How Migration Status Shapes Susceptibility of Individuals’ Loneliness to Social Isolation

Objectives: Our research provides competing hypotheses and empirical evidence how associations between objectively social isolation and subjective loneliness differ between host populations, migrants, and refugees. Methods: The analysis uses data of 25,171 participants from a random sample of the German population (SOEP v.35). We estimate regression models for the host population, migrants, and refugees and test five hypotheses on the association between social isolation and loneliness using a Bayesian approach in a multiverse framework. Results: We find the strongest relative support for an increased need for social inclusion among refugees, indicated by a higher Bayes factor compared to the hosts and migrants. However, all theoretically developed hypotheses perform poorly in explaining the major pattern in our data: The association of social isolation and loneliness is persistently lower for migrants (0.15 SD−0.29 SD), with similar sizes of associations for refugees and the host population (0.38 SD−0.67 SD). Conclusion: The migration history must be actively considered in health service provision and support programs to better cater to the needs of the different groups.


SM 1 -Loneliness -Measurement Invariance
We ran measurement invariance analyses over the three groups of analyses in our study. Overall model fit is very good (based on CFI > 0.85 and RMSEA below < 0.1 criterion) in all three groups (Table S1a, for measurement quality adjusted cut-offs, see [1]). The model used is represented in figure S1. Comparing different models based on subsequently stronger restrictions, we can see that scalar measurement invariance holds across sex, age, and migration status (based on the ΔCFI and ΔRMSEA < 0.01 criterion [2,3]). This means that both the association of social isolation and loneliness as well as the levels of loneliness can be meaningfully compared across the three migration groups. The difference we find are therefore unlikely to derive from substantial differences in the way the three-item loneliness scale works in the three groups.  Figure S1 -Loneliness (LONE) questionnaires used in the SOEP a The questionnaires of SOEP are not copyrighted and free of charge [4]. Presented are the English translations of the German original questionnaires. Source: [5] Figure S2 -Factor structure for Loneliness (LONE). Refer to Figure S1 for item formulation in the survey and to Table S2 for summary statistics of the items

SM 2 -Coding decisionsgeneral overview
In the following, we present the coding of all variables used in the analysis, adding to the replication of this study. This variable consists of five individual variables asking for the role relation providing emotional support. Each variable is re-coded as dummyindicating whether a role relation was named.
Afterwards, the information is consolidated to one variable, indicating whether any emotional support is subjectively granted. This variable consists of five individual variables asking for the role relation providing informational support. Each variable is re-coded as dummyindicating whether a role relation was named.
Afterwards, the information is consolidated to one variable, indicating whether any informational support is subjectively granted. This variable consists of five individual variables asking for the role relation providing appraisal support. Each variable is re-coded as dummyindicating whether a role relation was named.

SM 3 -Social isolation index cut off choicesin detail
We base the construction of social isolation on the seminal work on the need to belong by Baumeister and Leary (1995) [8]. The authors set out two principles for the sense of belonging that guide our definition of social isolation. First, the principle of satiation refers to the need for a minimum level of social connectedness to be present. This means that individuals evaluate themselves as lonely primarily if a certain degree of social connectedness is not present. It implies a threshold effect of social connectedness on loneliness. From this principle we derive relevance of analyzing social isolation, as a categorical concept, instead of degrees of social connectedness. Second, the substitution principle refers to the idea that certain social connections can replace others, hence shielding from isolation to a certain extend. This is reflected in the composition of this variable.
Social connections can cover different dimensions of social life, for example family and household, social activities, or social support [9]. If an individual lacks these social linkages within a certain dimension, we will define the individual as being deprived in this particular social dimension in contrast to being integrated.
If individuals are deprived in several dimensions, thereby not satisfying the satiation criterion, we will consider them to be overall socially isolated.
Concretely, we measure social isolation across three domains consisting of several indicators [9]: This means that an individual is defined as being social isolated if the number of dimensions it is integrated into is equal or lower than a certain threshold t s si .  With respect to the effect size threshold chosen in 1 , one could of course consider other values for this cut-off. Figure S6 shows the relationship between this choice and the degree of support 1 would get using our data and model.
The higher the threshold is chosen (meaning only very large differences in effect size are considered to be consequential), the less support 1 gets. We chose a reference cut-off of 0.2 SD, because this value about the size of the maximum difference in loneliness that is found between different age groups (age range 20 to 80) in a previous study using German data [10]. It is therefore a cut-off that considers only substantial differences (approximately as large or larger than strongest differences found across all age) as evidence in favor of 1 . Consequently, the strong support we find for H1 corroborates the visual impression of figure 3 in the manuscript that the differences between the migrant group and the host and refugee group are indeed substantial in size and meaningful.

SM 5 -Multiverse analysis and discussion
Recent research proposes that studies based on secondary data analysis report all plausible specifications of their data coding and sample definitions [11,12]. It reduces the probability of reporting findings, specific to certain idiosyncratic decisions in the process of the data analysis [13,14]. Based on the definition of social isolation and the different cut offs presented additionally to alterations in sample definition and coding, we report all plausible specifications in a multiverse framework (specifications are listed in Figure S6).
As the section on the social isolation index indicates, researchers not only take decisions on how to construct different measures of a concept. Through these decisions, they are able to have influence on the results presented.
In our analyses, we take several major coding decisions. In the following, we explain these different     is the social isolation indicator. is the parameter of interest that we will compare across the three groups to evaluate the five hypotheses. is a matrix of control variables, and is the corresponding vector of coefficients.
One index needs to be mentioned separately: indexes age and gender specific groups. The model is therefore a multilevel model. Individuals nest within 24 gender specific age groups and is the random effect for each group with standard deviation . is the individual specific error-term with standard deviation . We therefore allow the association of social isolation with loneliness to vary across gender specific age groups. This is important as in a second step the estimates of the migrant and refugee group are post-stratified and averaged, with the same distribution across gender specific age groups as the host population. The post-stratification procedure accounts for the possibility that differences in the association found in the data could be attributed to the strong differences in age and gender composition of the three samples. Therefore, the hypotheses are evaluated based on these post-stratified parameters from the aforementioned multilevel regression models: is the number of observations in each of the gender-specific age groups in the host population.

SM 8 -Bayesian Evaluation of Informative Hypotheses (BEIH)
The BEIH framework is designed for a comparative evaluation of competing hypotheses. It is based on a Bayesian approach to statistical modeling and differs in certain respects from the common frequentist approach [15,16]. The general estimation procedure for the posterior distribution of the parameters we use is the Integrated Nested Laplace Approximation (INLA) [17,18] implemented as a package for R (www.rinla.org).
Our hypotheses imply a ranking of the association strength of the central parameters ̅ . In a Bayesian framework we can estimate the probability that such a ranking -and by extension the proposed hypothesis -is supported by model and data. We therefore get ( | ( )) where s indexes the specification of the data and the model as noted above.
The key feature of the BEIH method is to compare the observed support ( | ( )) for the hypothesis from the estimated posterior distribution of the coefficients to the expected support ( ) for the hypothesis (prior probability). The prior probability is calculated assuming random ordering of the coefficients [19,20]. From the relation of the two probabilities, we get the Bayes factor: If the Bayes factor is larger than 1, the hypothesis formulated has more predictive power than given by chance. Otherwise, if the Bayes factor is smaller than 1, the hypothesis is less probable than by chance.
As we test more than two hypotheses against one another, we additionally calculate posterior model probabilities (PMP): ; ∈ 2 , 2 , 2 , 2 The PMP states how much support one hypothesis receives compared to the overall support that all hypotheses under investigation receive. The range of the PMP is from 0 to 100%. The higher the value, the stronger the support for the hypothesis in question compared to the competing hypotheses [20].
To illustrate the Bayesian Evaluation of Informative Hypotheses (BEIH) and the ranking of the different hypotheses, we use the increased need hypothesis (H2a) as an example.

ℎ < <
The hypothesis proposes a ranking of the strength of association between social isolation and loneliness. ßh represents the parameter for the host population, ßm the parameter for migrants of the first generation and ßr the parameter for refugees. In this case, the hypothesis does not propose equal strength of association but a ranking. This is indicated by the equality sign between parameters. Derived from an increased need to have social contacts, the hypothesis postulates the largest association between social isolation and loneliness for the group of refugees, with decreasing association parameters for migrants and refugees.
Applying BEIH we first specify alternative hypotheses with the different rankings proposed between parameters (see Table 1).
Next, every hypothesis possesses a defined prior that is the probability of finding the hypothesis in the data by chance. The more restrictions or inequalities we place between parameters in one hypothesis, the less support we will find in the data by chance. For example, 3 represents the hypothesis without any rankings between parameters. It accepts all possible inequalities between the coefficients. Consequently, the contextual relevance hypothesis receives a prior of one, while the four hypotheses belong to the set of context moderation hypothesis have priors based on the number of constraints between parameters. The refugee exceptionalism hypothesis (H2b) is much more elaborate that H3, with one restriction in relation to how the association found in the refugee population should be compared against the host-and migrant population. Most restrictions are placed between the hypothesis including two signs of order, such as the increased need hypothesis (H2a). The likelihood to find these hypotheses by chance further decreases. Hence, their prior probabilities are smaller as well.
Applying our regression models on the data using INLA, we retrieve a posterior distribution. From this distribution, it is possible to draw random samples. From a sample of e.g. 100 000 draws we can now ask the question: How often does e.g. hypothesis hold true in our sample from the posterior distribution?
We calculate the marginal likelihood of observing one hypothesis and compare it to the expected likelihood given by chance (our prior distribution). Given the observed support for the posterior distribution and the expected support from the prior of the hypotheses, we can calculate the so-called Bayes factor for each hypothesis (BF) [21], a comparison between the actual outcome and expectation by chance. The proportion 1 denotes the grade of support from the posterior distribution, t standing for the hypothesis under consideration. After that we compare the hypothesis to the alternative, for instance that there is no ordering ( 1 ). 1 is defined as the proportion of the prior distribution (expectation) that is in agreement with the hypothesis . The formula to derive the Bayes Factor is:

Introduction
It is uncontested that that there are differences in the prevalence of social isolation and loneliness between migrants, refugees, and host populations. Migrants are more often subject to social isolation than host populations, as their networks in the new environment need to be (re-) established [22,23]. Additionally, they are also prone to experiencing higher rates of loneliness due to cultural differences and language barriers [24,25]. The same result has been found for refugees [24]. Nonetheless, there is also evidence that migrants' level of loneliness diminishes with time spent in the country of destination, approaching loneliness levels of the host population [26]. Whether comparable trends exist for refugees has yet to be established in longitudinal studies. Moving beyond the investigation of the prevalence in social isolation and loneliness, we focus on the association of the two constructs in our study. The economic, legal, and social differences in context motivate our investigation into the question whether there are relevant differences in the way social isolation is associated with loneliness among regular migrants, refugees, and the host population.
We develop five competing hypotheses about the association of social isolation and loneliness when comparing host, migrant, and refugee populations. These hypotheses imply that the three groups might differ in their evaluation of social networks and support given their different economic, legal, and social circumstances (  [20,27], testing the robustness of our results in a multiverse framework [11,12].
Competing hypotheses H1: The contextual relevance hypothesis -From an evolutionary perspective, feeling lonely is a warning sign of the human body. It indicates the deviation from a norm of socializing and hence the presence of a potential hazard in being unprotected without social support of other humans [28]. Research suggests that this mechanism has been established relatively early in human history and has coined the structure of the human brain to be sensitive to feelings of loneliness [28][29][30]. Hence, from a perspective of evolution we would expect susceptibility to loneliness in all human cultures and conditions. Further, a stronger version of this hypothesisgiven a non-clinical, non-institutionalized context -would expect social isolation to predict loneliness to a similar degree, regardless of the context, and in consequence also regardless of migration background. This focus on commonalities between migration groups could be dubbed the evolutionary dominance hypothesis. Given that social circumstances and exposure to prior (possibly critical or traumatic) experiences vary greatly between migrants, refugees, and host population, we propose the competing contextual relevance hypothesis. Thus, stressing the differences between the groups, we expect differences in the association of social isolation and loneliness between host, migrant and refugee population to be of substantive size. In detail, we expect the maximum difference between the associations to be above a threshold of 0.2 standard deviations (for a more detailed discussion of the choice of this value, see SM 4 in the supplemental material).
Expanding on the contextual relevance hypothesis, we propose four hypotheses that make competing predictions the differences in the association between social isolation and loneliness.
H2a: The increased need hypothesis -The post-migration phase requires new skills and knowledge to fully participate in society. Social networks are an important structure, and have the potential to aid integration of migrants [31] and refugees [32,33]. Given the peculiarity of the displacement experience, refugees tend to suffer even stronger resource losses, including income and property loss, expenses of the displacement, physical and mental strain during migration as well as loss of social contact and trust in neighbors, colleagues, and family [34][35][36][37]. Given the higher demand for social inclusion and support among refugees due to resource loss, the consequences of objective social isolation should weigh more strongly in perception on refugees. We hence expect the association of social isolation with loneliness to be strongest among refugees, and weaker for other migrants. It is supposedly weakest for the host population who on average have the lowest need to substitute resources.
H2b: The refugee exceptionalism hypothesis -Alternatively to H2a but in a similar line of argument, it can be hypothesized that the differences between the three groups is not gradual in nature, but categorical.
Refugees face a more difficult situation in the host country regarding social, cultural, and legal integration.
The involuntary disruption of social networks is fundamentally different from that of other migrants and the host population. This unnatural break from social resources sets refugees apart with respect to their vulnerability and hence a need to receive support. Violence of the past remains visible in the aftermath of refugee migration, for instance manifesting in post-traumatic stress disorder [36,38]. Moreover, refugees experience involuntary family separations, entailing fear of family members remaining in danger [39][40][41][42][43].
Finally, refugee housing further isolates the newcomers from the host population and other migrants, with an effect on refugee mental health [44]. A functioning social network, in quantity but also in quality support, is valuable in this context specific strain [45,46]. The lack of social resources under these excluding circumstances might lead to an increased emotional response to the externally induced social isolation.
Hence, we expect the association between social isolation and loneliness to be strongest for refugees, with no systematic differences between host and migrant population.
H2c: The numbing hypothesis -This hypothesis makes the opposite prediction to H2b. It is based on the insight that refugees have a higher risk of suffering from Post-Traumatic Stress Disorder (PTSD) and depression due to the extreme circumstances amid their resettlement [47]. Psychological responses to trauma can include a series of bodily reactions such as depersonalization and derealization symptoms [48]. have in an emotional situation, also connected to emotion suppression [50]. We hypothesize that numbing also affects the reaction of refugees towards experiences of social isolation. In the refugee situation, numbing means the dampening of their perception of loneliness. We therefore expect a lesser association between social isolation and loneliness among refugees compared to the host and migrant population.
H2d: The anticipation hypothesis -No matter whether consulting economic theory [51][52][53][54], health research [55,56], or insights on social networks [54,[57][58][59], it appears that migrants and refugees moving to another country systematically differ from those they leave behind. Though not fully conclusive, previous studies show that migrants are healthier and more socially connected than the average person in their country of originan indicator for self-selection. They actively consider the opportunities and opportunity costs.
For refugees, the trade-off is even stronger due to the nature of the migration process. Both groups might more readily come to terms with insufficient networks for the time being. Based on these assumptions about anticipation of reduced social connections in the post-migration phase, the last hypothesis postulates that migrants show a lower association between social isolation and loneliness than the host population. We expect refugees to show the weakest association of the three groups.