Income and Housing Satisfaction and Their Association with Self-Rated Health in Different Life Stages

PEER REVIEW HISTORY BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from

BMJ Open publishes all reviews undertaken for accepted manuscripts. Reviewers are asked to complete a checklist review form (http://bmjopen.bmj.com/site/about/resources/checklist.pdf) and are provided with free text boxes to elaborate on their assessment. These free text comments are reproduced below.

ARTICLE DETAILS

TITLE (PROVISIONAL) Income and housing satisfaction and their association with self-rated health in different life stages. A fixed effects analysis using a German panel study. AUTHORS Knöchelmann, Anja; Seifert, Nico; Guenther, Sebastian; Moor, Irene; Richter, Matthias

VERSION 1 - REVIEW

REVIEWER Alexander Miething Department of Public Health Sciences, Stockholm University, Sweden REVIEW RETURNED 27-Sep-2019

GENERAL COMMENTS Reviewer comments: ―Income and housing satisfaction and their association with self- rated health from a life course perspective. A fixed effects analysis using the German Socio-Economic Panel.‖ http://bmjopen.bmj.com/ This interesting and novel study identified perceptions of income and housing (dis)satisfaction as possible source of health inequalities in a longitudinal setting. The study is well and clearly written. The methods are appropriate. Despite these strengths, I have several comments and questions the authors should address and consider in their revision.

Major comments: on October 2, 2021 by guest. Protected copyright. #1 The concept of relative deprivation is a relevant theoretical framework in this study. Although a plausible description of how income deprivation relates to health is provided, the manuscript would benefit from acknowledging previous research about the mechanisms in the relationship between income and health. For example, it should be made clear that (not only) material conditions but also non-material pathways (closely related to the concept of relative deprivation) contribute to the socio-economic/ income gradient in health. (e.g. R. Wilkinson) Several times the author refer to ―material conditions‖ that determine health and contribute to health inequalities. Although this perspective is not wrong, it neglects the non-material (aka psychosocial) pathway proposed in earlier research (e.g. by R.Wilkinson, I.Kawachi and others). As the concept of relative deprivation is linked to psychosocial hypothesis – some more references about income deprivation should be included. #2 The provided definition of relative deprivation (p. 4., l.15-25) could BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from be sharpened. (…) According to Runciman (and more contemporary literature and scholars), relative deprivation is not only driven by upward social comparisons (―with others in higher social positions‖), also reference groups and frameworks are important. It should be made clear that reference groups and significant (similar) others play an important role for reasonable income comparisons. Accordingly, income differentials are particularly unfair if they emerge within groups with similar characteristics in terms of education, professional skills and occupational position. For example, income gaps between two individuals with similar educational degrees may be perceived as more unfair than income difference between a skilled and un-skilled person. In brief, the concept of relative deprivation refers to income differences (income gaps) that cannot be explained with education, competences and skills. The following references might be of interest:

Lorgelly, P.K., & Lindley, J. (2008). What is the relationship between income inequality and health? Evidence from the BHPS. Health Economics, 17, 249-265. Pedersen, A.W. (2004). Inequality as Relative Deprivation: A Sociological Approach to Inequality Measurement. Acta Sociologica, 47, 31-49.

#3 Did authors accounted for a possible collinearity between income and housing satisfaction. Was the correlations tested between both measures? Related to this, a possible interdependency between housing and income satisfaction should be discussed in the theory section of the introduction. For example, dissatisfactory housing conditions might influence individuals‘ evaluations of their income (although their income might be high by other objective standards). In this discussion section it is stated that the (two) models were mutually adjusted for income and housing satisfaction. This should http://bmjopen.bmj.com/ be made clear in the methods or result section already.

#4 The authors describe their method design as ―life course approach‖, which is somewhat misleading. According to my understanding, life course approaches take into account (critical) transitions and developmental changes occurring over time, for example from childhood to adolescence, adolescence to adulthood etc. I am not on October 2, 2021 by guest. Protected copyright. really convinced that this is given here, although a relatively long study period (1994 to 2016) was considered. Nevertheless, I agree with the conclusions in the discussion (e.g. p.12, l.21) that accumulative processes might have contributed to the identified associations between income/ housing satisfaction and self-rated health (as for instance suggested on p.13, l.39). To make it clear, my critique concerns the choice of wording in the abstract, keywords, and introduction. The authors‘ conclusion about possible life course effects suggested seem to be highly plausible.

#5 The study refers to a specific context (Germany). Therefore, the study would benefit from a brief description of the (socio-economic and political) context, and how it might has contributed to the findings.

Data & Methods #6 The authors note that effect sizes (AMEs) were rather weak. BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from Obviously, it is difficult to interpret the magnitudes of presented associations without reference measures/ indicators. Likewise, the presented plots – indicate rather the significance than the size/ magnitude of associations (which is an interesting finding per se!). However, I slightly wonder whether the authors want to consider some of the following alternative: - How do the AME‘s of income/ housing satisfaction compare to the AME‘s of other covariates? Actually, it would be interesting to see how the AME‘s of income/ housing satisfaction correspond to the AME‘s of (absolute) changes in income (e.g. in units of 1000 Euros). - A relatively fine-graded scale of self-rated health was used. The AME‘s / magnitudes of associations will be more pronounced when a dichotomized dependent variable is used. As the use of dichotomized self-rated health is quite common in health research, it might also alleviate to compare the findings of the present study with other studies in the field. - Alternatively, the AME‘s could be converted into a probability matrix – indicating how changes in income/ housing satisfaction affect the probability of experiencing good/poor health. For a more intuitive interpretation, self-rated health should be dichotomized then.

#7 It stated that ―… the health effects can be quite large for individuals who experience a large drop or rise in satisfaction.‖ (p.13, l.44) It would be nice to see the marginal benefits of increasing income/ housing satisfaction regarding self-rated health. For example, are gains/ improvements in SRH larger by changes in satisfaction in bottom or top group?

#8 It is stated (p.8, l.5) that age, age², and age³ were included to control

for curvilinear age-effects. The different implications of age² and http://bmjopen.bmj.com/ age³ should be made clear.

#9 It is unclear how the splines were derived. Please add a sentence or two to the method section.

Minor comments: - p.13: ―key resource for participation in the community.‖ – maybe on October 2, 2021 by guest. Protected copyright. better to write ―social participation‖ instead? - p.14: ―Emerging adults‖ – slightly awkward wording. ―becoming adults‖ might be better. - Table 1, line 45: a number (―1‖) is missing - The spelling ―Runciman‖ in the reference should be corrected. - Reference to Stata 14 also Stata 15 used.

REVIEWER Maria Nyholm Halmstad University Box 823 301 18 HALMSTAD Sweden REVIEW RETURNED 31-Oct-2019

GENERAL COMMENTS The paper aims to investigate the effect of income and housing BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from satisfaction on self-rated health over the life course. Fixed effects regression was used for calculations. The ―story line‖ is missing and the knowledge gap is not very well defined. The independent variables need to be clearer. How satisfied are you with your place of housing? Validated? What does this scale measure? The results section with tables needs to be improve to clarify the ―story line‖.

REVIEWER Euijung Ryu Mayo Clinic, USA REVIEW RETURNED 07-Nov-2019

GENERAL COMMENTS This study aimed to test association between housing and income satisfaction and perceived health over the life course using a population-based longitudinal cohort. It is relatively well written with good motivation of the study. However, it requires more detailed description of the variables and statistical methods, especially on how each variable was defined and what was included in the final models including what was done in cases when variables are highly correlated. One thing to note is that it appears (although not commented by the authors at all) the outcome was treated as a continuous scale, but it is a categorical variable which does not require to be equally spaced. Therefore, it is important to check if the study results hold by using proper categorical-based modelling. Specific comments are as follows: 1. The authors mentioned they used fixed effect regression without mentioning how the outcome was treated. Was it considered as a continuous scale or ordinal variable, or others? Without this information, simply mentioning fixed effect regression does not mean anything at all.

http://bmjopen.bmj.com/ 2. In Abstract/Results, the third sentence (about the average marginal effects for income satisfaction for self-rated health) is hard to understand without know what these numbers mean. E.g., what does 0.02 mean in the context of self-rate health (what is the scale of this categorical variable used in the model)? The current Result section present only effect size with no statement about whether it is statistically significant or not (or whether the effect size is clinically meaningful). What that, it is hard to justify the statement in Conclusion section. on October 2, 2021 by guest. Protected copyright.

3. In page 3, it is not a correct statement to say ―calculate fixed effects models‖. Models cannot be calculated. It‘s a tool to estimate fixed effects.

4. In page 3, the following statement is hard to understand what the authors mean. Please reword it. ―Yet, it has to be noted that these only apply for a change of one scale point per year, which is highly unlikely‖. If one scale point (whatever it means) is not meaningful, the authors needed to work with scales that actually have a meaning.

5. In page 6, the statement ―this study does not use patient data‖ needs rewording. This study DOES use patient data (i.e., the variables used in this analysis are from patient data).

6. In page 6/lines 3-8, the authors need to clarify what it means by ―excluding observations with missing data on any of the variables‖. BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from What do ―observation‖, ―data‖, and ―variables‖ refer to? Did they mean to say they excluded any variable (whatever variables used in the analysis) if that variable has at least one missing data over multiple waves of surveys? The current statement is unclear on who and what variables what then ended up keeping in the analysis. Also, the authors need to specify how many they ended up excluding subjects in the analysis and what it means in terms of generalizability of the study cohort.

7. In page 8, the vast majority of texts under Covariates seem to fit better in Statistical Analysis section. For the Covariates section, more details are needed for each covariate considered. For example, what is period effect? Were all the variables listed considered as time-varying? If not, which ones were fixed and which ones were varying. How was equivalized disposable household income calculated? Not all the reader familiar with the modified OECD scale.

8. In page 8/lines 41-46, it is not clear by controlling for all time- constant confounders in fixed effect regressions. Even if random effect models are considered, those time-constant confounders will/can be controlled. It requires more clarification on what it means by ―whether observed or not‖. Some of covariates listed in lines 46- 48 need to be described here as well.

9. In Stat Analysis section, it is unclear how many variables were considered in the final model.

10. This is a longitudinal data. What time point was used for generating Table 1. At the first survey? Self-rate health is a categorical variable. It does not make sense to treat it as a continuous scale (i.e., mean/SD has no meaning). How were

quintiles calculated? By the definition of quintiles, it does not make http://bmjopen.bmj.com/ any sense to have the same range for all quintile if calculated in this cohort (by each gender separately or as a whole?). Also, it makes no sense to talk about range and means for dummy variables (need to present them as percentages). Again, this should be described in previous section.

11. For Figures 1 and 2, is the change in SRH from previous wave or is it from the first wave until the last wave? on October 2, 2021 by guest. Protected copyright.

12. It will be informative to compare the results without adjusting for income and housing conditions to see how much satisfaction variables add in predictability.

13. There is no mention on the limitation of this study and whether it can be generalizable to other setting.

VERSION 1 – AUTHOR RESPONSE

Reviewers' Comments to Author:

Reviewer: 1

Reviewer Name: Alexander Miething

Institution and Country: Department of Public Health Sciences, Stockholm University, Sweden Please state any competing interests or state ‗None declared‘: None declared BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from

Reviewer comments:

―Income and housing satisfaction and their association with self-rated health from a life course perspective. A fixed effects analysis using the German Socio-Economic Panel.‖

This interesting and novel study identified perceptions of income and housing (dis)satisfaction as possible source of health inequalities in a longitudinal setting. The study is well and clearly written. The methods are appropriate.

Despite these strengths, I have several comments and questions the authors should address and consider in their revision.

Authors: We would like to thank you for your thorough and helpful review, which helped strengthening our manuscript.

Major comments:

The concept of relative deprivation is a relevant theoretical framework in this study. Although a plausible description of how income deprivation relates to health is provided, the manuscript would benefit from acknowledging previous research about the mechanisms in the relationship between income and health. For example, it should be made clear that (not only) material conditions but also non-material pathways (closely related to the concept of relative deprivation) contribute to the socio- http://bmjopen.bmj.com/ economic/ income gradient in health. (e.g. R. Wilkinson)

Several times the author refer to ―material conditions‖ that determine health and contribute to health inequalities. Although this perspective is not wrong, it neglects the non-material (aka psychosocial) pathway proposed in earlier research (e.g. by R.Wilkinson, I.Kawachi and others). As the concept of relative deprivation is linked to psychosocial hypothesis – some more references about income deprivation should be included. on October 2, 2021 by guest. Protected copyright. Authors: We added additional information on the psychosocial pathway, which links relative deprivation with health. We also added a few sentences in the discussion section as it can also serve as a possible explanation for our results.

―The impact on health can be explained by psychosocial pathways, where social comparisons and experiences of deprivation are associated with insecurity, anger and stress. These feelings can affect health via risky health behaviours (e.g. alcohol consumption, eating habits, smoking) and biological embedding (e.g. blood pressure, allostatic load). [19–21]‖

The association between income and housing satisfaction and health might also be explained by psychosocial pathways. According to this, feelings of deprivation or dissatisfaction which emerge from social comparisons can lead to frustration, insecurity and anger, which in turn result in risky behaviour and biological embedding, e.g. higher blood pressure. [19–21]

#2 The provided definition of relative deprivation (p. 4., l.15-25) could be sharpened. (…) According to BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from Runciman (and more contemporary literature and scholars), relative deprivation is not only driven by upward social comparisons (―with others in higher social positions‖), also reference groups and frameworks are important. It should be made clear that reference groups and significant (similar) others play an important role for reasonable income comparisons. Accordingly, income differentials are particularly unfair if they emerge within groups with similar characteristics in terms of education, professional skills and occupational position. For example, income gaps between two individuals with similar educational degrees may be perceived as more unfair than income difference between a skilled and un-skilled person. In brief, the concept of relative deprivation refers to income differences (income gaps) that cannot be explained with education, competences and skills.

The following references might be of interest:

Lorgelly, P.K., & Lindley, J. (2008). What is the relationship between income inequality and health? Evidence from the BHPS. Health Economics, 17, 249-265.

Pedersen, A.W. (2004). Inequality as Relative Deprivation: A Sociological Approach to Inequality Measurement. Acta Sociologica, 47, 31-49.

Authors: We would like to thank you very much for your feedback on our definition of relative deprivation and for the provision of relevant references. We changed the introduction to give a better introduction to the concept of relative deprivation.

―In contrast, the concept of relative deprivation implies that individuals compare themselves with to others in certain groups. Reference groups might be a) a group the individual wants to become a part of (normative reference group), b) the group they are already a member of (membership group) or c) a group the individuals estimates as most contrastive (comparative reference group). [3] Although different combinations of comparisons may be applied, the focus is often set on a reference group in which all three aspects occur. [3] Individuals mostly compare themselves to others with similar attributes in higher social positions and that the degree of deprivation depends on the difference between what the individual desires and what they believe other people have and where it stands. [3– http://bmjopen.bmj.com/ 5]‖

Did authors accounted for a possible collinearity between income and housing satisfaction. Was the correlations tested between both measures? Related to this, a possible interdependency between on October 2, 2021 by guest. Protected copyright. housing and income satisfaction should be discussed in the theory section of the introduction. For example, dissatisfactory housing conditions might influence individuals‘ evaluations of their income (although their income might be high by other objective standards).

In this discussion section it is stated that the (two) models were mutually adjusted for income and housing satisfaction. This should be made clear in the methods or result section already.

Authors: We did not adjust the different models for income and housing satisfaction, but for objective measures such as relative income position or housing conditions. These covariates were introduced in the methods section. The correlation was tested and turned out to be moderate. A sentence was added to the methods section.

―The correlation between income and housing satisfaction was moderate (r=0.42).‖

We discussed a possible interdependency between income and housing section in the introduction section and added the following sentences: ―Housing is an important factor for people‘s well-being and according to standard economy theory an BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from increase in wealth is associated with an increase in the quality of living conditions. [24] Therefore, a possible interdependency between income and housing satisfaction can not be ruled out, but evidence on this is scarce.‖

The authors describe their method design as ―life course approach‖, which is somewhat misleading. According to my understanding, life course approaches take into account (critical) transitions and developmental changes occurring over time, for example from childhood to adolescence, adolescence to adulthood etc. I am not really convinced that this is given here, although a relatively long study period (1994 to 2016) was considered. Nevertheless, I agree with the conclusions in the discussion (e.g. p.12, l.21) that accumulative processes might have contributed to the identified associations between income/ housing satisfaction and self-rated health (as for instance suggested on p.13, l.39). To make it clear, my critique concerns the choice of wording in the abstract, keywords, and introduction. The authors‘ conclusion about possible life course effects suggested seem to be highly plausible.

Authors: We changed life course approach to ―life stages‖.

The study refers to a specific context (Germany). Therefore, the study would benefit from a brief description of the (socio-economic and political) context, and how it might has contributed to the findings.

Authors: We included information in the German context and the resulting generalizability of our results. http://bmjopen.bmj.com/

Germany there are a number of measures to prevent poverty and homelessness. Thus, even if on October 2, 2021 by guest. Protected copyright. someone is dissatisfied with one's own housing or income situation, it can not be assumed it results in a life-threating situation. Yet, school trips, cinema visits are not included in the calculation and must also be covered by the basic income. Therefore, sufficient social participation cannot always be achieved. Therefore, it can be presumed that the effects vary in countries where the welfare system is organised differently.‖

Data & Methods

The authors note that effect sizes (AMEs) were rather weak. Obviously, it is difficult to interpret the magnitudes of presented associations without reference measures/ indicators. Likewise, the presented plots – indicate rather the significance than the size/ magnitude of associations (which is an interesting finding per se!). However, I slightly wonder whether the authors want to consider some of the following alternative: BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from

- How do the AME‘s of income/ housing satisfaction compare to the AME‘s of other covariates? Actually, it would be interesting to see how the AME‘s of income/ housing satisfaction correspond to the AME‘s of (absolute) changes in income (e.g. in units of 1000 Euros).

- A relatively fine-graded scale of self-rated health was used. The AME‘s / magnitudes of associations will be more pronounced when a dichotomized dependent variable is used. As the use of dichotomized self-rated health is quite common in health research, it might also alleviate to compare the findings of the present study with other studies in the field.

- Alternatively, the AME‘s could be converted into a probability matrix – indicating how changes in income/ housing satisfaction affect the probability of experiencing good/poor health. For a more intuitive interpretation, self-rated health should be dichotomized then.

Authors: We are thankful for these suggestions and after careful consideration, we decided against implementing them for the following reasons:

1. In our view, it is difficult to interpret the AME‘s of the covariates because the set of control variables may not be appropriate for them. They were included in the model as potential confounders of the association between satisfaction and self-rated health. For example, while income likely confounds the relationship between income satisfaction and health, income satisfaction likely acts as a mediator in this relationship between income and health. Thus, the income ‗effect‘ does not reflect the total effect, but the direct effect that is not explained by income satisfaction. We therefore focused on suggestions (2) and (3) to facilitate the interpretation of effect size.

2. and 3. Although we acknowledge that the variable is categorical in nature, we opted for linear fixed-effects models that assume equal spaces between the categories for the following reasons:

• Our starting point for the model choice was that fixed effects models are in our view the most appropriate model choice for these statistical analyses, because the association between satisfaction http://bmjopen.bmj.com/ and health is likely confounded by third variables. While for some direct measures are available in the data (e.g. income, household composition), for other potential confounders (e.g. personality, socialization or childhood experiences) they are not. These unobserved confounders can thus not be included in the model to avoid confounding bias. Fixed-effects models are a potential solution to this problem by allowing us to account for all time-constant variables, even when they are not directly measured in the data.

• Fixed effects models for ordinal outcomes are currently not frequently available and there on October 2, 2021 by guest. Protected copyright. has also been a discussion about the amount of bias in these techniques. Ordered logit model are also based on the assumption of proportional odds, which does not hold in many applications.

• The conditional logit regression (i.e. logistic fixed effects regression) considers all persons who did not experience a change in both the explanatory and outcome variables over time as non- informative. Hence, persons with constantly good or poor health would have been dropped from the analysis, even if they become more or less satisfied over time. Because the dichotomized self-rated health variable is highly stable over time, this would have resulted in a considerably reduced sample size. In contrast, linear fixed effects models require only a change in the independent variable. In addition, odds ratios cannot be compared across subgroups (age groups in our case) because their scaling is affected by overall model fit, which likely differs between age groups ((please see Mood 2010, Brzoska et al. 2017). This is a major concern in conditional logit models, for which average marginal effects—the most frequently suggested solutation to this problem—and other solutions are not readily available and any interpretation of interaction effects must therefore be grounded in odds ratio effects. The linear fixed effects model is not affected by such issues. • The dichotomization of variables always results in a loss of variation, which can be suboptimal BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from for fixed effect analyses that compare the same person to himself over time. The actual health status may change, but observed value for the dichotomized indicator does not.

• Fixed effects linear probability models assume that the outcome probability is a linear function of the explanatory variables and predicted probabilities may fall outside the unit interval. Although the resulting heteroskedasticity in the errors can be handled by calculating robust standard errors, we still think that the aforementioned assumptions are too strong for this model to be viable in our statistical analysis. The amount of bias is unclear, and we consider treating our self-rated health measures as continuous variable as the more conservative approach.

• This variable has been used as continuous outcome in life-course studies for Germany, e.g. in Leopold & Leopold 2018, Leopold 2019.

To summarize: all statistical models require certain assumptions, and after carefully considering all available options, we still believe that analyzing self-rated health as continuous variable in linear fixed- effects models is the most plausible and conservative approach.

Literature:

• Brzoska P, Sauzet O, Breckenkamp J. Unobserved Heterogeneity and the Comparison of Coefficients across Nested Logistic Regression Models: How to Avoid Comparing Apples and Oranges. Int J Public Health 2017;62(4):517–20.

• Mood C. Logistic Regression: Why We Cannot Do What We Think We Can Do, and What We Can Do About It. European Sociological Review 2010;26(1):67–82.

• Leopold L. Health Measurement and Health Inequality Over the Life Course: A Comparison of http://bmjopen.bmj.com/ Self-rated Health, SF-12, and Grip Strength. Demography 2019;56(2):763–84.

• Leopold L, Leopold T. Education and Health across Lives and Cohorts: A Study of Cumulative (Dis)advantage and Its Rising Importance in Germany. J Health Soc Behav 2018;59(1):94–112.

#7 on October 2, 2021 by guest. Protected copyright.

It stated that ―… the health effects can be quite large for individuals who experience a large drop or rise in satisfaction.‖ (p.13, l.44)

It would be nice to see the marginal benefits of increasing income/ housing satisfaction regarding self- rated health. For example, are gains/ improvements in SRH larger by changes in satisfaction in bottom or top group?

Authors: We are thankful for this suggestion and agree that it is a relevant topic for the association between satisfaction and health. However, categorizing our satisfaction measure would have resulted in a very high number of interaction effects (between age, age², age³ and the satisfaction categories), which are not only difficult to interpret but also difficult to handle statistically. We therefore decided against this approach

#8 It is stated (p.8, l.5) that age, age², and age³ were included to control for curvilinear age-effects. The BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from different implications of age² and age³ should be made clear.

Authors: We are happy to clarify this point and have to admit that we did a minor mistake here because age³ is not included in the models. We changed this and clarified the implications of age and age²:

―These included age and age², which imply a non-linear relationship between age and health, whereby health declines increasingly faster in older ages.‖

It is unclear how the splines were derived. Please add a sentence or two to the method section.

Authors: We appreciate this remark and have to admit that we did make a mistake here. In fact, we did not model splines but dummy variables for age. We changed the legend of the figures accordingly.

Minor comments:

#10 p.13: ―key resource for participation in the community.‖ – maybe better to write ―social participation‖ instead?

Authors: We changed this part, which now states ―A subjectively sufficient income might have a more pervasive effect on an individual‘s life than housing satisfaction, because income is the key resource for social participation.

http://bmjopen.bmj.com/

#11 p.14: ―Emerging adults‖ – slightly awkward wording. ―becoming adults‖ might be better.

Authors: We changed the sentence to: ―Becoming adults is associated with gaining education and training needed as a foundation for their future income and professional perspective.‖ on October 2, 2021 by guest. Protected copyright.

#12

Table 1, line 45: a number (―1‖) is missing

Authors: We added the number.

#13

The spelling ―Runciman‖ in the reference should be corrected.

Authors: We corrected the spelling of Runciman.

#14 BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from

Reference to Stata 14 also Stata 15 used.

Authors: We changed the reference to correctly refer to Stata 15.

Reviewer: 2

Reviewer Name: Maria Nyholm

Institution and Country: Halmstad University, HALMSTAD, Sweden

Please state any competing interests or state ‗None declared‘: None declared

The paper aims to investigate the effect of income and housing satisfaction on self-rated health over the life course. Fixed effects regression was used for calculations.

The ―story line‖ is missing and the knowledge gap is not very well defined.

Authors: We changed the introduction based on the comments from the other reviewers and hope that this will clarify the ―story line‖ and make the knowledge gap clearer.

The independent variables need to be clearer. How satisfied are you with your place of housing? Validated? What does this scale measure? http://bmjopen.bmj.com/ Authors: Satisfaction scales are frequently used in happiness research to measure an individual‘s evaluation of different aspects of their life. Income satisfaction has also been used as an easy-to- measure indicator of subjective deprivation by Miething (2013). This interpretation is grounded in the theory of multiple discrepancies, according to which individual satisfaction can be seen as the result of multiple comparisons of the current situation with what an individual (a) had in the past, (b) what similar others have, and (c) the individual aspirations.

on October 2, 2021 by guest. Protected copyright.

Literature:

• Miething A. A matter of perception: exploring the role of income satisfaction in the income- mortality relationship in German survey data 1995-2010. Soc Sci Med 2013;99:72–79.

The results section with tables needs to be improve to clarify the ―story line‖.

Authors: We changed the results presentation and hope that it is suitable for improving the ―story line‖.

Reviewer: 3 BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from

Reviewer Name: Euijung Ryu

Institution and Country: Mayo Clinic, USA

Please state any competing interests or state ‗None declared‘: None declared

This study aimed to test association between housing and income satisfaction and perceived health over the life course using a population-based longitudinal cohort. It is relatively well written with good motivation of the study. However, it requires more detailed description of the variables and statistical methods, especially on how each variable was defined and what was included in the final models including what was done in cases when variables are highly correlated. One thing to note is that it appears (although not commented by the authors at all) the outcome was treated as a continuous scale, but it is a categorical variable which does not require to be equally spaced. Therefore, it is important to check if the study results hold by using proper categorical-based modelling. Specific comments are as follows:

The authors mentioned they used fixed effect regression without mentioning how the outcome was treated. Was it considered as a continuous scale or ordinal variable, or others? Without this information, simply mentioning fixed effect regression does not mean anything at all.

Authors: We appreciate this comment as is we indeed forgot to mention how the variable was treated. We clarified this in the manuscript and added the following sentence:

―The original scale was reversed, so that higher values indicate a better SRH, and treated as continuous variable.― http://bmjopen.bmj.com/ Although we acknowledge that the variable is categorical in nature, we opted for linear fixed-effects models that assume equal spaces between the categories for the following reasons:

• Our starting point for the model choice was that fixed effects models are in our view the most appropriate model choice for these statistical analyses, because the association between satisfaction and health is likely confounded by third variables. While for some direct measures are available in the data (e.g. income, household composition), for other potential confounders (e.g. personality, socialization or childhood experiences) they are not. These unobserved confounders can thus not be on October 2, 2021 by guest. Protected copyright. included in the model to avoid confounding bias. Fixed-effects models are a potential solution to this problem by allowing us to account for all time-constant variables, even when they are not directly measured in the data.

• Fixed effects models for ordinal outcomes are currently not frequently available and there has also been a discussion about the amount of bias in these techniques. Ordered logit model are also based on the assumption of proportional odds, which does not hold in many applications.

• The conditional logit regression (i.e. logistic fixed effects regression) considers all persons who did not experience a change in both the explanatory and outcome variables over time as non- informative. Hence, persons with constantly good or poor health would have been dropped from the analysis, even if they become more or less satisfied over time. Because the dichotomized self-rated health variable is highly stable over time, this would have resulted in a considerably reduced sample size. In contrast, linear fixed effects models require only a change in the independent variable. In addition, odds ratios cannot be compared across subgroups (age groups in our case) because their scaling is affected by overall model fit, which likely differs between age groups ((please see Mood 2010, Brzoska et al. 2017). This is a major concern in conditional logit models, for which average BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from marginal effects—the most frequently suggested solutation to this problem—and other solutions are not readily available and any interpretation of interaction effects must therefore be grounded in odds ratio effects. The linear fixed effects model is not affected by such issues.

• The dichotomization of variables always results in a loss of variation, which can be suboptimal for fixed effect analyses that compare the same person to himself over time. The actual health status may change, but observed value for the dichotomized indicator does not.

• This variable has been used as continuous outcome in life-course studies for Germany, e.g. in Leopold & Leopold 2018, Leopold 2019.

Literature:

• Mood C. Logistic Regression: Why We Cannot Do What We Think We Can Do, and What We Can Do About It. European Sociological Review 2010;26(1):67–82.

• Leopold L. Health Measurement and Health Inequality Over the Life Course: A Comparison of Self-rated Health, SF-12, and Grip Strength. Demography 2019;56(2):763–84.

• Leopold L, Leopold T. Education and Health across Lives and Cohorts: A Study of Cumulative on October 2, 2021 by guest. Protected copyright. (Dis)advantage and Its Rising Importance in Germany. J Health Soc Behav 2018;59(1):94–112.

In Abstract/Results, the third sentence (about the average marginal effects for income satisfaction for self-rated health) is hard to understand without know what these numbers mean. E.g., what does 0.02 mean in the context of self-rate health (what is the scale of this categorical variable used in the model)? The current Result section present only effect size with no statement about whether it is statistically significant or not (or whether the effect size is clinically meaningful). What that, it is hard to justify the statement in Conclusion section.

Authors: We added information on self-rated health to the abstract.

#3 BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from

In page 3, it is not a correct statement to say ―calculate fixed effects models‖. Models cannot be calculated. It‘s a tool to estimate fixed effects.

Authors: We are thankful for the reviewer for pointing to this mistake and now use the term ―estimate models‖ throughout the manuscript.

In page 3, the following statement is hard to understand what the authors mean. Please reword it. ―Yet, it has to be noted that these only apply for a change of one scale point per year, which is highly unlikely‖. If one scale point (whatever it means) is not meaningful, the authors needed to work with scales that actually have a meaning.

Authors: We deleted this statement.

In page 6, the statement ―this study does not use patient data‖ needs rewording. This study DOES use patient data (i.e., the variables used in this analysis are from patient data).

Authors: We are thankful for the hint that this point needs further clarification. The SOEP is a population-based panel survey for Germany. It does not contain data from patients, which to us implies an assessment by doctors or medical experts. This point has been clarified in the following way:

―The study is based on data from the German Socio-Economic Panel study (GSOEP, version 33), a http://bmjopen.bmj.com/ population-based longitudinal panel survey of private households in Germany. The SOEP is conducted by the German Institute for Economic Research (DIW Berlin), providing detailed information about changes and trends in the living conditions of the population living in Germany. Several additional samples were added since the start of the survey to account for the changing demographic composition of the population.‖

on October 2, 2021 by guest. Protected copyright. #6

In page 6/lines 3-8, the authors need to clarify what it means by ―excluding observations with missing data on any of the variables‖. What do ―observation‖, ―data‖, and ―variables‖ refer to? Did they mean to say they excluded any variable (whatever variables used in the analysis) if that variable has at least one missing data over multiple waves of surveys? The current statement is unclear on who and what variables what then ended up keeping in the analysis. Also, the authors need to specify how many they ended up excluding subjects in the analysis and what it means in terms of generalizability of the study cohort.

Authors: We are thankful for the hint that this point needs further clarification. The SOEP data is no cohort study, but rather a panel study, in which individuals are surveyed at multiple points in time. Because the same individuals are surveyed multiple times, panel data can be seen as having a multilevel structure in which observations (i.e. person-years) are clustered within persons. Thus, we meant to say that if at least one of the variables contains a missing value for a person in a given survey year, the whole observation (i.e. the person-year) has to be excluded from the analysis BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from sample.

This is a standard procedure in panel data analysis and generally recommended, e.g. by Brüderl & Ludwig 2015.

Given the word limit of BMJ Open, we decided against defining these terms in the paper. However, we clarified the inclusion and exclusion criteria for readers who are not familiar with panel data analysis:

―The sample contains information from persons who were surveyed up to 23 times (observations) during the period between 1994 and 2016. Only observations in which a person was aged 20 to 75 years were included in the sample to minimize the risk of bias due to selective mortality in older ages. After excluding observations for each person in which at least one of the variables contains a missing value in a given survey year, and persons for whom less than two observations in total remained, 182.238 and 202.042 observations from 23.702 men and 26.302 women were included in the final sample.‖

In page 8, the vast majority of texts under Covariates seem to fit better in Statistical Analysis section. For the Covariates section, more details are needed for each covariate considered. For example, what is period effect? Were all the variables listed considered as time-varying? If not, which ones were fixed and which ones were varying. How was equivalized disposable household income calculated? Not all the reader familiar with the modified OECD scale.

Authors:

(1) In medical sociology and public health covariates are commonly reported in the section ‗Measures‘, which is why we decided against changing the manuscript in this regard. http://bmjopen.bmj.com/

(2) To model the effects of time in statistical analysis, variables such as age, birth cohort and period can be included in the models. Period refers to specific effects of a single point in time that affect all individuals in the same way, such as the influence of financial crisis. Because the financial crisis likely influenced income satisfaction and health, a period effect has to be modeled to account for this source of confounding. Moreover, because it is often difficult to identify all relevant period effects,

survey year dummy variables are included to account for all specific effects. This is also a standard on October 2, 2021 by guest. Protected copyright. procedure in panel data analysis.

We added the following clarification:

―period effects (i.e. specific events at single points in time that affect all individuals in the same way, such as the influence of financial crisis) by including dummy variables for survey year‖

(3) Because we estimated fixed effects models, which use only variation within persons over time to control for hard-to-observe confounder that do not change over time, all variables in the models must be time-varying. This has been stated in the section ‗Covariates‘ of the manuscript:

―All fixed effects models were adjusted for potential time-varying confounders.‖

(4) We also clarified how the equivalized disposable household income was calculated:

―This scale assigns as weight of 1 to the household head, of .5 to each person aged 14 and over and of .3 to all children below 14 years of age. The quintiles were calculated for each calendar year using survey weights. They thus reflect the income distribution in the whole population living in Germany in BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from a given year.‖

In page 8/lines 41-46, it is not clear by controlling for all time-constant confounders in fixed effect regressions. Even if random effect models are considered, those time-constant confounders will/can be controlled. It requires more clarification on what it means by ―whether observed or not‖. Some of covariates listed in lines 46-48 need to be described here as well.

Authors: Random and fixed effects models differ in their assumptions about the association between the ―random effect‖ (which represents the common influence of all variables that do not change over time and are not included in the model, such as childhood and personality). In a random effects model, it is assumed that these unobserved variables are uncorrelated with the explanatory variables, i.e. income and housing satisfaction in our study, while the fixed effect model assumes that such a correlation exists. We believe that the assumption of a correlated random effect is more appropriate and plausible, because childhood factors and personality traits (which are not measured and thus summarized in the random effect) likely influence the subjective perceptions and evaluations of income, housing and health. Thus, there is likely a correlation between the random effect and satisfaction, which has to be accounted for to avoid confounding bias. Hence, fixed effects models are more appropriate for our analysis. Reviewer 1 seems to agree with our model choice.

We clarified what we mean by ―whether observed or not‖ for readers not familiar with fixed effects models.

―Fixed effects regressions were chosen because they use only the variation within a person over time and thus control for all time-constant confounders, even if no direct measures of them are available in the data (i.e. whether observed or not). [33, 34] These potentially include psychological traits,

childhood conditions, which are difficult to measure in surveys, but also observed factors such as birth http://bmjopen.bmj.com/ cohort.‖

In Stat Analysis section, it is unclear how many variables were considered in the final model. on October 2, 2021 by guest. Protected copyright. Authors: All variables were considered. We clarified this in the ‗Statistical Analysis‘ section:

―To further mitigate the problem of confounding bias, all time-varying covariates described in the previous section were included in the models.‖

#10

This is a longitudinal data. What time point was used for generating Table 1. At the first survey? Self- rate health is a categorical variable. It does not make sense to treat it as a continuous scale (i.e., mean/SD has no meaning). How were quintiles calculated? By the definition of quintiles, it does not make any sense to have the same range for all quintile if calculated in this cohort (by each gender separately or as a whole?). Also, it makes no sense to talk about range and means for dummy variables (need to present them as percentages). Again, this should be described in previous section.

We are thankful for this remark and clarified that Table 1 refers to the whole analysis sample: ―Descriptive statistics for the analysis sample (including all observations across time) are given in BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from Table 1.‖

The quintiles are calculated from the income distributions of each survey year to consider the changing income distribution over time. We added this information:

―The quintiles were calculated for each calendar year using survey weights. They thus reflect the income distribution in the whole population living in Germany in a given year.‖

The mean of a dummy variable is equivalent to the relative frequency and frequently reported in studies using panel data analysis. Percentages can be calculated by multiplying the means by 100.

#11

For Figures 1 and 2, is the change in SRH from previous wave or is it from the first wave until the last wave?

Authors: In fixed effects models, the person-specific mean is substracted from each variable in order to discard all variation between persons. The transformed data reflect deviations from the person- specific means across all time points, thus within-person changes over time. See Brüderl & Ludwig 2015 for further information.

#12

It will be informative to compare the results without adjusting for income and housing conditions to see how much satisfaction variables add in predictability.

Authors: We agree that it would be interesting to assess how much satisfaction variables add in http://bmjopen.bmj.com/ predictability. Yet, this was not the objective of our study. We aimed to assess the association between income and housing satisfaction and health. In order to achieve reliable results it is indispensable to control for income and housing satisfaction.

#13 on October 2, 2021 by guest. Protected copyright. There is no mention on the limitation of this study and whether it can be generalizable to other setting.

Authors: We added information on the specific conditions in Germany and the generalizability to other countries.

―Although the GSOEP is representative for the German population, generalisation to other countries may be difficult. Individual differences in health are strongly related to income inequality in general and studies have shown that countries with more unevenly distributed income, as indicated by the Gini coefficient, are more likely to have higher levels of health inequalities. [38, 39] Therefore, the presented results are only transferable to countries with a similar income distribution. Furthermore, In Germany there are a number of measures to prevent poverty and homelessness. Thus, even if someone is dissatisfied with one's own housing or income situation, it can not be assumed it results in a life-threating situation. Yet, school trips, cinema visits are not included in the calculation and must also be covered by the basic income. Therefore, sufficient social participation cannot always be achieved. Therefore, it can be presumed that the effects vary in countries where the welfare system is organised differently.‖ VERSION 2 – REVIEW BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from

REVIEWER Alexander Miething Department of Public Health Sciences, Stockholm University, Sweden REVIEW RETURNED 09-Jan-2020

GENERAL COMMENTS The conducted revisions significantly improved the manuscript. My comments and concerns were sufficiently addressed. Some language issues remain. The manuscript should undergo language editing and streamlining by a native speaker before publication. The following corrections should be considered: p.4: It should read: ―…. c) a group the individual estimates as most contrastive…‖ p.4, last line: ―… that the intensity differs.‖ I suppose it should read ―that the intensity of social comparisons differs.‖

p.6: It should read ―Our second hypothesis is that income and housing… ‖ instead of ―income or housing‖.

p.7: This long sentence should be splitted into two: ―After excluding observations for each person in which at least one of the variables contains a missing value in a given survey year, and persons for whom less than two observations in total remained, 182.238 and 202.042 observations from 23.702 men and 26.302 women were included in the final sample.‖

p.17: ―Furthermore, In Germany‖ should be changed to ―Furthermore, in Germany‖

p.17: avoid multiple ―therefore‖ in subsequent sentences. http://bmjopen.bmj.com/

REVIEWER Euijung Ryu Mayo Clinic USA REVIEW RETURNED 11-Feb-2020

on October 2, 2021 by guest. Protected copyright. GENERAL COMMENTS 1. In Article Summary, the second bullet point is about the statistical method used (fixed effects model). Why does this considered as a strength of the study and compared to what? All statistical models (fixed or random) have pros and cons, not necessarily one is superior over another if modelled appropriately. Although the authors tried to distinguish it (or reference #410, more precisely) from very well-established statistical term (fixed effect model), the model used here is just a variation of the fixed effect model with different parameterization. If I am not mistaken, reference #41 also mentioned how to tweak random effect model for situations like. If the authors want to emphasize the importance of their approach, please word it differently and so it does not confuse readers who are familiar with widely accepted statistical terms. The standard (i.e., without reconstructing Y and X) fixed effect model for panel data will not do what‘s stated in this manuscript.

2. Additionally, the second bullet point is too vague given that the Summary section should stand alone with high-level information. Also, there is simply no such a model that can account for ―all BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from possible confounders‖. If the authors meant to say observed and unobserved residual variations, it should be word it accordingly to be clear what it means.

3. In the response to Reviewer #3/question 1, the author‘s response in below is not justifiable. Having confounders are not a reason for picking statistical models. If modelled appropriately, any kind of regression models can account for confounders, and I do not believe there are any association studies that do not involve confounders.

― fixed effects models are in our view the most appropriate model choice for these statistical analyses, because the association between satisfaction and health is likely confounded by third variables.‖

4. For the same question, the authors did not address whether it is acceptable to assume ordinal categories are equally spaced. In addition to the potential issue mentioned by the authors (outside of the probability boundary), the assumption about equal space is important to gauge whether treating continuous is acceptable or not. Currently, the authors did not comment.

5. I would agree with the authors not dichotomizing the outcome. However, this does not justify why the authors should use a model designed for continuous variables. If ordered logit models do not meet proportional odds assumption, there are other options still treating it as categorical variables, which includes partial proportional odds model and nominal odds model. The authors did not justify why they think treating it as continuous variable is more conservative approach. Nominal categorical model will definitely a conservative approach.

6. Supplemental tables still have information using spline approach, http://bmjopen.bmj.com/ but no mention on such approach in the main text.

VERSION 2 – AUTHOR RESPONSE

Reviewer: 1

Reviewer Name: Alexander Miething on October 2, 2021 by guest. Protected copyright.

Institution and Country: Department of Public Health Sciences, Stockholm University, Sweden

Please state any competing interests or state ‗None declared‘: None declared

Reviewer comments:

The conducted revisions significantly improved the manuscript. My comments and concerns were sufficiently addressed.

Thank you. We are happy that we were able to address your concerns and comments.

Some language issues remain. The manuscript should undergo language editing and streamlining by a native speaker before publication. According to your advice, we sent the manuscript to a language editing office. Due to the large BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from number of changes, we have refrained from using track changes and from copying the changes in this document. We hope that the quality of the manuscript improved.

The following corrections should be considered: p.4: It should read: ―…. c) a group the individual estimates as most contrastive…‖ p.4, last line: ―… that the intensity differs.‖ I suppose it should read ―that the intensity of social comparisons differs.‖ p.6: It should read ―Our second hypothesis is that income and housing… ‖ instead of ―income or housing‖.

We have changed the wording according to your suggestions.

We split the sentence as follows:

―Persons for whom less than two observations were assessed and observations for each person in which at least one of the variables contained a missing value in a given survey were excluded. In total, 182.238 and 202.042 observations from 23.702 men and 26.302 women were included in the http://bmjopen.bmj.com/ final sample.‖

p.17: ―Furthermore, In Germany‖ should be changed to ―Furthermore, in Germany‖

We have changed the wording according to your suggestions.

on October 2, 2021 by guest. Protected copyright. p.17: avoid multiple ―therefore‖ in subsequent sentences.

Thank you very much for your thorough review. We reworded these sentences.

―Hence, sufficient social participation cannot always be achieved. It can be presumed that the effects vary in countries where the welfare system is organized differently.‖

Reviewer: 3

Reviewer Name: Euijung Ryu

Institution and Country: Mayo Clinic, USA

Please state any competing interests or state ‗None declared‘: None declared #1 BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from

In Article Summary, the second bullet point is about the statistical method used (fixed effects model). Why does this considered as a strength of the study and compared to what? All statistical models (fixed or random) have pros and cons, not necessarily one is superior over another if modelled appropriately. Although the authors tried to distinguish it (or reference #410, more precisely) from very well-established statistical term (fixed effect model), the model used here is just a variation of the fixed effect model with different parameterization. If I am not mistaken, reference #41 also mentioned how to tweak random effect model for situations like. If the authors want to emphasize the importance of their approach, please word it differently and so it does not confuse readers who are familiar with widely accepted statistical terms. The standard (i.e., without reconstructing Y and X) fixed effect model for panel data will not do what‘s stated in this manuscript.

Fixed effects regression has two different meanings in statistics, which are both frequently used in statistics.

In multilevel analysis, the difference between random and fixed effects refers to whether parameters do (not) or are (not) allowed to vary between subgroups. In panel data analysis, the difference between random and fixed effects models refer to different assumptions about the correlation between the time-constant error term and the explanatory variable. The random effects model assumes that this correlation is equal to zero (i.e. does not exist), while the fixed effects model assumes that such a correlation exists. To account for it, a fixed effects model applies standard OLS estimation to transformed data, in which all variables are expressed as deviations from the unit- specific mean. Our work follows the second assumption, as we are analysing panel data.

We agree that the wording of the second bullet point was imprecise and changed it accordingly:

―In contrast to previous studies, our results are based on fixed effects models that account for all stable hard-to-observe confounders (e.g. personality), which likely confound the relationship between health and satisfaction. http://bmjopen.bmj.com/ However, reverse causation (i.e. health influencing satisfaction) cannot be ruled out.‖

Additionally, the second bullet point is too vague given that the Summary section should stand alone

with high-level information. Also, there is simply no such a model that can account for ―all possible on October 2, 2021 by guest. Protected copyright. confounders‖. If the authors meant to say observed and unobserved residual variations, it should be word it accordingly to be clear what it means.

We rephrased the second bullet point as pointed out in the first comment.

In the response to Reviewer #3/question 1, the author‘s response in below is not justifiable. Having confounders are not a reason for picking statistical models. If modelled appropriately, any kind of regression models can account for confounders, and I do not believe there are any association studies that do not involve confounders.

We agree that having confounders it not an argument for choosing between regression models and that any regression can account for confounders. However, this notion assumes that direct measures of all confounders are available in the data, which is often not the case in observational studies. For example, the GSOEP does not include any measure of personality traits. Thus, with standard BMJ Open: first published as 10.1136/bmjopen-2019-034294 on 4 June 2020. Downloaded from regression models, we would not have been able to account for these confounders by including them in the models. If not accounted for, such unmeasured confounders might lead to confounding bias, thus threatening the internal validity of our results. Hence, we believe that having unmeasured confounders is a valid argument for choosing a regression model that is able to account for this source of bias over other regression models that are not.

We agree that the wording was imprecise and changed it accordingly:

―Because the association between satisfaction and health is likely confounded by third variables, for which no direct measures are available in the data and which thus cannot be easily controlled for, fixed effects models were regarded as the most appropriate model choice for these statistical analyses.‖

For the same question, the authors did not address whether it is acceptable to assume ordinal categories are equally spaced. In addition to the potential issue mentioned by the authors (outside of the probability boundary), the assumption about equal space is important to gauge whether treating continuous is acceptable or not. Currently, the authors did not comment.

I would agree with the authors not dichotomizing the outcome. However, this does not justify why the authors should use a model designed for continuous variables. If ordered logit models do not meet proportional odds assumption, there are other options still treating it as categorical variables, which includes partial proportional odds model and nominal odds model. The authors did not justify why they think treating it as continuous variable is more conservative approach. Nominal categorical model will definitely a conservative approach.

All statistical approaches are based on assumptions, which might be more (or less) valid in some http://bmjopen.bmj.com/ contexts than in others. We had to choose the approach with the most plausible and appropriate set of assumptions in our given context.

We were faced with a trade-off situation between accounting for a very likely and potentially severe bias due to unobserved confounders and a potential bias due to not modeling the outcome variable entirely appropriately. Unfortunately, there is no generally accepted approach to fixed effects modeling for ordinal outcomes that yields unbiased and consistent estimates. Likewise, there is currently no approach available to account for unmeasured confounders in partial proportional and on October 2, 2021 by guest. Protected copyright. nominal odds models. Thus, in order to account for unmeasured confounders such as personality, only fixed effects models for continuous and binary outcomes are currently available. To clarify why we chose fixed effects models, we added the following sentences to the limitations sections.

―Moreover, in order to be able to account for unobserved stable confounders, we had to treat our measure of self-rated health as a continuous variable, assuming that the ordinal categories are equally spaced. However, we believe a potential confounding bias poses a higher threat to internal validity.‖

Supplemental tables still have information using spline approach, but no mention on such approach in the main text.

Thank you very much for your thorough review. We changed the heading of the supplemental tables.