PNAS Nexus, 2022, 1, 1–8 https://doi.org/10.1093/pnasnexus/pgac195 Advance access publication date: 21 September 2022 Research Report Structural measures of personal networks predict migrants’ cultural backgrounds: an explanation from Grid/Group theory a, b,c b b,c,d,e José Luis Molina *, Juan Ozaita , Ignacio Tamarit , Angel Sánchez , Christopher McCartyf and H. Russell Bernardg a GRAFO-Department of Social and Cultural Anthropology, Universitat Autònoma de Barcelona (UAB), 08193 Bellaterra, Spain b Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III de Madrid (UC3M), 28903 Madrid , Spain c Unidad Mixta Interdisciplinar de Comportamiento - Unidad Social (UMICSS) UC3M-UV-UZ, UC3M, 28903 Madrid , Spain d Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50009 Zaragoza , Spain e UC3M-Santander Big Data Institute (IBiDat), 28903 Getafe, Spain f Department of Anthropology, University of Florida (UFL), Gainesville, FL 32611 , USA g School of Human Evolution and Social Change, Arizona State University (ASU), Tempe, AZ 85281, USA ∗ To whom correspondence should be addressed. Departament d’Antropologia social i cultural, Facultat de Lletres, c/ de la Fortuna s/n, 08193-Bellaterra (Spain). Email: joseluis.molina@uab.cat Edited By: Noshir Contractor Abstract Culture and social structure are not separated analytical domains but intertwined phenomena observable in personal networks. Drawing on a personal networks dataset of migrants in the United States and Spain, we show that the country of origin, a proxy for diverse languages and cultural institutions, and religion may be predicted by specific combinations of personal network structural measures (closeness, clustering, betweenness, average degree, etc). We obtain similar results applying three different methods (a multinomial logistic regression, a Random Forest algorithm, and an artificial neural network). This finding is explained within the framework of the Grid/Group theory that has long posed the interdependence of social structural and cultural features of human groups. Keywords: cultural signature, social signature, personal networks, grid/group theory, migration Significance Statement: Drawing on a rich dataset about migrants in two countries (the United States and Spain), we predict the country of origin and, to a lesser degree, the religion of individual migrants using three different methods. This finding shows that structural and cultural dimensions are intertwined, as suggested by the Grid/Group theory. Moreover, each group of migrants exhibits a particular net- work pattern or “cultural signature,” much like the “social signature” that individuals uniquely exhibit in their structure of social interactions. This finding opens new avenues for studying the interdependence between social and cultural phenomena and the study of cultural diversity through a structural lens. Introduction the level of control on shared classifications of the world, includ- The study of human societies has sought meaningful patterns of ing the ascription of people to these categories (“what can I do”); behavior either in the structure of interactions (“the social struc- and group, or the level of control of ego’s membership in bounded ture”) or in the ensemble of values, norms, beliefs, and mate- groups (“who am I”; see Fig. 1A). The grid axis measures the level of rial realizations of their members (“the culture”) (1, 2). Nadel (3, control that the ensemble of values, norms, and given categories 4), among others (5, 6), points out the difficulty of simultane- exert on the individual. A “high grid” implies that the self is bound ously considering social structure and culture because status and to the ascribed social category to which it pertains. Consequently, role description are typically undertaken through formal meth- these categories firmly constrict the range of alternative behav- ods, whereas the cultural content of such positions is naturally iors and the associated internalized values. A pariah in a caste described through qualities and attributes. One of the few at- system would be an extreme instance of this case. Conversely, a tempts to reconcile the analysis of both dimensions of human “low grid” allows individuals to choose among alternative behav- societies was posed by Mary Douglas and her colleagues (7–10) iors and achieve new roles (at least in theory), typically through with Grid/Group theory (11, 12). This theory states that all human competition. Melanesian big men or capitalist entrepreneurs are societies can be meaningfully classified along two axes: grid, or instances of this case. Competing Interest: The authors declare no competing interest. Received: January 14, 2022. Accepted: September 19, 2022  C The Author(s) 2022. Published by Oxford University Press on behalf of National Academy of Sciences. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. 2 | PNAS Nexus, 2022, Vol. 1, No. 4 Fig. 1. (A) Original formulation of the Grid/Group theory by Douglas [1996 (1973)]; and (B) ideal types of society (8). The group axis measures the level of constraint that the social sitivity,” “frequency of interaction,” and the “boundedness of the unit exerts on the individual. A “high group” implies a high density group” (which can be measured with, among other methods, clus- of interaction among group members, long-term commitment, tering, betweenness, and average degree). For the grid dimension, strong identification with the group, and defense of the corporate the authors suggest indicators intended to measure the extent of interests. Conversely, “low group” constraint gives “individuals the externally imposed rules, like “role specialization,” “asymmetry of freedom to interact as individuals with other individuals,” linking role exchanges,” “role achieved or ascribed,” and the level of “ac- loosely bounded social units. A monastic order and freelance pro- countability” in case of inadequate role performance. fessionals would be instances of both extreme cases, respectively. The Grid/Group theory is strongly influenced by Durkheim’s Generally speaking, both coordinates are meant to be related or (16, 17) notions of the different levels of control exerted on the “compatible”—e.g. an individualistic society (low grid/low group) individuals through the system of shared classifications (which will conceive nature as raw materials ready to be used, while a hi- includes religion) and the formulation of four ideal types of social erarchical society (high grid/high group; see Fig. 1B) will address phenomena combining two axes: “moral regulation” (∼grid) and access to nature in a ritualistic way through an elaborated set of “social integration” (∼group). In this vein, Triandis (18) deemed prescriptions (8). the Grid/Group proposal to be one of the earlier conceptualiza- Despite the different versions of Grid/Group theory (11), and tions of his “Individualism–Collectivism” theory, which has en- the lack of a coherent set of theoretical statements, we find that gendered a rich literature (19–21). Gelfand (22) reframed this pro- the basic assumption of the theory can be supported empirically, posal recently as “Tight–Loose cultural orientations,” which allow opening an avenue for predicting cultural variation in human so- a meaningful classification of nations, states, organizations, and cieties from samples of social structures, operationalized here as even personality types across the world along this axis, primar- ensembles of personal networks. In this vein, there are some pro- ily relying on surveys. This latter proposal could be understood posals of operationalization, made by either qualitative case stud- as similar to the grid dimension (the level of cultural control of ies (13, 14) or by systematic cultural comparison (15). In particular, individuals’ cognitions and behavior), and also intended to en- the book Measuring Culture (9) elaborates on a series of indicators able cross-cultural comparisons. Like in this case of Gelfand we for both group and grid dimensions for different levels of analy- use the country of origin as a proxy of the cultural dimension. sis (e.g. minorities, organizations, tribes, countries, and so on). For By contrast, network data available for testing the group dimen- the group dimension, the authors suggest a polythetic panoply of sion were scarce and challenging to collect until recently. Here, we network measures as “proximity of individuals” (closeness), “tran- use a rich set of personal network data to identify the country of Molina et al. | 3 Table 1. Distribution of migrant personal network cases across Table 2. Distribution of migrant personal network cases across countries. religions. Origin/destination USA Spain Total Religion USA Spain Total Men Women Men Women Men Women Men Women Dominicans 47 46 37 24 154 Christians 77 65 59 60 261 Moroccans 0 0 25 41 66 Muslims 2 0 71 51 124 Senegambians 0 0 54 13 67 Other 21 26 30 10 87 Argentinians 0 0 38 39 77 100 91 160 121 472 Puerto Ricans 36 37 0 0 73 Colombians 11 3 0 0 14 Cubans 5 2 0 0 7 bians, Argentinians, and Puerto Ricans accounting for more than Guineans 0 0 6 4 10 70 cases. Table 2 shows the distribution of cases by “Religion.” In Haitians 1 2 0 0 3 Mexicans 0 1 0 0 1 this case, the category “Christian” includes Catholics (N = 234) and 100 91 160 121 472 Protestants (N = 32); the whole sample was comprised of 49.6% Catholics. origin and religion of 472 migrants from Africa and Latin Amer- The analytical methods ica to the United States and Spain. Several authors have shown We framed the problem as a six-class, single-label classification that individuals develop patterns of social interaction, or “social task. The goal of this task is to predict the country of origin signatures,” that are remarkably stable through time, even with a of a person based on properties of his or her ego network. If high rate of turnover and across different channels of communi- these measures provide useful information to categorize a cul- cation (23–25). We test the existence of such patterns at the aggre- tural trait, then the plausibility of the Grid/Group theory frame- gate level—cultural signatures—and interpret the results in light work increases. As an additional result, we repeat the process with of the Grid/Group theory (i.e. the covariation of group and grid di- religion as the target cultural trait, including a new subset of vari- mensions). ables. The variables used to predict the country of origin are close- The personal networks dataset ness, clustering, average degree, assortativity, and betweenness. These variables are combined with average perceived closeness The dataset was collected from 2004 to 2006 for the project De- with alters in origin country (closeness origin) and with alters in velopment of a Social Network Measure of Acculturation and its the destination country (note that this is a measure of the rela- Application to Immigrant Populations in South Florida and North- tionship ego–alter) (closeness residence). We also include the vari- eastern Spain, funded by the National Science Foundation (BCS- able μ, that characterizes the way an individual organizes his ego 0417429). Personal networks were collected with the aid of the network in terms of perceived closeness to the alters (31). Along software EgoNet, in a four-module survey that lasted, on aver- with these predictors, we included the variables gender (sex), level age, about 1.5 h. Questions about ego, including both demographic of education (educ), and time of residence in the destination coun- variables and outcome variables that we wanted to predict us- try (fmig2) as control variables. ing 95 network characteristics. Second was a question to elicit al- For the religion variable, we apply the same set of controls and ters or the “name generator.” For this study, we used the following the same structural predictors. As we lacked a variable that tells prompt: “Please give us the names of 45 people you know who us the presence of religion in the alters, we employed a new sub- know you by sight or by name, with whom you have had some set of variables related to the assortativity with respect to other contact in the past two years, either face-to-face, by phone, mail alter attributes we have. These attributes are: the sex of the al- or e-mail, and whom you could still contact if you had to. You can ters (Asex), race (Arac), type of relationship (Arel), tendency to talk use acronyms for naming people.” This free list name generator about personal problems with ego (Apro), age (Aol2), contact fre- with a fixed number of alters was designed to draw from all lev- quency (Afrq), and closeness of the alters with ego (Clos). These els of both strong and weak ties (26–29). The third module asked variables are still structural because they measure the preferen- egos about each alter’s characteristics like gender, country of ori- tial attachment between alters with the same values for these gin, period of residence in the destination country, level of edu- variables, revealing the relevance of these factors in the social cation, and perceived emotional closeness between ego and alter, vicinity of ego. among other questions. Finally, the fourth module asked egos to The set of variables we just described serve us as predictors evaluate the perceived relationship between each pair of alters that we leverage using different algorithms: with the question “How likely is it that alter X and alter Y con- tact each other independently of you?” The choices were “very Linear Models: We used a multinomial logistic regression (32) likely,” “maybe,” and “not at all likely.” After completing the four (MNL). This model predicts the probability of a certain modules, the respondents were interviewed using a visualization class-distributed variable using the functionality of a tra- of their personal network as a way to ask them questions about ditional logistic regression—i.e. a sigmoid function to de- their social context (Fig. 2) (30). termine probability based on certain inputs. Its main ad- Table 1 shows the distribution of cases across country of origin. vantage is the interpretability, as the coefficients may be It is worth mentioning that Dominicans were interviewed in both directly linked to the influence of a factor in the probability the United States and Spain. The few cases represented by Colom- of belonging to a certain class. We used this model with two bians, Cubans, Guineans, Haitians, and Mexicans were aggregated different procedures: an inferential part where we used the under the category of “others” (N = 36). For the rest, the range of whole dataset to fit the model and understand its parame- cases is from 66 (Moroccans) to 154 (Dominicans), with Senegam- ters, and a predictive part where we try its predictive power 4 | PNAS Nexus, 2022, Vol. 1, No. 4 Fig. 2. Personal network of a Senegambian migrant in Spain with 45 alters (ego is not represented in the drawing). Color shows that all the alters come from Senegambia and live in Spain (black), except one of them at the time living in Senegal (orange). Men are represented by triangles and women by circles. The size represents the frequency of interaction with ego. The program Egonet displayed in this case two clusters using the algorithm Spring Embedding. on unseen data (i.e. the test set) and provide an accuracy were standardized to have 0 mean and 1 SD. Lastly, a stan- metric. dard hyperparameter tunning was made using k-cross fold The results of the MNL were analyzed via the LLR P-value, validation with k = 5. 198. the pseudo R-squared and the comparison between log- To better calibrate how good the results are, we compare their likelihood and LL-null. The latter will let us distinguish performance with some dummy classifiers: a uniform dummy how good our model is by comparing it with a model with- classifier that classifies all migrant origins with an equal prob- out predictors. Meanwhile, the LLR P-value provides us, like ability; a stratified dummy classifier that assigns probabilities other P-values, a way to compare the validity of our hy- depending on its representativeness; and, finally, a “most fre- pothesis. These measures are standard and their interpre- quent” dummy classifier that always selects the most frequent tation can be found in several textbooks (33). The pseudo R- class. squared tell us about the fit (34) and its value tells us about To analyze the importance of the different features used by the improvement between a null and the current model, the Random Forest, we leveraged the SHAP (Shapley additive ex- providing the same kind of interpretation R2 metric pro- planations) values (37). This tool was developed to compute the vides but within a different range of values. Shapley values, a concept derived from Game Theory to allocate Nonlinear Models: We tried two standard nonlinear modeling surpluses in coalition games in a fair way. This solution has been techniques, a Random Forest and a simple Neural Network reconverted to an analysis tool of global interpretability of ma- (32, 35, 36). The accuracy of both methods is comparable, so chine learning and tree models, where surpluses are successes we focus our description here on the one providing better and the players are the features. A positive (negative) SHAP value results, the Random Forest. As part of the data preparation, indicates that the feature (in this case, the probability of belong- we randomized the dataset and split it into two groups, 80% ing to a specific country or religion) is reinforced (diminished) for the train data and 20% for the test data. Then the data Molina et al. | 5 Table 3. Results of the multinomial logistic regression. MLN Dominicans Puerto Ricans Argentinians Moroccans Senegambians Closeness 3, 6 ± 1, 3 3, 0 ± 1, 6 3, 4 ± 1, 3 2, 6 ± 1, 3 1, 9 ± 1, 3 Betweenness − 0, 77 ± 0, 32 − 0, 64 ± 0, 38 − 0, 68 ± −1, 35 − 1, 46 ± 0, 41 − 0, 90 ± 0, 40 Clustering − 0, 64 ± 0, 25 − 0, 56 ± 0, 26 1, 01 ± 0, 34 0, 26 ± 0, 29 0, 11 ± 0, 29 Average degree − 4, 0 ± 1, 35 − 3, 1 ± 1, 6 − 6, 3 ± 1, 4 − 4, 6 ± 1, 4 − 2, 9 ± 1, 4 Closeness origin 1, 10 ± 0, 32 0, 68 ± 0, 26 0, 19 ± 0, 35 1, 03 ± 0, 40 0, 07 ± 0, 41 Closeness − 0, 08 ± 0, 27 − 0, 46 ± 0, 30 0, 50 ± 0, 34 0, 27 ± 0, 32 − 0, 04 ± 0, 29 residence Row labels show the most relevant network measures, while column labels represent nationalities. Numbers represent coefficients and their SD . Table 4. Summary results of the multinomial regression. Table 5. Accuracy parameters for the Random Forest model and the dummy classifiers. Nationality Religion Classifiers RF Uni Str MF Log-likelihood −626.76 −356.88 LL-null −797.81 −467.51 Nationality accuracy 0.48 0.16 0.20 0.32 LLR P-value 1.29 ×10−49 4.03 × 10−22 Religion accuracy 0.58 0.33 0.41 0.55 Pseudo R-squared 0.2144 0.2366 The keys for the table are RF (Random Forest), Uni (uniform), Str (stratified), and MF (most frequent). by the variable. The distribution of these values shows us which variables contribute more to the model’s prediction, ordered Table 6. Random forest model accuracy parameter for the case of accordingly. Dominicans. Nationality RF Results All Dominicans 0.83 Let us begin introducing the inference results from the MNL. In Dominicans split into two classes 0.37 Table 3, we show the coefficients and SE of the most important features for each country of origin. These coefficients are usually interpreted in terms of ratios, representing the relative probabil- ity of belonging to a group compared to the group of reference, The case of Dominicans, which are present in the two destina- which in this case is the group of people from different countries tion countries (the United States and Spain), allows us to test fur- (“Others”). Therefore, it measures the importance of the variable ther the Random Forest model’s ability to classify by nationality to determine a certain country of origin (or religion). from personal network measures adequately. Table 6 presents the The coefficients help us identify the network factors that dif- accuracy parameter for both cases: all Dominicans, irrespective of ferentiate each origin. There are some common characteristics the destination country, and Dominicans in each country, as sepa- to all the ego networks in our dataset, such as a high value of rated classes. The results show that the prediction is better for the closeness and a low value of Betweenness. But some variables first case (83% for all Dominicans) than for Dominicans consid- also help us distinguish different groups: betweenness ordered ered separately (37%), pointing to the fact that common network bottom up can make a qualitative difference between being part traits shared by this migrant group in two different destination of an African group of migrants (Moroccan, Senegalese) and the contexts provide additional information to the classifier (see the rest of the dataset. In the same vein, closeness differentiates the separated analysis in Supplementary Material). Senegambian group from everyone else. Finally, the main differ- However, the results are less efficient for the task of predict- ences can be checked out with the clustering values. This vari- ing religion, with only a 5% over the most frequent classifier. We able differentiates the group of Argentinians from the ones of the note that Christians are over-represented in the sample, account- Caribbean and the ones from Africa. Table 4 shows the value of ing for half of the population. Despite the lesser statistical rele- the LLR P-value virtually zero, which suggests that our model is vance achieved with this method, the classifier learns some gen- much preferable to a null one. uine features of this cultural variable. This can be also be corroborated with the value of the Pseudo Interpreting nonlinear models can be challenging, but there are R-squared, which interpreted together with the low P-value (33), powerful techniques to overcome this issue. In Fig. 3, we show the allows us to state that these models capture relevant information. summary plots of SHAP values distribution for distinct features We now present the results from the nonlinear models for- and each migrant group. For each one of the plots, each x-axis is merly defined and compare them with dummy classifiers. Table 5 an individual feature, each point is an individual from our dataset presents a summary of the accuracy metrics for the Random For- whose color indicates the value of the feature. A high, positive est classifiers for the variables nationality and religion. The Ran- (negative) SHAP value indicates that the feature contributes pos- dom Forest model provides a 47% improvement over the best itively (negatively) to classify on a given country of origin. If the dummy model for country of origin—we note that a MNL model points are also separated by color, the interpretation is the exis- trained on the same data produces a 16% increase over the same tence of a relationship between the value of the feature and its null model. This supports the claim that these personal networks contribution to the final prediction. It is important to note that contain information about the definition of the specific migrant the features in the plot are the most relevant ones (the ones with group. the highest SHAP values). 6 | PNAS Nexus, 2022, Vol. 1, No. 4 Fig. 3. SHAP plots of the predictor variables aggregated by country. The color indicates the value of the feature, relating its value distribution with the distribution of SHAP values. The correlation between these two distributions characterizes a given nationality. Fig. 3 presents the observed variation among nationalities. In In the case of religion, the results are less conclusive as the the case of Argentinians, the main predictor is a low value of av- sample is not well distributed across this variable. After including erage degree combined with a high value of clustering, which re- assortativity as a predictor, Christian religion correlates with a low inforces each other. Puerto Ricans have a high closeness value, sex assortativity, while Muslim religion correlates with a high sex average degree, and a low clustering value. Dominicans also ex- assortativity, results aligned with the sex segregation rules of each hibit this low clustering value, but they are closer to their origin. case (see Supplementary Material). Senegambians have a low value of betweenness, and Moroccans Overall, our results may be interpreted as hypothesized at the have a high value of closeness with the host country. Some vari- beginning of this paper—i.e. that a specific combination of struc- ables diminish the probability of belonging to a certain country: tural measures of the ensembles of alter–alter matrices predicts this is the case of closeness in the case of Senegambians or Mo- the country of origin of each migrant group. roccans. It is interesting to note that some of the relationships that appear in the SHAP values are also present in the MNL re- sults, indicating that the nonlinear effects are indeed direction- Discussion ally consistent the linear ones. See, for example, the effect of the distribution of closeness values in Senegalese and Moroc- The following findings suggest that looking at the group dimen- cans. Notice in Fig. 3, in the closeness row, that the same color sion with the aid of personal networks and structural measures (red) is at the same tie (left) of the distribution. This also hap- can identify traces of cultural institutions (the grid dimension), pens with the clustering values between Dominicans and Puerto which varies across countries and regions with common historical Ricans, betweenness with Senegalese and Moroccans, and to a background. Obviously, there is no exact match between specific lesser degree, in the clustering between Dominicans and Puerto network measures and cultures, but different network profiles are Ricans. associated to cultural backgrounds. Molina et al. | 7 (A) Structural measures of personal networks predict a cul- Three different methods (MNL, Random Forest, and a neural tural trait like “country of origin” or “religion.” The overall network) account for similar results. These results suggest that results from both methods (MNL and Random Forest, Ta- personal networks can be conceived of as samples of the social bles 3 and 5) provide support for the idea that it is possible structures that frame the group dimension, capturing the effects to predict the country of origin from network measures re- of cultural institutions (the grid dimension) in the alter–alter ma- liably and, with less accuracy, the religion except for the trix of interactions. These results are especially relevant nowa- case of Muslims, a category less mixed than the other two days where social interactions are routinely registered by a myr- (“Christian” and “Other”). This finding can be interpreted iad of digital systems (40), the group dimension. within the Grid/Group theory framework, which states the Following the theory, we could predict cultural variation from interdependence of social structures and cultural phenom- a structural lens. We are also aware of the limitations of this ap- ena. In this vein, personal networks can be conceived as proach. First, Grid/Group analysis or Cultural Theory is neither samples of social structures, which reflect to some extent a coherent nor a developed set of clear theoretical statements formal and informal cultural institutions (i.e. kinship and and measurements. Nevertheless, we suggest that our intent the gender/sex system, religious cults, education, political to predict cultural variation from personal network structures organization, and so on). (the “group” dimension) may complement the “Individualism– For instance, the low average degree and the high cluster- Collectivist”/“Tight–Loose” literature, which could be considered ing of the personal networks of Argentinians in our dataset as a measure of the “grid” dimension (i.e. the level of control of may reflect a more individualistic society (“low group”) social norms on individuals, as defined by Gelfand) (20). Predic- compared with Senegambians (see Fig. 1), which exhibit tions from one theory could be tested by the other and vice versa. a high closeness among the alters (“high group”). We ex- Second, we acknowledge the limitation of taking migrants from pect to find a different set of corresponding cultural insti- a given country as representatives of a culture because these mi- tutions for each case (like kinship, religion, ethnic identifi- grants can be over-represented from specific minorities or groups cation, and so on). Interestingly, this “compatibility” of both in the sending country, which generally are not culturally homo- dimensions of human groups claimed by the theory limits geneous. In the same vein, the variable religion is oversampled for the range of variation of social diversity. Christians, which hinders the learning capacity of some analyti- (B) Each migrant group exhibits a specific network pattern. The cal procedures. However, we think that the country of origin is a research literature on “social signature” draws on the cog- reasonable proxy for diverse “cultural institutions” understood as nitive mechanisms that underpin the hierarchical structur- the mainstream sets of values, models, and rules shared by peo- ing of personal networks. The Mu (μ) variable measures this ple from a given region in all its diversity. For instance, language, “regime.” The relative low variability of Mu values across kinship, and indeed religion do vary across migrant groups, and groups (from −3.83 to 2.30) supports the existence of such this variation should leave distinctive traces in the personal net- constraints for all cases. But, while the “social signature” works. Interestingly, we showed that migrant groups from wide literature focuses on the allocation of time by ego to inter- geographical areas such as the Caribbean or West Africa shared action with alters (the ego–alter matrix), we draw in this some structural features, which can point to the imprint left by paper on the alter–alter matrix measures for identifying common cultural institutions. specific cultural traits. Specifically, each migrant group ex- Third, despite our controls by gender, age, and time of residence hibits a particular combination of structural measures. For in the destination country, research on personal networks shows instance, the Dominicans’ combination of low clustering that individual characteristics, like socioeconomic background and high closeness with origin may match with the impor- and the specific point in the life course, have consequences for tance of softball competition in the migrant community, both composition and structural measures (27–29). which, at least in Spain, fostered intra-group interactions Consequently, we should expect more variation on samples and the strong identification with origin. For the Moroccan drawn to represent the general population of a given country than case, the high perceived closeness with the alters living in in samples from migrant groups. Spain can be interpreted as a minority sharing a common Finally, structural measures are closely related, which may lead Islamic culture in a European country. Finally, Puerto Ri- to misinterpretation of the results, even after controlling for mul- cans’ high closeness and average degree may suggest the ticollinearity. existence of a densely knitted Latino minority in the United We hope that more nuanced measures of the group/grid di- States. mensions can help develop a better understanding of the inter- Last but not least, the focus on personal network data dependencies between social structures and cultural phenomena as samples of social structures highlights this meso-level beyond simple determinism, which can be tested cross-culturally analysis’s potential for addressing theoretical questions (41). about society and culture as posed by Breiger (38) and Lazega (39), among others. Acknowledgments We thank the feedback received by participants in the conferences Conclusions where we presented earlier versions of this paper, especially Sun- The analysis of structural measures of migrant personal networks belt 2022 (Cairns, Australia) and Personal Networks during Chal- shows that it is possible to infer not just their country of origin or lenging Times: The Power and Limitations of Social Relationships their religion, but that each of them exhibit a particular combi- in Everyday Life (Bar-Ilan University, Tel Aviv). nation of network measures compared with others. This finding is relevant theoretically because it shows an avenue of research oriented to overcome the duality of culture and structure and sup- Supplementary Material port the Grid/Group analytical framework. Supplementary material is available at PNAS Nexus online. 8 | PNAS Nexus, 2022, Vol. 1, No. 4 Funding 19. van Hoorn A. 2015. Individualist–collectivist culture and trust radius: a multilevel approach. J Cross Cult Psychol. 46:269–276. This research has been funded by the National Science Founda- 20. Schwartz SH. 1990. collectivism vs individualism. J Cross Cult tion (BCS-0417429), the MINECO-FEDER (PGC2018-098186-B-I00, Psychol. 21:139–157. J.O., A.S.), the Comunidad de Madrid (PRACTICO-CM), and the 21. Singelis TM, Triandis HC, Bhawuk DPS, Gelfand MJ. 1995. UC3M (CAVTIONS-CM-UC3M). Horizontal and vertical dimensions of individualism and col- lectivism: a theoretical and measurement refinement. Cross- cultural Res. 29:240–275. Authors’ Contributions 22. Gelfand M. 2019. Rule makers, rule breakers: Tight and loose cul- J.L.M., J.O., and H.R.B. designed the paper focus; J.O., I.T., and A.S. tures and the secret signals that direct our lives London: Scrib- prepared the data and performed the analysis; J.L.M., J.O., A.S., and ner. C.M. wrote the paper, which was reviewed by all authors. C.M. and 23. Saramaki J, et al.. 2014. Persistence of social signatures in human J.L.M. designed the original research and collected the data. communication. Proc Natl Acad Sci. 111:942–947. 24. Heydari S, Roberts SG, Dunbar RIM, Saramäki J. 2018. Multichan- nel social signatures and persistent features of ego networks. Appl Netw Sci. 3. Data Availability 25. De Li R, Liu JG, Guo Q, Zhang YC. 2018. Social signature identifi- All data are included in the manuscript and/or supporting infor- cation of dynamical social networks. Phys A Stat Mech its Appl. mation. 508:213–222. 26. Granovetter M. 1995. Getting a job: a study of contacts and ca- reers.Chicago: University of Chicago Press. References 27. Bidart C, Degenne A, Grossetti M. 2020. Living in networks: the 1. Bernard HR, Killworth PD. 1979. Why are there no social physics. dynamics of social relations. Cambridge, MA: Cambridge Univer- J Steward Anthropol Soc. 11:35. sity Press. https://doi.org/10.1017/9781108882392. 2. Benedict R. 1934. Patterns of culture. Boston(MA): Houghton Mif- 28. Perry BL, Pescosolido BA, Borgatti SP. 2018. Egocentric network flin Harcourt. analysis: foundations, methods, and models. Cambridge, MA: 3. Nadel SF. 1957. The theory of social structure. London: Cohen & Cambridge University Press. https://doi.org/10.1017/9781316443 West Ltd.. 255 4. Dimaggio P. Nadel’s paradox revisited: relational and cultural 29. McCarty C, Lubbers MJ, Vacca R, Molina JL. 2019. Conducting per- aspects of organizational structures. 1993. In: Nohria N., Ec- sonal network research: a practical guide. New York: Guilford cles R., editors. Networks and organization. Boston(MA). Harvard Publishers. Business School Press. 30. Molina JL, Maya-Jariego I, McCarty C. 2014. In Giving mean- 5. Eisenstadt SN. 1989. Introduction: culture and social structure ing to social networks: methodology for conducting and ana- in recent sociological analysis. In: H. Haferkamp,editor. Social lyzing interviews based on personal network visualizations. S. Structure and Culture. Berlin-New York: Walter de Gruyter, p. Domínguez, B. Hollstein, editors Mixed Methods in Social Net- 352. work Research. Design and Applications. Structural Analysis in 6. Emirbayer M, Goodwin J. 1994. Network analysis, culture, and the Social Sciences.Cambridge, MA: Cambridge University Press, the problem of agency. Am J Sociol. 99:1411–1454. pp. 305–335. 7. Douglas M. 1996. Natural symbols. Explorations in cosmology. 31. Tamarit I, Cuesta JA, Dunbar RIM, Sánchez A. 2018. Cognitive re- London-New York: Routledge. source allocation determines the organization of personal net- 8. Thompson M, Ellis R, Wildavsky A. 1990. Cultural theory. Boul- works. Proc Natl Acad Sci. 115:8316–8321. der: Westview Press 32. Pedregosa F, et al.. 2011. Scikit-learn: machine learning in 9. Rayner S, Gross JL. 1985. Measuring culture: a paradigm for the Python. J Mach Learn Res. 12:2825–2830. analysis of social organization. New York: Columbia University 33. Hastie T, Friedman J, Tibshirani R. 2001. The elements of statis- Press. tical learning. Data mining, inference, and prediction. New York: 10. Douglas M, Wildavsky A. 1983. Risk and culture: an essay on the Springer. selection of technological and environmental dangers. Berkeley: 34. McFadden D. 2021. Quantitative methods for analysing travel University of California Press. behaviour of individuals: some recent developments. In Be- 11. Mamadouh V. 1999. Grid-group cultural theory: an introduction. havioural travel modelling. New York: Routledge, pp. 279–318. GeoJournal. 47:395–409. 35. Breiman L. 2001. Random forests. Mach Learn. 45:5–32. 12. Spickard JV. 1989. A guide to Mary Douglas’s three versions of 36. Franklin J. 2005. The elements of statistical learning: data min- grid/group theory. Sociol Relig. 50:151–170. ing, inference and prediction. Math Intell. 27:83–85. 13. Bale T. 1997. Towards a “cultural theory” of parliamentary party 37. Lundberg SM, Lee S-I. 2017. A unified approach to interpreting groups. J Legis Stud. 3:25–43. model predictions. Adv Neural Inf Process Syst. 30. 14. Atkins RA. 1991. Egalitarian community: ethnography and exe- 38. Breiger RL. 1974. The duality of persons and groups. Soc Forces. gesis. Tuscaloosa: University of Alabama Press. 53:181–190. 15. Caulkins DD. 1999. Is Mary Douglas’s grid/group analysis useful 39. Lazega E. 2020. Bureaucracy, collegiality and social change: for cross-cultural research? Cross-Cultural Res. 33:108–128. redefining organizations with multilevel relational infrastruc- 16. Durkheim É. 1991. Le Suicide : etude de sociologie. 6ème éd. tures. Cheltenham: Edward Elgar Publishers. Paris: P.U.F. 40. Zuboff S. 2019. The age of surveillance capitalism: the fight for 17. Durkheim É. 1990. Les Formes élémentaires de la vie religieuse : a human future at the new frontier of power. New York: Public le système totémique en Australie. éd 2ème. Paris: P.U.F. Affairs. 18. Triandis HC. 2018. Individualism and collectivism. New York: 41. Ember M, Ember CR. 2000. Testing theory and why the “units of Routledge. analysis” problem is not a problem. Ethnology. 39:349–363.