessments regularly conducted by the Swedish police, NOA (national operational section).In their report from 2021, they stated that there are 61 so-called 'utsatta områden', vulnerable areas whereof some are labelled particularly vulnerable (19 areas).The number of areas varies but they are exclusively areas of multifamily rental dwellings built during the Million program era, 1965to 1975(Vogel, 1992).The residential areas often include larger proportions of poverty and vulnerability, which is why they are of interest to this study (NOA, 2021).NOA's definition of vulnerability for these areas is mainly based on crime, drug trafficking and violence, which is somewhat different compared to our aims where 'vulnerability' instead means economic and social vulnerability of individuals.However, their definition of particularly vulnerable residential areas in Sweden uses several factors that together give a picture of a population of low socio-economic status (cf.with low collective efficacy, Sampson (2012)) where criminals have an impact on the local community.Thus, for a vulnerable person to live in an area designated as vulnerable according to the Swedish police is an important contextualization of a person's life course.
Conceptually we build on Wacquant's 'relegation' when it comes to urban segregation.Relegation means to assign an individual or population "to an obscure or inferior position, condition or location" (Wacquant, 2016(Wacquant, , 1077))."Relegation is a collective activity, not an individual state; a relation (of economic, social and symbolic power) between collectives, not a gradational attribute of persons."(1078).Wacquant stresses (like many scholars) that it is not the place and/or the individuals in a certain place that should be the focus of inquiry but rather the multiscalar processes leading to the what Wacquant calls "territories of relegation".In this study we explore possible territories of relegation by identifying locations of distressed and vulnerable populations, and we also apply the concept of 'fringes' to identify inferior positions or locations.These 'fringes', can in our case be peripheral, rural areas and not only in connection to cities and or metropolitan areas (Vallström & Svensson, 2021).Thus, fringes do not only refer to urban stigmatized or relegated territories.Wacquant discusses class, ethnicity and state as important factors, 'a constellation', contributing to the spaces or territories of relegation (Wacquant, 2016).We will expand on each of these factors below.Compared with US research, class is more important in European cities according to Wacquant; therefore, he uses the term 'ethno-class concentrations' (describing migrants who have moved into former working class areas) for European cities.
Thus, the state part of the 'constellation' according to Wacquant concerns the unequal distribution of resources and opportunities through the political process and the state.Thus, vulnerable individuals and places with fewer resources will have less influence on the political process, and importantly; area-based policies are often, and in the Swedish case, criticized for not working well enough (Holmqvist & Bergsten, 2009).Political domains concerned with housing, education, health, social security, planning and so on, are surprisingly ineffective in dealing with the problems of spatial inequality of vulnerability.Wacquant describes in his scholarly work the very retrenchment of the social state (2008).Now considering class as a part of the constellation contributing to territories of relegation, Wacquant writes about riots in his book on urban outcasts (2008).The relationship between the working class and the state, political and economic structure, builds on a division which is needed to maintain an economic system based on capitalism.However, this division creates tensions that sometimes give rise to unrest (compare outbreaks of riots, Kawalerowicz and Biggs 2015;Malmberg et al. 2013).That is, there is an underlying economic order that maintains the divisions in society, including vulnerable groups being pushed toward relegated areas.These ideas are prevalent in the works by Wacquant (2008Wacquant ( , 2016) ) where he explains the development further; starting from the 1980s is a period of transitioning of the European society into a post-industrial one, a society in which Wacquant claims there is "advanced marginality" (2016,1081).An important ingredient of the post-industrial society is the so-called fragmentation of the working class as regards the introduction of the gig-economy and insecure precarious work, unlike earlier times when more permanent industrial employment was the norm (Myhill et al., 2021).
Lastly, ethnicity as an important factor, of Wacquant's 'constellation', contributing to the spaces or territories of relegation.From US scholars a spatial mismatch of jobs and labour, feminization of poverty, and ethnic minorities in more or less geographically isolated areas are seen as the main problems.These explanations were clearly shown in the scholarly work in the 1980s by Wilson (1987) in his book The Truly Disadvantaged: The Inner City, the Underclass, and Public Policy.In the Swedish case, the neighbourhoods in question are not the inner city ones, rather the Million program areas built in suburbs in the period 1965-1974.An explanation of the problem is that minority groups are isolated from the formal labour market and from mainstream society (Vogiazides & Mondani, 2020).Also, smaller cities and towns with public rental residential areas from the Million program era are subjects for this spatial sorting process, resulting in segregation, preluding the spatial mismatch.Actually, and according to Borg (2019), the spatial segregation is extra powerful here because of the public housing sector being relatively small in small sized cities and towns.The process of poorer residents and immigrants dominating the public housing areas is in housing research terms called residualisation (Borg, 2019).In this study, we map the life courses of vulnerability to find out whether they overlap with Swedish Million program areas, and we also indicate the proportions of population foreign born in the vulnerable and distressed life-course trajectories.From the above we state that place and space are inherently part of our definition of vulnerability, supported by the theoretical foundations in urban social geography.

Study Design, Data, Methods and Analysis
This analysis assumed that latent vulnerability in register data is present in unobserved subgroups of individuals who experience short or long periods of unemployment, illness, low income, poverty, or have a need for social allowance or other welfare support, or live with a partner who requires such support (Bask, 2010).In addition to the above indicators, we included type of housing, whether equalized disposable income was larger than median, whether the household has children and whether they were living in a couple, to fully describe trajectories and for latent classes to relate to one another, beyond just indicators of poverty and vulnerability.To extract such trajectories from the data, we used LCA, MLR in the software Mplus (Henry & Muthén, 2010) for cohorts born between 1945 to 1980 for the years 1990 to 2019.
We used longitudinal, individual, registry data accessed on-line in MONA (Microdata Online Access) at the Statistics Sweden, SCB.The specific collection of registers and variables used is part of a project called Geographical context, which covers data for all residents in Sweden, from 1990 to 2019 and has been approved by the Swedish authority for ethical vetting (approval no.2020-05521).Data is gathered by Swedish authorities and delivered to SCB, and SCB is keeping the longitudinal microdata available for researchers.All data is anonymized and has an individual reference number unique to the Geographical Context project.The attrition rate for each of the life phases was low, about 150 000 individuals per life phase was deleted due to not living in Sweden more than 9 years out of 15 years (1.8 million per life phase, Table 2).Furthermore, certain individuals were removed due to incomplete data concerning income, geo-coordinates, or other relevant indicators.Note that the attrition observed was not systematic.
LCA is a valuable method for reducing large numbers of trajectories to a smaller number that captures the variation in timing and sequence in life course transitions (Amato et al., 2008;Virtanen et al., 2011).Transitions during the life course occur in different order and at different ages, which can give rise to many different types of trajectories.With finite mixture modelling (Vermunt & Magdison, 2004), longitudinal data across different life domains can be used to identify typical, latent life course trajectories which individuals follow.
In a first step, the individual's life trajectory was represented by indicator variables that specified for each year whether the individual had received e.g., social allowance (Ilmakunnas & Moisio, 2019) and so on for all indicator variables.With data covering the period from 1990 to 2019, individuals were followed for 30 years, but the analysis focused on shorter periods of 15 year age-windows, with a 5 year overlap, in order to follow ages in three life phases.In Table 1 the ages of individuals born in specific years are shown (we thus protect our analysis from cohort specific patterns) for the period 1990 to 2019 for which we have the data.The three life phases are marked in Table 1.With indicator variables representing each individual year, the individual's life trajectory was captured by about 180 different variables (15 years × 12 indicators).(We do not assume independence over time, because the LCA allows for correlations between all observed variables (over time, as well as both within and between different indicators).Indeed, this is one of the strengths of our approach, namely that there are no assumptions about temporal relationships (e.g.Markov)).In order to arrive at a number of five latent classes, LCs, we analysed models with three to eight different LCs and analysed reductions in the Bayesian information criteria (BIC), which indicated that there is less to be gained from increasing the number of classes above eight2 concerning BIC, but also less to gain for reasons of presenting the analysis.Figure 1 shows the 3, 4, 5, 6, 7 and 8 classes solutions for the three life phases and the BIC value.The process of arriving at a number of classes balances between theoretical and statistical trade-offs (Nylund-Gibson et al., 2022, p. 8).Apart from collecting and tabulating fit for different models (BIC) and study patterns (compare different number of classes) we also took into account the possibility to interpret the results and also to make usable maps when deciding on the number of classes.The aim of this study was to identifie, define and further explore vulnerability in a spatial perspective, which is not always the case.For that reason we were interested to first, single out latent vulnerability (rather coarsely with the 5 LCs), and second, to analyse their geographical locations, and in a third step use the distilled two LCs to spatially explore distressed LCs.With register data follows a large population, here we have 1.8 million per life phase included in the LCA and presumably a large possible number of latent classes with the number of indicators we included.A large population, as available to us, and a large number of indicators (12) do seem to lead to good performance of LCA and stability in class solutions (Wurpts & Geiser, 2014).For our initial purpose of finding vulnerable life courses to further analyse, we believe we captured those life courses of interest with the number of latent classes we have chosen.
To further compare patterns and decide on how many classes best describes the data, we evaluated the 5 class model and the 7-class model exploratively for all ages and with more descriptive variables.For example, when we compared 5-classes and 7 classes model, we detected a divide in the latent classes that could be characterized by early, respective, late family formation if choosing 7 LCs instead of 5 LCs for the youngest life phase.Thus, for our purposes, we concluded that the content of the 7 class solution did not add any important or meaningful information (description of classes and class sizes in results).Furthermore, assignments of individuals to a class in the models for the life phases were done with a high probability, ranging from 0.975 to 0.991 (shown in Table 1 Supplementary information).
As the average latent class probability were high we interpreted the models to predict class membership well.Also, Entropy values greater than 0.80 indicate a good separation of the identified groups and our estimates were above 0.97 for the three models.In a second step, to identify vulnerable groups, we proceeded with using the vulnerable groups only in an LCA of distress applying the same indicators and the same procedure.Among indicators of vulnerability, one important variable was 'at risk of poverty' (AROP), based on equalized disposable household income, coded 1 if income was less than 60 percent of the national median disposable income of the total adult population.Moreover, we included an indicator that we called in stress, which combined receipt of sick leave compensation, unemployment benefit, or early retirement (long term sickness benefit for unemployed) benefit for an individual.Social allowance is sign of poverty, as it is an allowance that is means tested by the local social authority according to national regulations.The housing allowance indicator shows if costs for housing is supported, most often the support is received by households with children but also other types of households may be eligible.The housing allowance is directed to households irrespective of their housing tenure form.The indicator alive, only for individuals above the age of 54 that is, only for the oldest in the oldest life phase, is a clear indicator of vulnerability and of health, in the life phase under investigation.
We also included two variables of the economic situation of the partner.These were firstly; based on partner unemployment, partner sickness, partner early retirement and secondly; whether the partner had low earned income.The first translated into partner in stress.
The indicator of being in a couple or not (Perelli-Harris et al., 2016) was based on family status-while divorced and never married can be single.A second demographic variable indicated presence of children in the household.It was based on family type, Table 2. Being in a couple or living single and having a child in the household is not part of the vulnerability examination, it is rather a characteristic to differentiate between types of vulnerability.The first income variable was based on earned income and was coded 1 if earned income was above 50 percent of the median, that is, a fairly good income in relation to the group.We also used the indicators of low earned income as well as high earned income (earned income included primarily labour income, but also entrepreneurial income).Residing in a single family house as opposed to living in an apartment is an indicator of life course circumstances included to differentiate between latent classes.Single family housing is privately owned and specify financial resources and to some extent geographical location.
In order to distinguish between several latent classes of vulnerability some variables included are not necessarily indicators of vulnerability as; living in a couple, having children in the household, an equalized disposable income larger than median or living in a single-family house.We argue however that these indicators give a fuller picture of the latent classes.For example, these types of indicators might help us to distinguish between two types latent classes both showing high proportions of vulnerability, but that differ due to their household characteristics.We argue that individuals in these types of situation, where one is living with a partner and have children in their household and the other, living single and no children in the household, have taken different paths in their life course trajectories.This also implies that their experiences of vulnerability will be different and also solutions to overcome it.We argue these individuals have taken different life course trajectories.In this way, the non-vulnerability indicators are there to distinguish between multiple latent classes.
Although important for vulnerability, we were not able to capture whether unemployment or social allowance receipt were caused by substance abuse, mental illness, physical disabilities or intellectual disabilities since our data did not include these strands of indicators.We believe that these conditions are not excluded but rather hidden (to a certain degree) in sickness benefit, unemployment and early retirement (long term sickness among unemployed) indicators.Another limitation when it comes to measuring vulnerability with Swedish register data is that we could only capture individuals who were registered in Sweden; thus, unregistered individuals (expelled individuals staying in the country, undocumented refugees, victims of trafficking and more) who often experience vulnerability were not included in our study.
Further variables were used after the LC analyses to descriptively analyse the different trajectories found, in Supplementary information.Furthermore, we also used maps to analyse the geographical patterns across LCs.For the maps, proportions of the LCs across neighbourhoods of 200 individuals (total population) based on east and north coordinates were used (Hennerdal, 2019).

Results
The results section consists of three parts.The first part describes the vulnerable groups that have been identified across our three life phases (Fig. 2, Table 3), the second part analyses the geographical patterns of the vulnerable groups (Fig. 3, Table 4), and in the third and final step, we further explore sub-groups of the identified vulnerable individuals, i.e. distressed LCs, called DCs for the oldest life phase (Figs. 4 and 5 and Table 4).

Identifying Vulnerable Groups Across Three Life Phases
The In each life phase, we found two latent classes that could be identified as vulnerable by our own examination of proportions of the indicators; in stress, AROP, social allowance, low earned income and low income, compared to the other latent classes, see Fig. 2 and Table 3.In Fig. 2 proportions of each indicator for Young adulthood, Early Middle age and Late Middle age are shown for an age span of 15 years.The diagrams are read as e.g.LC4, Affluent norm (25-39 years), where the indicators Child in household and living In couple is rising to over 90% and income indicators are high and, vulnerability indicators are low. 3he size of the LCs is fairly even.For Young adulthood the proportions of individuals in LCs 1 to 5 are, 0.25, 0.19, 0.12, 0.20 and 0.23.For Early middle age the proportions in LCs from number 1 to 5 are, 0.27, 0.16, 0.18, 0.15 and 0.24 and lastly for the Late middle age cohort the proportion in LCs 1 to 5 are, 0.13, 0.25, 0.25, 0.19 and 0.18.
The two top rows of five diagrams are accounted for in Table 3, descriptions of vulnerable life courses.The other latent classes in diagrams, that do not show vulnerability are also shown in Fig. 2, but since they are out of the scope for this paper, they will not be addressed further.In the third and final step of the analysis, we will return to the vulnerable LCs for the Late middle age, which are used for another LCA to distillate different distressed life course trajectories only.
In sum, the vulnerable latent classes could be distinguished from a total of five latent classes per life phase, all of which show more favourable development.The fact that life courses are described as singles and families/couples, we do not argue being a finding, it is just a part of the description of different types of vulnerability and type of life course.Typically, the latent classes with favourable developments consist of households that have attained higher incomes and earnings, where a majority enter the home-owning sector and few experience stress or low earned income.
For all the life phases, the total proportion of the two vulnerable LCs is about 31 percent.That is, we find that 31 percent of the individuals across the three life phases we have studied, are living in a vulnerable position in society.This might seem a large proportion but it actually corresponds to the proportion that has been found in previous research on the Swedish population, namely the proportion of the population having welfare problems/living in deprivation as measured by (Halleröd & Larsson, 2008).

Geography of Vulnerability
In the second step, we investigated the geography of the vulnerable latent classes that we have described above.We did this by looking firstly at the distribution of vulnerable latent classes across municipality types (Gillingsjö & Ekholm, 2016) and secondly, across neighbourhoods classified on the basis of the distribution of the local population, nearest 1600 neighbours, income deciles contexts, Table 4, and thirdly, by analysing the maps in Fig. 3. Income decile context deserves some explanation.It is based on a variable of deciles of equalized disposable income for the population 15 years and older.It is measured among 1,600 nearest neighbours for the years 1990-2015, all years, pooled data for 26 years for 214,644 geo-coordinate pairs.A cluster analysis resulted in 12 clusters: Very high income 1, 2, High income 1, 2, Mixed 1, 2, 3, 4, Low income 1, 2, Very low income 1, 2, also used in Andersson et al., 2022.The Very high income 1 cluster has a high concentration of individuals in the highest income decile.
The Very low income 2 cluster, conversely, has a high concentration of individuals in the lowest decile.In between these extremes, the clusters have progressively fewer individuals in the highest income deciles and progressively more individuals in the lowest income deciles.The most even distribution is found in the Mixed 2 cluster, where each decile is represented by close to 10% of the population.

Examples of Vulnerable Latent Classes in Municipalities and Neighbourhoods Across Sweden
Regarding the LC, Early family formation, low income, they are mostly found in the fringes of the metropolitan areas of Sweden (first row map, Fig. 3).According to the map, they are living in Million program areas, which also house many foreign born (this LC has 44 percent born in another country).Early family formation, low income, is not found in any other part of Sweden to a high degree, that is, they have a residential pattern that is very concentrated to certain parts of the metropolitan areas with very low incomes (see Table 4).
In the observation period, 1990 to 2019, the cohorts (born 1965-1980) are among the most likely parents of today's young in the same vulnerable areas.That is, we will find children and young adults growing up in vulnerable families (this LC), to a density of about 30 to 80 percent among the 200 closest neighbours.This concentration forms particular social contexts for children and youth.
Regarding life phase Early middle age trajectories, LC2 Singles in distress (EM2), shows a spatial distribution with high representation in some parts of the metropolitan areas Fig. 3, but for the EM2 lower representation elsewhere in rural areas, Table 4, fourth top column.Instead, Families in distress (EM4) avoids the expensive areas in the metropolitan areas and live elsewhere in rural areas and outside of cities (rural and tourism municipalities, Table 4).This pattern differs from the LC Early family formation, low income in the youngest life phase since the individuals belonging to LC Early family formation lived in Million program areas in the metro areas as accounted for above.
Late middle age, Singles in distress (LM5), resides in the metropolitan areas, (Table 4) and in very low income decile contexts.Trajectory LC1, Couples in distress (LM1), have high proportions outside the metropolitan areas but also at the fringes of the metropolitan areas and in the metro areas of Göteborg and Malmö, Fig. 3. Summing up, families with children and couples often reside in single family housing which is explaining the higher concentrations (intense red dots) all over the country and not just in outskirts of metropolitan areas and cities.

Vulnerability distilled in a second LCA
The final step in analysing vulnerable latent classes was to perform a second LCA including only LC1 and 5 for the Late middle age life phase 45 to 59 years.This explorative part of the analysis thus included 567 437 vulnerable individuals divided into five new latent classes, only for Late middle age, Fig. 4, hereafter called DC, distressed classes.The life phase chosen is advantageous to study exploratively in that the ages 45-59 are expected to be stable and established concerning education, employment and children, and we were also able to include a proxy for health, which is if the individual is alive or not at the end of the trajectory.
The five distressed latent classes, DCs are presented in Fig. 4 below.As we can see in the top left frame in Fig. 4, a special characteristic of DC1, named Less distressed couples, multifamily houses, is that individuals are predominantly in a couple (green line) and that they are living in an apartment (low proportion of individuals in a single family house).About 50 percent of individuals in this trajectory type are in stress, that is, and to repeat; they receive sick leave compensation, unemployment benefit, or early retirement/sickness benefit.Also, they have low earned income including about 40 percent of individuals.The stress and low earned income are a concern for their partner as well.Very few have high earnings, but a good proportion, about 30-50 percent, have above median for disposable household income, hence the name 'less' distressed.
A first characteristic of DC2, in the top right frame in Fig. 4, Increasingly distressed singles is their low earned income; that they are singles without children, but 35 percent are living in a house.Averaging over the life phase, 70 percent are in stress and with low earned income, which seems comparably high.Also, at risk of poverty increases over the life phase to almost 40 percent.
Distinguishing DC3, distressed low survival, is that only 60 percent are still alive at 55 years.One out of five has a partner in the early phase but later live as singles.When the life phase starts at 45 years of age the trajectory shows about 35 percent being in stress.Also, at 45 years, about 25 percent live in single family housing with a housing allowance; however, both proportions decline with age, thus apartment-living dominates.Characterizing DC4 Extra distressed with social allowance, is again a large proportion of individuals with low earned income, but also at risk of poverty and receiving a social allowance.Half of the individuals following this life course are in a couple and starting the life phase with a child at home.The trajectory shows the largest proportion of at risk of poverty out of all distressed classes.The majority live in an apartment, but receive housing allowance.About half in this trajectory type are in stress.A proportion of 40 percent have a social allowance.
The DC5, Less distressed couples single family housing, are the ones with the largest majority in single family housing (> 90 percent) as well as living in a couple (comparable to DC1 except for housing).About half have low earned income and are experiencing stress, and some are at risk of poverty.Their partner is to a similar, but slightly lesser extent, with low earned income and experiencing stress as well.
The observations from the profiles in Fig. 4 are confirmed in that distressed classes 1 and 5 with 'less distress' include individuals that in this sample have a slightly higher education (19 and 18 percent respectively), higher mean disposable income and are to a lesser degree workers (81 and 82 percent respectively) (except DC3 at 75%).4However, Halleröd and Larsson state precisely that income poverty measures do not always capture individuals living under poor conditions and suffering from welfare problems (2008).In this respect we use the term latent vulnerability.
The vulnerable latent classes found in the first step of analysis, did show high proportions of individuals born outside of Sweden.However here it is important to note that with the refinement of distress in several LCs only two classes come out with high percentages of people born in another country.This is for the life course DC1 (43%) that is concentrated to the metropolitan areas and cities; they are not dispersed over Sweden at large, and for the DC4 Extra distressed with social allowance, that have a high proportion of both born outside of Sweden (61%) and visible minorities (36%).5

The Distressed Classes Across Municipality Type and Income Decile Contexts
The municipal spatial residential patterns of the distressed life course trajectories are shown in Table 4, rightmost columns.Individuals following a life course trajectory characterized by distress have an average dissimilarity index6 of 13, a higher dissimilarity than for the total sample (value 8-9).On the one hand they reside in rural municipalities or in sparsely populated areas, and on the other hand they reside in metropolitan areas, suburbs and large cities.That is, they reside in urban or rural extremes according to the classification of Swedish municipalities.
Regarding the income group context, it seems to work less well, or gives a more unexpected result for the distressed group than for the total sample.All the DCs except one also have overrepresentation in the very high income contexts.Considering how the income group contexts are constructed, the result is however not impossible.The income group context indicates a certain share of very high income individuals and not a homogenous context; in this case the context also gives room for vulnerable populations.However, the Extra distressed with social allowance DC4 is overrepresented only in the very low income clusters and has the highest DI, and from the above we know they live in metropolitan areas.

Results from Maps
From the map in Fig. 5, DC1, Less distressed couples, multifamily houses, can be seen living in cities in addition to the metropolitan areas.They are highly concentrated in city centres in the southern part of Sweden, shown by the dot-like pattern on the map, Fig. 5. Increasingly distressed singles (DC2) live in the metropolitan centres but also in rural locations outside attractive areas.Distressed low survival (DC3) have a town-clustered residential pattern due to not living in single family housing, but otherwise have high representation scattered, with no particular geographical pattern.Extra distressed with social allowance (DC4) are not found in rural areas; rather in vulnerable areas and Million program areas in the metropolitan areas.There are only a few locations in which this class has the highest proportions, i.e., the highest representation in an area.Less distressed couples single family housing (DC5), show a pattern in which the metropolitan areas and cities are noticeably avoided, probably because single family housing is expensive there.

Analysis of the Geographical Patterns of Distressed Trajectories
We find two DCs that can be found in rural areas in the single family housing type, with couples (DC5) and singles (DC2) (the latter DC2 is also to some extent present in the metropolitan areas), Fig. 5.One reason for their distressed situation in rural areas could be the maldistribution of resources and opportunities.This has to do with the fact that vulnerable individuals and groups are underprivileged and that this will be shown in the political process, resulting in an inequitable distribution of resources which can be aggravated in peripheral places.Rural areas are described as 'the rest of Sweden' (Vallström & Svensson,  ).These are areas that have lost population and workplaces and that formerly were connected to the industrialization of Sweden.Moreover, tertiary education is not as common as in the metropolitan regions and larger cities (Nielsen & Hennerdal, 2019).Also, while metropolitan areas and larger cities provide choice in health, education and care public services, people in the rural areas must be content if the services are available at all.
Apart from an 'unwilling' political process towards fringe rural areas, there are signs of a structural class conflict giving rise to the vulnerability in the rural parts of Sweden that we observe.Upper middle classes and middle classes are, in the sense of the same classes in e.g.Stockholm metropolitan area, seldom living in these rural fringe areas.This polarization plays out spatially and shows a relationship between the working class and the political and economic structure.The once prosperous cities, and rural areas in the phase of industrialization are on the fringes of today's post-modern neoliberalized economy.
There are in particular two DCs that are dispersed in almost all cities; couples in multifamily housing (DC1) and distressed with low survival (DC3), Fig. 5.Those in stress with low survival lose their partner and exit their single family housing (if they have it) during the life phase.A high proportion of such life course trajectories in a neighbourhood might have an impact on the area's social resilience; such a neighbourhood might not be able to resist criminality and/or inherited deprivation in the coming generations.In housing research terminology this is similar to residualisation in which only vulnerable population still resides in public rental housing in cities and towns (Borg, 2019).We can only propose that the life course also includes ill-health in the longer term, but we do not have better health data available.
DC4 has a clear pattern of living in urban or metropolitan vulnerable areas; the Extra distressed with social allowance.They are found predominantly in Million program areas.Despite analysing the life phase of late middle age individuals, areas where the proportion of DC4 is high have not reached stability regarding employment or other stress factors.Also, we know the very same areas are considered poor even for younger generations (Younger life courses indicating vulnerability; YA3, YA2 and EM2 and EM4 had high proportions in the very same areas).The population is sometimes described as having a lack of opportunity and motivation and as urban outcasts (Wacquant, 2016).
Connecting to a related strand of literature on suburban areas' main problems, these problems are described as a spatial mismatch of jobs and labour, a feminization of poverty, and ethnic minorities (foreign-born) in areas that are more or less geographically isolated (Wacquant, 2008(Wacquant, , 2016)).The descriptive analysis shows a majority (61 percent) in this DC4 to be foreign-born, which is partly explained by the housing market.At the completion of the Million program (public rental), the housing projects were dismissed by those who could move away to an owned home.Thus the multifamily dwellings were easier to access for those needing a home when migrating to Sweden and if resources were scant (Andersson et al., 2022).

Concluding Discussion
Identifying and defining several latent vulnerable life courses from the total working population was possible.That is, identifying people living in the social and spatial fringes of the Swedish population.In our study we found two life courses out of five in each of the three life phases, Young adulthood, Early middle age and Late middle age, that could be defined as vulnerable.Interestingly the proportion of life course trajectories in vulnerability was about the same for all life phases and corresponded to an earlier Swedish welfare study aiming to define deprivation (Halleröd & Larsson, 2008).
Limitations of this paper were associated with the process of determining a number of latent classes.We balanced between theoretical and statistical trade-offs as described in the methods section (Nylund-Gibson et al., 2022).Therefore, we strived to ensure transparency in the choices made during this analysis.The abundance of data available for this paper was in some ways problematic; it has the potential to generate numerous latent classes.This can be a drawback when it comes to presenting and mapping results in a comprehensible manner.At the same time the wealth of data points to one of the pros that the many indicators in our large material makes for more stable latent classes (Wurpts & Geiser, 2014).Another limitation is a baseline LCA.A smaller material, with fewer years of data, focusing on specific cohorts rather than changes over time, would have allowed for the exploration of other types of LCA (RMLCA).
The main contribution of this study was to add a geographical dimension in understanding vulnerability.Our results indicated that different life courses of vulnerability were present in different geographical contexts when analysing all life courses between the ages of 25 and 59 in the Swedish population from 1990 to 2019.One example could quite well explain the pre-election and general Swedish (and European) debate focusing on ethnicity, migration and crime challenges.In the observation period, 1990 to 2019, the cohorts (born 1965-1980) are among the parents of today's young in particularly vulnerable areas (the latent class, Early family formation with low income).That is, we will find children and young adults growing up in vulnerable families, to a density of about 30 to 80 percent among the 200 closest neighbours.Thus, this is showing the life conditions of the parental generation to today's young, who are having challenges with schooling and on the labour market.These children are also being exposed to more criminality than in other areas (NOA, 2021).
But there is more to the geography of vulnerability.When analysing only distressed life courses (DCs), distilled from the first round of vulnerable LCs, for the supposedly established Late middle age life phase, there was a clear difference in the types of vulnerability found in different geographical contexts across Sweden.There were, to use the language of Wacquant, different relegated spaces in Sweden; families living in single family housing in rural areas, singles living in multifamily housing in towns and cities and the extra distressed latent class in particularly vulnerable areas in the fringes of the metropolitan areas.The differences between distressed rural areas and vulnerable urban areas were most apparent in the proportion of people born outside of Sweden, rather than in family living arrangements.These findings have implications for adapting mitigation measures to vulnerability and distress in different places and should inform the political debate.Vulnerability is thus not only present in urban areas including a denoted population born outside Sweden, it is present in different forms in other geographical fringes of Sweden as well.
What came out clear was the spatial distribution according to tenure form that we included in the latent class analysis.Distress is associated with single family housing in rural and less expensive areas and to apartment-living in vulnerable areas in metro-areas or in smaller towns and cities.Shifting housing policies like rising rents in rental housing, or higher interest rates on mortgages and other changes related to tenure forms will therefore hit different types of distressed groups differently.In addition, tight housing markets and housing markets with less demand will make the living conditions for different types of groups differ, e.g.crowded living conditions in tight housing markets and/or deficient housing standards.The different types of distress found in this study is therefore important to contextualize in order to mitigate all sorts of vulnerability.
In conclusion, we would like to suggest that further research on life course should use comprehensive frameworks like the one suggested by this research and by Spini et al. (2017).There are many advantages to studying life course trajectories by including several dimensions, working with longitudinal data and using a spatial perspective.For this research on life course vulnerability, the framework was created based on a wish to emphasize this multitude of latent vulnerability and different types of distress and contextualize these by means of Swedish geography.Using this framework, we believe, can be successful in further studies of vulnerability trajectories.

Fig. 1
Fig. 1 Scree plot Bayesian information criteria (BIC) for different number of classes in each of the three life phases 25-39, Early family formaƟon, medium income

Fig. 2
Fig. 2 Indicator share and age for trajectories.Columns; 25-39, 35-39, and 45-59 years, for 5 LCs.Two upper rows of diagrams, LCs in vulnerability, middle row diagrams are LCs of medium income, two lower rows, are LCs with affluence

Fig. 4
Fig. 4 Five Distressed classes (DCs) from two LC that showed vulnerability in a first LCA for Late middle age

Fig. 5
Fig. 5 Maps of Sweden with inset maps of the three metropolitan regions of Stockholm, Göteborg and Malmö, showing high and low concentrations of distressed latent classes (DC) in neighbourhoods of 200 inhabitants in 2004.The maps with dotted frames for DC1 and DC3 show city segregation, the maps with dashed frames, DC2 and DC5 show rural patterns, and the black bold framed map DC4 shows vulnerable residential areas

Table 1
Ages of birth cohorts in data 1990 to 2019 grouped in the three life phases

Table 2
Life phases with ages, numbers and birth years, and 12 indicators used in LCA for all years Slotkin (1954)oung adulthood, 25 to 39 years; Early middle age, 35 to 49 years; and Late middle age, 45 to 59 years partly follows on the nomination bySlotkin (1954)in which he, based on earlier research, labels ages from 28 the stage of maturity.However, today 'maturity' is probably delayed compared with the 1950s, why we label the youngest cohort from 25 years, Young adulthood.Ages starting at 43 Slotkin labels "testing stage of early middle age", and from age 48 an "indulgence in later middle age", and finally, not included in this study, ages from 64 and up he calls the "completion stage of old age" (p.171).

Table 3
Description of vulnerable latent classes for the three life phases Fig. 3 Maps of Sweden, with inset maps of Stockholm, Göteborg and Malmö metropolitan regions.Proportion of vulnerable LC, trajectory types, among the closest 200 neighbors in 2004.First map Young adulthood, second, Early middle age and last Late middle age, (one map example of spatial patterns of vulnerability trajectories per life phase)

Table 4
Spatial segregation of trajectories in all life phases and for distressed classes only for the Late middle age.Darker shading indicates over-representation and lighter shading under-representation