Mental Health and Parent–Child Residential Distance for Older People: Cross-Sectional Study Using a Comprehensive Survey of Living Conditions in Japan

: Parent–child residential distance is a focus of housing policies in Japan, which is experiencing an aging society. This study aimed to clarify the relationship between mental health and parent–child residential distance for older parents. This study design was a cross-sectional study of older parents. The data utilized were anonymized data from the 2016 Comprehensive Survey of Living Conditions. A two-way ANOVA test set the outcome variable as the K6 scale and the three predictors as age, gender, and parent–child residential distance. A statistically significant difference was found in the interaction between parent–child residential distance and age group. In particular, the average mental score of older parents over 75 years old living together with their children was above the cutoff value indicating serious mental illness. Meanwhile, the mental scores of older parents whose children lived in the same city did not differ significantly between those aged 65 to 74 years old and those aged 75 years and older. This study concludes that mental health is poorer among late-old-stage parents living closer to their children. This conclusion implicated the promotion of parent and child households moving to the same city from the viewpoint of mental health.


Introduction
The United Nations points out that making cities inclusive, safe, resilient, and sustainable is an important issue for sustainability as part of the Sustainable Development Goals [1].The concept of urban sustainability is fundamentally concerned with preserving the health and well-being of society within a broader framework of environmental change [2].Regarding the urban sustainability issue, many developed countries are experiencing aging societies [3].According to the changing demographics of the population, we need to change social support systems for older people in many aspects of society.In 2022, in Japan, 36.21 million people were 65 years old and older, which accounted for 28.9% of the total population [4].Some other countries will also soon face an aging population [5].It was reported that a wide range of context-specific technological, socio-economic, institutional, and governance interventions will be needed to effectively take advantage of the opportunities and minimize the risks posed by aging populations for urban sustainability [6].In order to change social support systems for older populations, the realization of age-friendly cities is urgently needed [7].Age-friendly cities promote active aging by providing opportunities for health, participation, and security to enhance the quality of life of older people [8].The World Health Organization framework sets out eight interconnected domains for agefriendly cities: outdoor spaces and buildings, transportation, housing, social participation, respect and social inclusion, civic participation and employment, communication and information, and community and health care [8].Among these eight domains, the housing environment has become increasingly important [9,10].For example, housing tenure is example, housing tenure is correlated with self-related health for Japanese people [11].Therefore, urban policymakers need to develop new solutions related to the housing environments that contribute to improving the health of older people.
This study focused on parent-child residential distance as a solution to the housing environment for realizing age-friendly cities.A positive relationship was found between a better quality of life and a closer distance between parents and children [12].Particular advantages include the ease for child households to provide care for parent households [13].This is because parent-child relationships are more deeply connected than other types of social relationships.However, it has been pointed out that the strong ties between parents and children do not have only advantages but also disadvantages, depending on the family situation [14][15][16].In particular, the issue of parent-child relationships is an important topic in the context of long-term nursing care [17].This is because Japan's welfare policy has shifted to supporting the rapidly growing older population at home rather than in institutions [18].Therefore, studying the relationship between mental health and parent-child residential distance would provide valuable insights for appropriate nursing care to change social support systems for older populations.
Regarding the residential distance between parents and children, this study focused on the housing environment of HLSN (parent-child households living in the same neighborhood) and HLSC (parent-child households living in the same city).HLSN and HLSC indicate that the parent and child households are close to each other in the same neighborhood or city.HLSN and HLSC differ from HLT (parent-child household living together), in which the parent and child households live together in the same residence.HLSN and HLSC are translated as kinkyo in Japanese.In 2006, the need for HLSN and HLSC was stated in the Basic Plan for Housing in Japan by the Japanese Ministry of Land, Infrastructure, Transport and Tourism (MLIT) [19].Subsequently, MLIT incorporated the HLSN and HLSC measures into the Basic Plan for Housing, revised in 2011 [20].According to the national housing plan change, Kobe City has provided financial support for HLSN and HLSC for young families since 2013 [21].In recent years, an increasing number of municipalities and public companies have provided financial support for HLSN and HLSC [22,23].
This study aims to clarify the relationship between mental health and parent-child residential distance for older parents.A cross-sectional study design was adopted using anonymized data from the 2016 Comprehensive Survey of Living Conditions.This study set four types of parent-child residential distances: HLT represents parent-child household living together; HLSN denotes parent-child households living in the same neighborhood; HLSC denotes parent-child households living in the same city; and HLDC represents parent-child households living in a different city.Figure 1 shows the relationships between HLT, HLSN, HLSC, and HLDC, which are arranged from closest to farthest distance between parent-child households.

Parent-Child Residential Distance
Many researchers have studied the benefits of HLSN and HLSC in Japan.HLSN and HLSC were found to provide desirable benefits in family interactions, support, and satisfaction [24].In addition, HLSN and HLSC allow for both the parent and child households to achieve a balance between independence, care, and support [25].In particular, HLSN and HLSC were found to reduce the financial burden for child households [26].In addition, HLSN and HLSC were reported to shorten the period needed to rebuild their lives after a disaster [27].Regarding the residential distance between parent and child households, living within 15 min significantly increased their daily interactions [28].Therefore, many children want their households to be in the same neighborhood as their parent households (HLSN) in aging suburban residential areas [29,30].However, regarding the disadvantages of HLSN, an indicated risk is that the support of child households may interfere with older parents' outgoing behavior and inhibit their independence [31].These studies highlight the risks of parent-child residential distance regarding the health of older parents.Therefore, this study newly investigates the relationship between mental health and the parent-child residential distance for older parents.

Housing Environment and Mental Health
In many studies, housing environments have been reported to affect mental health in many ways [32][33][34][35][36]. Especially following the lockdown triggered by the COVID-19 pandemic, research on housing environments and mental health has progressed in many fields [37][38][39][40].However, researchers have been studying the importance of housing environments in mental health since before the pandemic.A nationwide cross-sectional study in China indicated that the influence of housing environments on health exhibits age-group heterogeneity [41].For older people, good housing conditions contribute to mental health [42].For example, older people living in appropriate housing environments have significantly improved mental health [43].Meanwhile, older people living in problematic housing environments have worse mental health [44].The worsening mental health of older adults is an important problem to be solved because it affects other health conditions.Compared to these previous studies, the originality of this study involved analyzing housing environments based on the residence distance between parent and child households.Studies on mental health in relation to parent-child relationships have focused on children in young households [45][46][47].Meanwhile, parents' mental health in the parent-child relationship is also essential for age-friendly cities.The research gap regarding the correlation between mental health and housing environments based on parent-child relationships must be filled.This analysis contributes to policy implications of HLSN or HLSC to achieve age-friendly cities in aging societies.

Study Design
The study design used in this work was a cross-sectional study of older parents in Japan.This study utilized anonymized data from the 2016 Comprehensive Survey of Living Conditions.This cross-sectional study set the three predictors as the age group, gender group, and parent-child residential distance.In addition, this study set the outcome as mental health.Because this study set three predictors, we did not control for confounding or covariate factors.The two age groups were early-old-stage (65-74 years old) parents and late-old-stage (75 years old and older) parents.In Japan, those aged 65 and older are considered older people.In addition, older people in the late-old stage are supported by the Japanese-specific insurance system [48].Therefore, it is appropriate to classify older parents based on the age of 75.Parent-child residential distance was classified into four types: HLT, HLSN, HLSC, and HLDC.
This study was designed based on three predictors: age group, gender group, and parent-child residential distance.The three predictors were qualitative variables.The age group was categorized into two nominal scales: early-old-stage (65-74 years) and late-oldstage (75 years and older).The gender group was categorized into two nominal scales: men and women.Parent-child residential distance was categorized by two questions.The first question was a single-answer question: "Do you have children from different households?"In addition, for households with children from different households, the second singleanswer question was asked: "Where do the children live?"The responses to this question included the same house, same site, same neighborhood, same city, and other.In Japan, many parent and child households are in the same house or site, even if their households are separated.Therefore, this study defined HLT as those who selected the same household in the first question or the same house or same site in the second question.In addition, this study defined HLSN as those who selected the same neighborhood, HLSC for those who selected the same city, and HLDC for those who selected others in the second question.
The outcome variable was the K6 scale (Kessler psychological distress scale).The K6 scale is an instrument used to screen for mental illness.Screening is also essential because worsening mental health has been found to affect other health outcomes and increase medical costs [49].On the K6 scale, the higher the total score, the more severe the mental health problem.The K6 set a score of 13 as the cutoff point, which indicates serious mental illness [50].The K6 scale was developed for the U.S. National Health Interview Survey with support from the U.S. government's National Center for Health Statistics.The Japanese version of the K6 scale is also used in the Comprehensive Survey of Living Conditions in Japan.The Japanese versions of the K6 scale demonstrated a screening performance that was essentially equivalent to that of the original English versions [51].
In addition, to analyze the causes of mental health changes, this study used a multipleanswer question about confidants when talking about stress.Specifically, the question asked: "Who do you talk to about your worries and stress?"The responses to this question included family, friends, supervisors and teachers, government agencies, doctors, and others.The selected responses were transformed into nominal scales.
This study design was approved by the Ethics Committee of the Graduate School of Human Life and Ecology at Osaka Metropolitan University (No. .

Data
The data used in the study were anonymized data from the 2016 Comprehensive Survey of Living Conditions [52].The Comprehensive Survey of Living Conditions is the national primary statistical survey conducted by the Japanese Ministry of Health, Labour, and Welfare (MHLW).The purpose of this survey is to obtain fundamental data necessary for the planning and administration of health, medical care, welfare, pensions, income, and other fundamental aspects of people's lives, as well as for the planning and administration of health and labor [53].The survey consists of five types of questions, namely those related to households, health, nursing, income, and savings.These surveys were conducted on paper.The MHLW has conducted the survey using five types of questions every three years since 1986.The MHLW provides researchers with anonymized data for research purposes only.The anonymized data are used in many academic articles and policymaking [11,[54][55][56][57].The authors were provided with the anonymized data with permission from MHLW (Contract number: 40045020220011) [58].The authors could not access personally identifiable respondent information during or after data collection.Although these anonymized data cannot be shared with the public due to government confidentiality obligations, researchers who meet the criteria for access to confidential data can obtain the datasets from MHLW.
The MHLW recruited respondents to the 2016 Comprehensive Survey of Living Conditions from April to July 2016 [53].Civil servant investigators collected data from June to July 2016.As national primary statistical data, this survey adopted stratified random sampling to address potential sources of sampling bias.For the 2016 Comprehensive Survey of Living Conditions, the MHLW selected respondents through stratified random sampling in 5410 districts from the census districts in 2010.The eligibility criterion was residents who lived in the 5410 districts.This criterion means that residents who were absent or living separately in the district were excluded from the respondents.The MHLW obtained informed consent from all the respondents.The respondents were allowed to decline the invitation to respond to the survey.However, due to the anonymized format of the questionnaire, informed consent was obtained through questionnaire responses.
Figure 2 shows the sample flow diagram.As shown in Figure 2, the number of respondents to the 2016 Comprehensive Survey of Living Conditions was 15,294.Of these respondents, this study excluded 10,499 respondents who were aged 64 years old or younger.As a result, the number of older people was 4795.In addition, due to missing data, this study excluded 759 respondents who did not provide an answer regarding parent-child residential distance because they did not have a child, refused to provide a response, or gave unreadable answers.The proportion of missing data in the total sample of older people was approximately 15%, which is appropriate for the paper-based national survey.The final sample size for this study was 4036 older parents.The samples comprised older parents of the HLT (n = 1788), HLSN (n = 396), HLSC (n = 670), and HLDC (n = 1192) groups.
Sustainability 2024, 16, x FOR PEER REVIEW 5 of 13 sampling to address potential sources of sampling bias.For the 2016 Comprehensive Survey of Living Conditions, the MHLW selected respondents through stratified random sampling in 5410 districts from the census districts in 2010.The eligibility criterion was residents who lived in the 5410 districts.This criterion means that residents who were absent or living separately in the district were excluded from the respondents.The MHLW obtained informed consent from all the respondents.The respondents were allowed to decline the invitation to respond to the survey.However, due to the anonymized format of the questionnaire, informed consent was obtained through questionnaire responses.
Figure 2 shows the sample flow diagram.As shown in Figure 2, the number of respondents to the 2016 Comprehensive Survey of Living Conditions was 15,294.Of these respondents, this study excluded 10,499 respondents who were aged 64 years old or younger.As a result, the number of older people was 4795.In addition, due to missing data, this study excluded 759 respondents who did not provide an answer regarding parent-child residential distance because they did not have a child, refused to provide a response, or gave unreadable answers.The proportion of missing data in the total sample of older people was approximately 15%, which is appropriate for the paper-based national survey.The final sample size for this study was 4036 older parents.The samples comprised older parents of the HLT (n = 1788), HLSN (n = 396), HLSC (n = 670), and HLDC (n = 1192) groups.

Statistical Analysis
The statistical analysis comprised a two-way analysis of variance (two-way ANOVA) test and cross-tabulation.The two-way ANOVA test set the K6 scale as the outcome variable and the age group and parent-child residential distance as two predictors.The twoway ANOVA test revealed the correlation between the two interactions and mental health scores.The two interactions were age group by parent-child residential distance and gender group by parent-child residential distance.Missing data were removed prior to statistical analysis.The results were presented as line graphs with 95% confidence intervals (95%CI).A two-way ANOVA test was appropriate because of the stratified random sampling of the 2016 Comprehensive Survey of Living Conditions.
Cross-tabulations were conducted to elucidate the causes of the change in mental health scores.The cross-tabulations were analyzed for the relationship between parentchild residential distance and confidants when talking about stress.Pearson's chi-square test was used to analyze significant differences in the cross-tabulations.In addition, the multiple-answer questions were analyzed using a residual analysis.The significance level was set at a p-value of 0.05.To evaluate significance, we utilized quartiles based on two criteria: ±1.96, indicating significant differences at the 5% level of p-value.
IBM SPSS Statistics 26 was sed as the statistical software for this study.

Statistical Analysis
The statistical analysis comprised a two-way analysis of variance (two-way ANOVA) test and cross-tabulation.The two-way ANOVA test set the K6 scale as the outcome variable and the age group and parent-child residential distance as two predictors.The two-way ANOVA test revealed the correlation between the two interactions and mental health scores.The two interactions were age group by parent-child residential distance and gender group by parent-child residential distance.Missing data were removed prior to statistical analysis.The results were presented as line graphs with 95% confidence intervals (95%CI).A twoway ANOVA test was appropriate because of the stratified random sampling of the 2016 Comprehensive Survey of Living Conditions.
Cross-tabulations were conducted to elucidate the causes of the change in mental health scores.The cross-tabulations were analyzed for the relationship between parentchild residential distance and confidants when talking about stress.Pearson's chi-square test was used to analyze significant differences in the cross-tabulations.In addition, the multiple-answer questions were analyzed using a residual analysis.The significance level was set at a p-value of 0.05.To evaluate significance, we utilized quartiles based on two criteria: ±1.96, indicating significant differences at the 5% level of p-value.
IBM SPSS Statistics 26 was sed as the statistical software for this study.

Samples
Table 1 shows the attributes of the samples according to the parent-child residential distance.The attributes were gender and age group.Table 1 shows no statistically significant differences in parent-child residential distance by age group (p = 0.360).In addition, no statistically significant differences were found in parent-child residential distance by gender (p = 0.412).The results suggest no cofounders in the sample data regarding age and gender.

Mental Health and Parent-Child Residential Distance
This section analyzed the relationship between parent-child residential distance and mental health.Therefore, a two-way ANOVA test was conducted with the outcome variable set as the K6 scale and the three predictors set as the age group, gender group, and parent-child residential distance.Figure 3 and Table 2 present the results of the two-way ANOVA test.
Table 2 shows that the F-value is higher for the age group (F = 4.962) than for the parent-child residential distance (F = 1.240) and gender group (F = 0.220).Regarding the differences, Figure 3 shows that the overall mental health score is higher for the late-oldstage group than for the early-old-stage group.However, no significant difference was found in the age group (p = 0.103), the parent-child residential distance (p = 0.441), or the gender group (p = 0.659) regarding their mental health scores.This means that mental health was not statistically related to age group, gender group, or parent-child residential distance alone.In addition, there is no statistically significant difference in the interaction between mental health and parent-child residential distance by gender group (F = 0.883, p = 0.449).
Meanwhile, Table 2 indicates a statistically significant difference in the interaction between mental health and parent-child residential distance by age group (F = 4.437, p = 0.004).Specifically, Figure 3 shows that the late-old-stage group was more stressed in HLT (14.523 [12.825, 16.221]), HLSN (11.118 [7.661, 14.571]), and HLDC (9.644 [7.597, 11.691]).The results suggest that older parents in the HLT, HLSN, and HLDC groups have lower mental health scores in the early-old-stage group than in the late-old-stage group.In particular, the average mental health score of the late-old-stage HLT group was above the cutoff value indicating serious mental illness (14.523 [12.825, 16.221]).In addition, the upper limit of the 95% CI of the late-old-stage HLSN group was above the cutoff value indicating serious mental illness (11.118 [7.661, 14.571]).The results suggest that many late-old-stage HLT groups and several HLSN groups tend to have serious mental illness.Meanwhile, it was found that HLSC did not vary significantly between the early-old-stage (6.829 [4.321, 9.338]) and the late-old-stage groups (6.968 [4.273, 9.663]).This result indicates that parents of HLSC have lower mental health scores, even in the early-old-stage and late-old-stage groups.
per limit of the 95% CI of the late-old-stage HLSN group was above the cutoff value indicating serious mental illness (11.118 [7.661, 14.571]).The results suggest that many lateold-stage HLT groups and several HLSN groups tend to have serious mental illness.Meanwhile, it was found that HLSC did not vary significantly between the early-old-stage (6.829 [4.321, 9.338]) and the late-old-stage groups (6.968 [4.273, 9.663]).This result indicates that parents of HLSC have lower mental health scores, even in the early-old-stage and late-old-stage groups.

Confidants about Stress
This section analyzes the reasons for the significant difference in the interaction between parent-child residential distance and mental health.Table 3 shows a cross-tabulation of parent-child residential distance and the confidants they talk to about their stress.Each respondent was asked a multiple-answer question about who they talk to about their stress, such as family and friends.Note: SS denotes the sum-of-squares.DF denotes the degree of freedom.MS denotes the mean square.The F-value denotes the F ratio.* denotes a p-value < 0.05.

Confidants about Stress
This section analyzes the reasons for the significant difference in the interaction between parent-child residential distance and mental health.Table 3 shows a cross-tabulation of parent-child residential distance and the confidants they talk to about their stress.Each respondent was asked a multiple-answer question about who they talk to about their stress, such as family and friends.
Table 3 shows that many people talk about their stress with family (n = 747), medical doctors (n = 540), and friends (n = 334).Regarding the confidants according to parent-child residential distance, Table 3 indicates a statistically significant difference only in family members (p = 0.009).This result means that parent-child residential distance did not correlate with confidants such as friends (p = 0.255), supervisors and teachers (p = 0.094), public institutions (p = 0.168), or medical doctors (p = 0.181).Regarding the family, the results of the residual analysis indicate that older parents in HLSN are more likely to talk to family members about their stress (n = 96, quartile > 1.96).These results suggest that the closer the parent-child residential distance is, the more likely older adults are to talk to their families about their problems.These results suggest that the greater the parent-child residential distance, the less likely older adults are to talk to family members.The results indicate that there is an appropriate distance for parents and children to live away from each other.In other words, mental health is exacerbated when the parent-child residential distance is too close or too far away.However, HLT is not correlated with family confidants.In the previous section, Figure 3 shows that many late-old-stage HLT groups had serious mental illness.The limitations of this study are that we could not determine the reasons for the high K6 score related to HLT.

Discussion
This study examined the relationship between mental health and parent-child residential distance for older parents in Japan.This study used anonymized data from the 2016 Comprehensive Survey of Living Conditions.A two-way ANOVA test was conducted with the outcome variable as the K6 scale and the two predictors as age group and parent-child residential distance.As key results, this study elucidated a statistically significant difference in the interaction between age group and parent-child residential distance.Specifically, it was found that mental health did not vary significantly with parent-child residential distance for the early-old-stage group.However, the late-old-stage group varied in mental health scores with parent-child residential distance.In particular, older parents of the HLT, HLSN, and HLDC groups were found to have higher mental health scores in the late-old-stage group than in the early-old-stage.In particular, many late-old-stage HLT groups and several HLSN groups tend to have a serious mental illness because they were above the cut-off value.These people are more likely to have a diagnosable mental illness severe enough to cause functional limitations and require treatment [51].In general, a poor mental health score was found to be related to other illnesses, such as depression, generalized anxiety disorder, and bipolar disorder [49,59].Meanwhile, older parents in the HLSC group found that mental health did not change from the early-old-stage to the lateold-stage groups.These results validated the benefits of HLSC, which have been pointed out in previous studies [24][25][26][27].The benefits of HLSC might be due to an appropriate parent-child residential distance.However, this study newly clarified that the parent-child residential distance is more appropriate for the HLSC group than the HLSN group from the perspective of mental health.These results allow us to hypothesize that there is an appropriate distance for parents and children to live from each other in the same city rather than in the same neighborhood.Furthermore, these findings are significant because the results suggest the need to focus on the housing environment of parents and children for research on mental health for older parents [32][33][34][35].This study's findings indicate that the reason why mental health is poor in the lateold-stage group might be correlated with residential distance between family member households.In contrast, the mental health of early-old-stage parents did not correlate with parent-child residential distance.Regarding the change, as older people age from the early-old stage to the late-old stage, they rapidly decline in physical ability.Therefore, late-old-stage groups are more likely to receive various types of welfare and care support.The findings regarding confidants indicate that there is an appropriate distance for parents and children to live from each other.This means that if a parent-child residential distance that is too close or too far away, it has a risk of reducing the opportunity for assistance from professional care staff.A close distance also strengthens social relationships between parents and children but limits the support provided by professional care staff.These disadvantages have been pointed out in previous studies [31].In addition, this is the opposite side of the benefit pointed out in previous studies [28].Close parent-child residential distances are often thought to be helpful.However, our findings demonstrate the benefit of professional care support for parents and children in all types of parent-child residential distances.This study's findings suggest the importance of maintaining an appropriate residential distance between parents and children to maintain the mental health of late-old-stage parents.To maintain an appropriate distance, it is also demonstrated that better and greater availability of professional caregiver support is beneficial for all types of parent-child residential distances.Caregiver support might enable late-old-stage parents to reduce their risk of mental health problems.Support also helps children to reduce their burden of caregiving and maintain close bonds with their parents.In Japan, the number of older people in the late-old stage has increased rapidly.This demographic change indicates the need for an increased population involved in welfare care to support late-old-stage parents.The burden of care support has caused an increasing number of child households to quit their jobs, which cannot be overlooked as a social problem.This study demonstrates the importance of policymaking promoting HLSC for age-friendly cities that enhance the quality of life of older people.Our findings reinforce the recommendation to promote HLSC rather than HLSN in government housing policies [19][20][21].This policy provides an action guide for parent and child households to support moving to the same city, not the same neighborhood.In addition, the ties of the parent-child relationship are universal throughout the world.Therefore, our findings might have external validity and generalizability not only in Japan, but also in other countries with aging populations; although housing policy systems differ from country to country.Our study recommends HLSC in housing policies for China and Korea, which are also facing aging societies in East Asia.
For many developed countries, including Japan, age-friendly cities are a key issue for urban sustainability [7].This study clarified the importance of parent-child residential distances for urban sustainability, which was pointed out by Jarzebski [6].Despite its importance, the parent-child relationship has been largely neglected in research.Our findings highlight the importance of focusing perspectives of parent-child residential distances on urban sustainability studies.Although this study examined the relationship between parent-child residential distance and mental health, it may also be related to other public health factors.The results of this study contribute to the development of further research in the field of urban sustainability towards the realization of age-friendly cities.
There are three limitations in this study.The first issue is that we could not determine the reasons for the high K6 score of the late-old-stage HLT group.Our analysis regarding confidants showed significant differences between the HLSN and HLDC groups.However, many late-old-stage groups of HLT had serious mental illnesses.Therefore, future analysis will analyze the reasons for the different results regarding confidants.The second issue is the lack of causality.In detail, this study does not clarify the temporal precedence between causes and effects.For example, these data did not include information on when the respondent moved into their current home or how long they had lived in that location.In addition, these data did not include a measure of the length of time that this living arrangement had existed, such as when the older parent or child moved and when the mental health problems first occurred.Future research will employ a study design with a higher level of evidence to elucidate the causal relationship between mental health and the parent-child residential distance for late-old-stage parents.The third concern is generalizability.This study was focused on Japan and may not be generalizable to other cultural or geographical contexts.This means that our findings are limited in scope in the international context due to the use of data sources from Japan.Future research should validate the findings of this study in other countries with different cultural contexts.

Conclusions
This study concludes that poor mental health scores are present among late-old-stage parents living closer to their children.In particular, many late-old-stage HLT groups and several HLSN groups tended to have serious mental illness.Meanwhile, this study found that mental health did not change for late-old-stage parents whose children lived in the same city.The findings of this study suggest the importance of an appropriate parent-child residential distance to maintain mental health for late-old-stage parents.This conclusion indicates the implications for housing policymaking that promote parent and child households moving to the same city but not the same neighborhood from the viewpoint of mental health.

Figure 1 .
Figure 1.Four types of parent-child residential distance.HLT represents parent-child households living together; HLSN denotes parent-child households living in the same neighborhood; HLSC denotes parent-child households living in the same city; HLDC represents parent-child households living in a different city.

Figure 1 .
Figure 1.Four types of parent-child residential distance.HLT represents parent-child households living together; HLSN denotes parent-child households living in the same neighborhood; HLSC denotes parent-child households living in the same city; HLDC represents parent-child households living in a different city.

Figure 2 .
Figure 2. Flow diagram of the study sample.

Figure 2 .
Figure 2. Flow diagram of the study sample.

Figure 3 .
Figure 3. Mental health and parent-child living type.The green line is the mental health score of the early-old-stage group (65-74 years old), and the red line is that of the late-old-stage group (75 years old and older).Error bars indicate a 95% C.I. HLT denotes parent-child households living together; HLSN denotes parent-child households living in the same neighborhood; HLSC represents parentchild households living in the same city; HLDC represents parent-child households living in a different city.

Figure 3 .
Figure 3. Mental health and parent-child living type.The green line is the mental health score of the early-old-stage group (65-74 years old), and the red line is that of the late-old-stage group (75 years old and older).Error bars indicate a 95% C.I. HLT denotes parent-child households living together; HLSN denotes parent-child households living in the same neighborhood; HLSC represents parent-child households living in the same city; HLDC represents parent-child households living in a different city.

Table 1 .
Characteristics of the study samples.: Early-old-stage group denotes older people aged 65-74 years old.The late-old-stage group denotes older people aged 75 years old and older.HLT denotes parent-child households living together.HLSN denotes parent-child households living in the same neighborhood.HLSC denotes parent-child households living in the same city.HLDC denotes parent-child households living in a different city.Table 1 also shows the outcome measure of samples according to the parent-child residential distance.The outcome measure indicates the average K6 score.The K6 score of HLT is the highest of the four types of parent-child residential distance (HLT = 10.483).Meanwhile, the average values of K6 other than HLT are comparable (HLSN = 8.267, HLSC = 7.011, HLDC = 8.158).The results indicate that the HLSC, HLSC, and HLDC groups do not differ significantly in terms of mental health. Note

Table 2 .
Interaction effects between mental health and parent-child residential distance.SS denotes the sum-of-squares.DF denotes the degree of freedom.MS denotes the mean square.The F-value denotes the F ratio.* denotes a p-value < 0.05.

Table 2 .
Interaction effects between mental health and parent-child residential distance.

Table 3 .
Confidants about stress.: * denotes p-value < 0.05, + denotes quartile > 1.96.HLT denotes parent-child households living together; HLSN represents parent-child households living in the same neighborhood; HLSC denotes parent-child households living in the same city; HLDC represents parent-child households living in a different city. Note