Cognitive abilities.

Scholars in the cognitive science of religion argue that the cognitive abilities of human beings evolved in the ways that underpin religious belief. For example, Barrett and his colleagues argued that humans are equipped with a sensitive agency-detection system for evolutionary reasons (i.e., to detect predators reliably, even at the risk of a false positive), and this “hyperactive or hypersensitive agency-detection device” enables people to perceive the existence of invisible agents (e.g., [1, 2]). Likewise, the presence of such perceived agents would be significantly stronger owing to human beings’ mentalizing ability or theory of mind. People who attribute mental states to such agents recognize them as having the ability to think, feel, and communicate with humans (e.g., [3]).

According to this argument, these cognitive abilities are associated with the individual differences in religious beliefs. Indeed, previous studies have shown that, for instance, people with a high mentalizing ability have stronger religious beliefs (e.g., [4–6]). Moreover, it has also been demonstrated that thinking styles that foster or inhibit the use of these cognitive abilities are related to the degree of believing in gods. Specifically, many works showed that people who employ analytic thinking as a dominant style were less religious than intuitive thinkers (e.g., [7–9]). However, the strength of the association between cognitive abilities (e.g., mentalizing) and religious beliefs is not as strong as previously assumed (e.g., [8, 10–12]). This may be because this cognitive approach explains how people can represent supernatural agents, but less so why people consider these agents to be true [13, 14].

1.1.2. Cultural transmission and CREDs.

It has long been recognized that people change their beliefs, opinions, and behaviors as a result of teaching, imitation, and other forms of social learning (e.g., [15]). Similarly, religious beliefs are transmitted culturally. Researchers on cultural evolution [14, 16, 17] have identified three mechanisms of such transmission: content-based, context-based, and CREDs. The content-based mechanism refers to the idea that cultural information of a specific content type (e.g., emotionally evocative ideas, minimally counterintuitive concepts) is likely to be transmitted. Minimally counterintuitive concepts are those with content that minimally violates people’s intuitive ontological knowledge (e.g., folk biology, physiology, and psychology). This concept is considered one of the cognitive underpinnings of religious concepts, but it has also been argued that it has the advantage of being easier to remember, and therefore easier to transmit (e.g., [18, 19]).

The context-based mechanism describes the person bringing the information to be transmitted. People are likely to learn cultural information from models that are similar to them, are successful, and have a social status. Learning from information that is observed frequently (conformist learning) and learning from family (kin-biased learning) are also part of the context-dependent mechanism.

CREDs are “displays (often actions) that indicate a model’s degree of commitment to, or belief in, verbally expressed representations” [14 p. 258]. According to the theory of CREDs, humans tend to learn cultural information, such as beliefs and opinions, from others via verbal communication, and there is a risk of being persuaded to learn false information. Thus, humans must have evolved defense mechanisms to avoid being verbally manipulated by self-interested cultural models who express beliefs or opinions to which they do not commit (see also [20]). Attending to CREDs is such a mechanism; people could diagnose verbally expressed beliefs as true if models showed behaviors that would appear costly if they had a belief that is at odds with those behaviors (CREDs). In other words, “without CREDs, learners are not committed to those recalled representations in a manner that propels behavior beyond simply repeating the expression itself” [14 p. 247]. It has been argued that CREDs work in the transmission of various cultural information, such as food preferences, opinions, and altruism (e.g., [21]). In the case of religion, religious beliefs often involve costly behaviors, such as frequent attending to religious services or extreme rituals. For such a costly behavior-belief set to be transmitted and to persist, CREDs are essential.

Early empirical works in the cognitive science of religion focused on content-based mechanisms (e.g., [18]), but recent studies have increasingly shown the importance of context-based mechanisms and CREDs in explaining to what extent people commit to religious beliefs. For example, Lanman and Buhrmester (2017) [22] developed a scale that assessed the extent to which the respondents were exposed to their caregivers’ religious CREDs (e.g., “To what extent did your caregiver(s) attend religious services or meetings?”) and demonstrated a score for the CREDs exposure scale to explain the individual differences in the belief in gods, even after controlling for religious socialization (i.e., to what extent the respondents’ important people talked about or taught religion with emphasis during their upbringing). This suggests that even if parents are religious, children are not necessarily religious unless parents show religious CREDs. More importantly, it suggested that people employ their parents’ CREDs over verbal communication to what to learn, even if parents are generally less likely to manipulate their children. Other previous studies have also shown the same line of evidence [8, 12, 23, 24]. The positive association between parents’ religious beliefs and those of their children [25–27] may support the importance of caregivers’ religious CREDs, albeit indirectly.

1.1.3. Other factors.

Other factors that account for the individual differences in religious belief have also been investigated (e.g., [28]). For instance, secularization theory suggests that religion works as a “tranquilizer” for existential concerns, such as fear of death, and thus, religious belief declines as existential security increases. Supporting this prediction, it has been shown that people who live in countries with economic development, income security, and health security are less religious (e.g., [29, 30]). Gervais et al. (2021) [8] also showed that, in the United States, people feeling existentially secure tend to be atheists. Other works have pointed out that religiosity works as a mating strategy; religiosity is often associated with sexually conservative behavior, and men and women who pursue monogamous, high-fertility strategies in mating tend to be religious (e.g., [31]).

1.2.1. Kin-biased and conformist learning.

In the literature on CREDs and religious beliefs, previous studies (e.g., [8, 12, 22, 24]) mainly examine kin-biased learning (i.e., caregivers’ religious CREDs). This is reasonable because it is no surprise that people imitate and learn from others who have been with them for a long time since infancy. Simultaneously, people tend to use CREDs over verbal approaches [14]. Therefore, parents’ CREDs should have a long-term impact on their children’s beliefs.

On the other hand, other cultural learning pathways have not been as well examined in this literature. For example, although many findings in social psychology studies suggest that social behavior is significantly influenced by the behavior of the majority in a society (i.e., conformity), conformist learning has rarely been examined in the case of religious beliefs. This is partly because of difficulties in detecting frequency-dependent effects on religious beliefs (e.g., estimating the number of people engaging in religious behavior) with high precision using a standard survey method.

Gervais and Najle (2015) [32] demonstrated the conformist learning of religious beliefs via CREDs by analyzing data from the World Values Survey (WVS), which is an international research program investigating the different values held by people worldwide since 1981 [Note 1]. From the WVS dataset, they sampled two groups with different birth years (one group involved people born between 1971 and 1981, and the other group involved people born before 1970) to determine whether the number of people in the older group who showed eager religious behavior predicted religious beliefs among those in the younger group. They established that younger respondents who lived in a country or region with a higher percentage of religiously eager older respondents were highly likely to believe in gods, thereby suggesting that the religious CREDs of older adults evoked conformist responses from younger people through conformist learning. This association was statistically independent of the extent to which individual differences in religious beliefs in the younger group could be explained through their retrospective answers regarding whether they were raised as religious people at home (kin-biased learning).

Apart from this individual-level analysis, it should be noted that Gervais and Najle (2015) [32] also achieved similar results in country- or international-level analyses. Based on the signal detection theory, Gervais and Najle (2015) [32] regarded the kin-biased learning cue (religious upbringing) as a signal, and they regarded the country or region as a unit. Through this approach, they calculated both the response sensitivity (d’, which indicates the degree of accuracy with which a signal is detected and responded to) and response bias (C, which indicates the frequency of people’s tendencies to respond to a signal, regardless of whether it is present) levels of the focal group. If people are sensitive to religious upbringing and thus believe in gods in general, the average sensitivity index d’ across countries differs from the chance levels significantly. Moreover, if people tend to conform to the behaviors of other individuals around them, they eventually believe in gods, regardless of any religious upbringing. Consequently, the bias index C is correlated with the percentage of religiously eager people in the older group. Gervais and Najle (2015) [32] showed that the results were precisely in line with both predictions. These findings, which overcame the limitations of a standard survey, suggested that religious beliefs are transmitted through conformist learning and kin-biased learning.

2.2.1. Religious beliefs.

Following the work of Gervais and Najle (2015) [32], we selected an item that directly asked whether the respondents believed in God or gods (Q16; “Please indicate which statement below comes closest to expressing what you believe about God”) as the primary measure of religious belief in the focal group. Six non-continuous (qualitatively different) responses were possible for this item (e.g., 1 = “I don’t believe in God,” 2 = “I don’t know whether there is a God and I don’t believe there is any way to find out,” 3 = “I don’t believe in a personal God, but I do believe in a Higher Power of some kind,” 4 = “I find myself believing in God some of the time, but not at others,” 5 = “While I have doubt, I feel that I do believe in God,” 6 = “I know God exists and I have no doubts about it”). Next, we dichotomized these responses to match the methodology employed by Gervais and Najle (2015) [32] and to enable signal detection analysis. We assigned a score of 0 (absent) for choices from 1 to 3 because these choices included the words “I don’t believe in God.” Similarly, we gave a score of 1 (present) to the respondents whose choices were from 4 to 6, which included the words “I believe in God.”

We also assessed religious beliefs in the focal group using an item asking participants about the extent to which they described their religiousness (Q31). As the choices for this item ranged from 1 (“Extremely religious”) to 7 (“Extremely non-religious”), we regarded this item as a 7-point Likert scale and used the rating (1 to 7) as another score for religious belief. In the analyses, we reversed the score, such that a higher score indicated stronger religious beliefs.

2.2.2. Kin-biased learning cues.

The following items were included in the ISSP: “When you were a child, how often did your mother attend religious services?” (Q24) and “When you were a child, how often did your father attend religious services?” (Q25). The answers to these items (1 = never; 9 = several times a week) in the focal group were used to investigate kin-biased learning. Due to our focus on CREDs, we defined the presence of parents’ religious CREDs based on whether the respondents’ answers to the items were 8 or 9 (weekly or more than weekly), or any other response. We coded answers 1–7 to Q24 as 0 (mothers’ CREDs were absent) and answers 8–9 were coded as 1 (present). Similarly, we coded the answers to Q25 (0 = fathers’ CREDs were absent, 1 = present). Notably, items on the frequency of the mothers’ and fathers’ attendance were separated. This allowed us to determine the parents’ CREDs that were significantly associated with their children’s religious beliefs, which Gervais and Najle (2015) [32] did not investigate.

2.2.3. Conformist learning cue.

To investigate conformist learning, we used the responses (1 = never– 9 = several times a week) to the following item: “How often do you take part in the activities or organizations of a church or place of worship other than attending services?” (Q28). Following the work of Gervais and Najle (2015) [32], in each country or region, we calculated the percentage of respondents in the older group who participated weekly (8) or several times a week (9).

2.3.1. Individual-level analyses.

As the respondents in our dataset were not statistically independent owing to the hierarchical structure of the data (i.e., each respondent was nested in a country or region), we assumed that the associations between kin-biased learning cues and the measure of religious beliefs varied depending on the country or region. Additionally, the conformist learning cue was a country- or region-level variable. Therefore, we employed multilevel modeling to test our predictions.

Following the work of Gervais and Najle (2015) [32], we conducted a stepwise hierarchical analysis. In the first step, we set the country or region as a random factor (i.e., level-2 residual) to examine how religious belief levels varied in terms of clusters. In the second step, we added the kin-biased learning cue as a fixed factor and as a random factor. The latter considered the kin-biased transmission of religious beliefs to differ between clusters (i.e., as a residual term associated with the level-1 predictor). In the third step, we added the conformist learning cue and the interaction between the two types of cues as fixed factors. These two cultural learning cues would explain religious beliefs if the beliefs were acquired through kin-biased and conformist learning. Gervais and Najle (2015) [32] found that the interaction was not statistically significant, and therefore, we anticipated the same result. We tested these predictions and explored which parents’ religious CREDs show a more robust association. Note that there was concern that the results of the analyses might be biased due to the likelihood of correlation between the two kin-biased tilt cues (i.e., multicollinearity). Therefore, we confirmed that this problem did not occur by calculating the VIF.

2.3.2. International-level analyses.

We also utilized an approach based on signal detection to investigate the association between the two types of cultural learning cues and religious beliefs. As described in Table 1, we treated parents’ religious CREDs as a signal (0 = absent, 1 = present) and the belief in gods measure as a response (0 = absent, 1 = present). Next, for each country or region, the sensitivity (d’) and bias (C) indices were calculated using the data from the focal group, following the standard procedure of signal detection theory [Note 3]. If kin-biased transmission occurred, people would be sensitive to their parents’ religious CREDs and come to believe in gods in general. Therefore, the average sensitivity index d’ across countries would be different from the chance level (i.e., zero). Moreover, if conformist learning occurs, people who live in countries or regions with higher percentages of older adults who show religious CREDs would believe in gods, regardless of their parents’ religious CREDs. Therefore, the conformist learning cue would explain the bias index C. As in the individual-level analysis, we tested these predictions separately, depending on whether the cue came from the mother or father.

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Table 1. The four outcomes of the approach based on signal detection theory.

https://doi.org/10.1371/journal.pone.0305635.t001

2.3.3. Additional analyses.

We also analyzed data from other generations of respondents to confirm the robustness of our findings. As described in section 2.1, our main focal group was the respondents born between 1971 and 1981. We also created other focal groups: younger and older. We subsampled the respondents born between 1981 and 1990 as the younger focal group, and those born before 1980 as the corresponding older group. Furthermore, the respondents born between 1961 and 1971 were subsampled as the older focal group, and those born before 1960 represented the corresponding older group. We investigated whether similar results would be obtained using younger and older focal groups, as well as their corresponding older groups.

3.1.1. Belief in gods.

We conducted hierarchical multilevel logistic regression analysis using the two kin-biased learning cues (level-1 variables; 0 = parents’ CREDs were absent, 1 = present) and the conformist learning cue (level-2 variable; percentage of the respondents in the older group who showed religious CREDs in each country or region) to explain the belief in gods (0 = absent; 1 = present). We also entered gender (0 = male; 1 = female) into the models at all steps to statistically control for the association between gender and the belief in gods (i.e., females are more religious than males in general), although this association was not our focus. The conformist learning cue was standardized because the range of this variable was so narrow that its coefficients in the logistic regression model would be too large (>10) and impractical [Note 4].

In the first-step model, we identified a non-negligible amount of variation involving the belief in gods between different countries or regions. The random intercept variance was 1.369, which was significantly different from zero, according to a likelihood ratio test involving the corresponding model without the level-2 random factor (χ² = 1820.62, df = 1, p < .001). The interclass correlation coefficient also indicated that approximately 30% of the chances of believing in gods were explained by inter-country differences (ICC = .294).

In the second step, we investigated the associations between the two kin-biased learning cues and the belief in gods together with the between-country variances of these associations [Note 5]. Therefore, in addition to the first-step model, the second model involved two kin-biased learning cues included as fixed factors, as well as two random slope terms associated with these cues. First, we investigated whether these random slope terms improved the corresponding model, which did not assume the random factors of the kin-biased learning cues, by entering them separately into the model. The deviance of the model with no random slope terms was 9002.8, and the deviance of the model with the random slope term associated with the mothers’ CREDs was 8994.7. This difference was statistically significant (χ² = 8.07, df = 1, p = .004). Additionally, the model without random slope terms improved significantly when the term associated with the fathers’ CREDs was included (deviance = 8989.5, χ² = 13.24, df = 1, p < .001). Therefore, we could justify the assumption of between-country variances in the associations between the two kin-biased learning cues and the belief in gods, after which we proceeded with the second step of the analysis. As we predicted, the second model showed that the presence of both the mothers’ CREDs (b = 0.61, OR = 1.85, 95% CI [1.46, 2.34], z = 5.14, p < .001, VIF = 1.19) and the fathers’ CREDs (b = 1.05, OR = 2.84, 95% CI [2.10, 3.85], z = 6.74, p < .001, VIF = 1.19) were associated with the individual differences in the belief in gods. The 95% CI indicated that respondents whose mother (father) showed religious CREDs had 1.46 to 2.34 (2.10 to 3.85) times higher chances of believing in gods. The fitness of this model (deviance = 8988.1) was significantly better than that of the model with no random slope terms (χ² = 14.65, df = 2, p < .001), thereby indicating that the associations between the two kin-biased learning cues and the belief in gods varied by country or region.

In the third step, we included the conformist learning cue as an independent predictor and as an interaction term together with the two kin-biased learning cues (Table 2). This approach improved the model in the second step (deviance = 8963.7, χ² = 24.40, df = 3, p < .001). The third step’s model demonstrated that the mothers’ CREDs (b = 0.59, OR = 1.81, 95% CI [1.43, 2.29], z = 4.93, p < .001, VIF = 1.22) and the fathers’ CREDs (b = 1.06, OR = 2.89, 95% CI [2.17, 3.86], z = 7.25, p < .001, VIF = 1.24) were associated with the belief in gods same as the second model. The conformist learning cue was also associated with the belief in gods (b = 0.69, OR = 1.99, 95% CI [1.50, 2.63], z = 4.80, p < .001). The 95% CI indicated that the average level of the belief in gods in each country was 1.50 to 2.63 times higher when the number of older adults who showed religious CREDs increased by 1 SD.

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Table 2. The third-step model of hierarchical multilevel logistic regression analysis for the belief in gods in the main focal group.

https://doi.org/10.1371/journal.pone.0305635.t002

As we anticipated, the interaction between the conformist learning cue and the mothers’ CREDs was unlikely (b = 0.09, OR = 1.09, 95% CI [0.86, 1.39], z = 0.71, p = .480) because the 95% CI was across zero (i.e., it is unclear that the association between mother’s CREDs and the belief in gods could be weakened or strengthened by a 1-point (1 SD) change in the conformist learning cue). However, the interaction between the conformist learning cue and the fathers’ CREDs were likely (b = −0.37, OR = 0.69, 95% CI [0.52, 0.92], z = −2.50, p = .012); the fixed slope of the father’s CREDs (b = 1.06) changed by –0.37 as the cultural learning cue increased by 1 SD. A simple slope analysis demonstrated that the association between the fathers’ CREDs and the belief in gods was weaker when the conformist learning cue was 1 SD higher (b = 0.69, OR = 2.00, 95% CI [1.38, 2.91], z = 3.64, p < .001) than when it was 1 SD lower (b = 1.43, OR = 4.18, 95% CI [2.70, 6.48], z = 6.41, p < .001). This suggested that the fathers’ religious CREDs resulted in increased chances of their children believing in gods among the countries or regions where fewer older adults exhibit religious CREDs. The odds ratios of the parents’ CREDs in each country or region are presented in Fig 1. The conformist learning cue for each country or region is indicated using different color gradients.

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Fig 1. The association between kin-biased learning cues and the belief in gods (odds ratios) across 42 countries or regions in the analysis of the data from the main focal group.

The dotted line indicates the fixed slope of the kin-biased learning cue in the overall sample. Color gradients indicate the conformist learning (CL) cue in each country or region. The horizontal axis indicates the odds ratio of kin-biased learning cues on a log scale.

https://doi.org/10.1371/journal.pone.0305635.g001

3.1.2. Religiosity.

We also conducted hierarchical multilevel linear regression analysis using the two kin-biased learning cues and the cue for conformist learning to determine the extent to which the respondents described their religiosity levels. This measure of religiosity was moderately associated with the measure of the belief in gods (correlation ratio: η² = .577).

This analytical strategy was identical to that of the analysis involving the use of the measure for the belief in gods as an outcome variable. The first-step model indicated a significant amount of variation in religiosity levels between different countries or regions. The random intercept variance (0.476) was significantly different from zero (χ² = 1787.2, df = 1, p < .001), and the ICC was .205. In the second step, both the mothers’ CREDs (b = 0.44, 95% CI [0.31, 0.56], t = 6.84, p < .001, VIF = 1.18) and the fathers’ CREDs (b = 0.55, 95% CI [0.40, 0.69], t = 7.56, p < .001, VIF = 1.18) were associated with religiosity. According to the 95% CI, the presence of mother’s (father’s) religious CREDs resulted in 0.31 to 0.56 (0.40 to 0.69) points higher in the religiosity score. The fitness of this second-step model was better than that of the corresponding model, which did not include the random slope terms associated with the two kin-biased learning cues (χ² = 45.5, df = 3, p < .001). As shown in Table 3, in addition to the mothers’ and fathers’ CREDs, the model in the third step revealed that the conformist learning cue was also associated with increased levels of religiosity (b = 0.34, 95% CI [0.17, 0.51], t = 3.83, p < .001). Thus, the average level of the religiosity score across countries or regions was 0.17 to 0.51 (average 0.34) points higher for a 1 SD increase in the percentage of older adults who showed religious CREDs. We also observed an interaction between the conformist learning cue and the mothers’ CREDs (b = −0.14, 95% CI [−0.24, −0.03], t = −2.50, p = .017). The association between the mothers’ CREDs and religiosity (b = 0.44, 95% CI [0.33, 0.56], t = 7.54, p < .001, VIF = 1.38) was weaker when the conformist learning cue was 1 SD higher (b = 0.31, 95% CI [0.17, 0.44], t = 4.55, p < .001) than when the cue was 1 SD lower (b = 0.58, 95% CI [0.40, 0.76], t = 6.37, p < .001). Although the interaction terms demonstrating the relationships between the conformist learning cue and the fathers’ CREDs did not reach statistical significance (b = −0.13, 95% CI [−0.26, 0.002], t = −1.94, p = .059), the 95% CI suggested that a 1 SD change in the conformist learning cue was associated with a decrease in the slope of the father’s CREDs. A simple slope analysis showed the same trend for the mothers’ CREDs. The coefficient of fathers’ CREDs (b = 0.57, 95% CI [0.43, 0.71], t = 7.99, p < .001, VIF = 1.38) became 0.44 when the conformist learning cue was 1 SD higher (95% CI [0.28, 0.60], t = 5.37, p < .001), whereas it was 0.69 when the cue was 1 SD lower (95% CI [0.48, 0.91], t = 6.32, p < .001). For each country or region, the betas of the parents’ CREDs are presented in Fig 2, with different color gradients indicating the conformist learning cue.

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Fig 2. The association between kin-biased learning cues and religiosity (beta) across 42 countries or regions in the analysis of the data from the main focal group.

The dotted line indicates the fixed slope of the kin-biased learning cue in the overall sample. Color gradients indicate the conformist learning (CL) cue in each country or region.

https://doi.org/10.1371/journal.pone.0305635.g002

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Table 3. The third-step model of hierarchical multilevel linear regression analysis for religiosity in the main focal group.

https://doi.org/10.1371/journal.pone.0305635.t003

In short, the individual-level analyses conducted in this study demonstrated that kin-biased and conformist learning cues explained the individual differences in religious beliefs across different countries or regions. Interestingly, the results of these analyses also suggested that the associations between kin-biased learning cues and religious beliefs were robust when the conformist learning cue was not apparent. Regarding the main focal group, the results of the individual-level analyses demonstrated that the fathers’ religious behaviors had a greater impact on the religious beliefs of their children compared to the mothers’ religious behaviors.

3.2.1. Mothers’ CREDs.

For each country or region, we calculated d’ and C using the mothers’ religious CREDs. The countries or regions for which d’ and/or C could not be calculated (e.g., where the mothers’ CREDs were not present among all the respondents in a country or region, the belief in gods was always present when the mothers’ CREDs were present) were excluded from the analysis. As predicted, a one-sample t-test (t (34) = 9.94, p < .001) and the 95% CI (0.56–0.85) showed that the average value of the index d’ (M = 0.72, SD = 0.42) differed from zero (Fig 3A). This indicated that the respondents in the focal group were highly likely to believe in gods if they saw their mothers attending religious services at least once a week throughout their childhood. The average value of the index C (M = 0.70, SD = 0.58) was also likely to be above zero (95% CI [0.50, 0.90], t (34) = 7.15, p < .001, Fig 3B). We then conducted a regression analysis to test whether C could be explained by the conformist transmission cue after both variables were standardized. The t-test (b = 0.63, t = 4.47, p < .001) and the 95% CI (0.35–0.91) indicated that the conformist learning cue was positively related to bias toward the belief in gods (R_adj² = .358; Fig 3C), and this result suggested that people living in countries or regions with high percentages of religiously eager older adults tended to believe in gods.

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Fig 3.

Response sensitivity (d’) and bias (C) toward mothers’ (A) and fathers’ CREDs (B) in the analysis of the data from the main focal group. The relationship between the conformist learning cue and response bias toward the mothers’ CREDs (C) and the fathers’ CREDs (D).

https://doi.org/10.1371/journal.pone.0305635.g003

3.2.2. Fathers’ CREDs.

We excluded 11 countries or regions for which d’ and/or C could not be calculated, after which we conducted analyses for the fathers’ CREDs, which were similar to those conducted for the mothers’ CREDs. The average d’ (M = 0.80, SD = 0.51, 95% CI [0.61, 0.98], t (30) = 8.65, p < .001) and C (M = 0.72, SD = 0.56, 95% CI [0.51, 0.92], t (30) = 7.08, p < .001) differed from zero (Fig 3A and 3B). Moreover, C was positively explained by the conformist learning cue (b = 0.68, 95% CI [0.42, 0.94], t = 5.08, p < .001, R_adj² = .453; Fig 3D).

In summary, the international-level analyses supported our predictions, thereby suggesting that the religious CREDs of parents and older adults independently affected the religious beliefs of the younger generation. The value of the index d’ associated with the fathers’ CREDs was slightly higher than that associated with the mothers’ CREDs, although the difference (−0.10) in the average d’ was not different from zero (95% CI [−0.21, 0.02], t (30) = 1.75, p = .090).

3.3.1. Younger focal group.

The simple bivariable correlation matrix of the key variables in the younger focal group is shown in S2 Table.

We conducted hierarchical multilevel logistic regression analysis using the two kin-biased learning cues and the conformist learning cue to explain the belief in gods. The first-step model showed that the chances of believing in gods differed between different countries or regions (random intercept variance = 1.459, χ² = 1744.6, df = 1, p < .001, ICC = .307). In the second step, we conducted analyses to determine whether the associations between the two kin-biased learning cues and the belief in gods varied between different countries or regions. Consequently, the second-step model assuming variations in these associations (i.e., the model with the two random slope terms) suggested a better fit than the corresponding model, which did not include variations. However, the differences in the deviance were not statistically significant (7709.2 vs. 7714.6, χ² = 5.39, df = 2, p = .068). In the third step, the conformist learning cue and the interaction between it and the kin-biased learning cues on the belief in gods were entered (S3 Table and S1 Fig). This model revealed that the mothers’ CREDs (b = 1.08, OR = 2.94, 95% CI [2.24, 3.84], z = 7.87, p < .001, VIF = 1.31), the fathers’ CREDs (b = 0.61, OR = 1.83, 95% CI [1.39, 2.41], z = 4.34, p < .001, VIF = 1.34), and the conformist learning cue (b = 0.65, OR = 1.91, 95% CI [1.43, 2.55], z = 4.37, p < .001, VIF = 1.01) were independently associated with increased chances of believing in gods. However, the interaction effect was not observed (|b|s < 0.20, ORs < 1.20, |z|s < 1.54, ps > .120).

We also conducted hierarchical multilevel linear regression analysis using religiosity as the outcome variable. The correlation ratio (η²) between the belief in gods and religiosity was .576. The first-step model demonstrated between-country differences in religiosity (random intercept variance = 0.529, χ² = 1662.8, df = 1, p < .001, ICC = .218), whereas the second-step model demonstrated between-country differences in the association between the presence of kin-biased learning cues and religiosity (χ² = 107.75, df = 2, p < .001). The third-step model (S4 Table and S2 Fig) indicated that the mothers’ CREDs (b = 0.61, 95% CI [0.46, 0.76], t = 8.13, p < .001, VIF = 1.18), the fathers’ CREDs (b = 0.63, 95% CI [0.43, 0.84], t = 6.15, p < .001, VIF = 1.17), and the conformist learning cue (b = 0.28, 95% CI [0.09, 0.47], t = 2.86, p < .007, VIF = 1.01) were independently associated with religiosity. The conformist learning cue interacted with only the mothers’ CREDs (b = −0.28, 95% CI [−0.41, −0.15], t = −4.08, p < .001, VIF = 1.14) but not with the fathers’ CREDs (b = 0.02, 95% CI [−0.16, 0.21], t = 0.25, p = .803, VIF = 1.13). This result suggested that the mothers’ CREDs had a stronger association with the religiosity levels when the conformist learning cue was unclear (1 SD low: b = 0.89, 95% CI [0.67, 1.11], t = 7.92, p < .001) than when it was clear (1 SD high; b = 0.33, 95% CI [0.15, 0.50], t = 3.67, p = .002).

Next, we conducted analyses based on the signal detection theory (S3 Fig). We examined whether the average of the sensitivity index (d’) differed from zero and whether the bias index (C) was positively correlated with the conformist learning cue. One-sample t-tests and the 95% CI suggested that the average d’ associated with the mothers’ CREDs (M = 0.85, 95% CI [0.69, 1.01], t (37) = 10.61, p < .001) and the fathers’ CREDs (M = 0.74, 95% CI [0.57, 0.91], t (31) = 8.77, p < .001) were both higher than zero. The difference between the values of the two indices d’ was unlikely to be different from zero (95% CI [−0.04, 0.19], t (31) = 1.30, p = .204). Regression analyses showed that the conformist learning cue positively explained the index C, which was associated with the mothers’ CREDs (b = 0.60, 95% CI [0.30, 0.90], t = 3.96, p < .001, R_adj² = .284) and the fathers’ CREDs (b = 0.62, 95% CI [0.32, 0.93], t = 4.01, p < .001, R_adj² = .327).

3.3.2. Older focal group.

The simple bivariable correlation matrix of the key variables in the younger focal group is shown in S5 Table.

The correlation ratio (η²) between the belief in gods and religiosity in the older focal group was moderate (.580). The first steps of the hierarchical multilevel regression analyses revealed statistically significant between-country variations between the belief in gods (the random intercept variance = 1.35, χ² = 1830, df = 1, p < .001, ICC = .291) and religiosity (random intercept variance = 0.454, χ² = 1793.7, df = 1, p < .001, ICC = .199). The second-step model involving the belief in gods did not support the assumptions regarding country-by-country variations in the associations between the two kin-biased learning cues and the belief in gods (i.e., the deviance of the second-step model was not different from that of the corresponding model, which did not include between-country variations: χ² = 1.59, df = 2, p = .451). However, the results of the third-step model were almost similar to those of the third-step models in the analyses of main and younger focal groups (S6 Table and S4 Fig). The mothers’ CREDs (b = 0.75, OR = 2.11, 95% CI [1.73, 2.57], z = 7.39, p < .001, VIF = 1.46), the fathers’ CREDs (b = 0.68, OR = 1.97, 95% CI [1.61, 2.41], z = 6.54, p < .001, VIF = 1.46), and the conformist learning cue (b = 0.68, OR = 1.97, 95%CI [1.52, 2.56], z = 5.06, p < .001, VIF = 1.01) were associated with the belief in gods. The interactions between the two types of learning cues were not likely (|b|s < 0.06, ORs < 1.06, |z|s < 0.60, ps > 0.59).

Meanwhile, the second-step model involving religiosity revealed between-country variations in the associations between the two kin-biased learning cues and religiosity (i.e., deviance of the second-step model significantly decreased from the corresponding model without between-country variations: χ² = 31.0, df = 2, p < .001). In the third-step model, the mothers’ CREDs (b = 0.50, 95% CI [0.37, 0.62], t = 7.86, p < .001, VIF = 1.37), the fathers’ CREDs (b = 0.38, 95% CI [0.28, 0.49], t = 7.29, p < .001, VIF = 1.47), and the conformist learning cue (b = 0.34, 95% CI [0.18, 0.51], t = 4.12, p < .001, VIF = 1.01) were all associated with religiosity (S7 Table and S5 Fig). Additionally, the interaction between the mothers’ CREDs and the conformist learning cue was observed (b = −0.17, 95% CI [−0.29, −0.05], t = −2.86, p = .006, VIF = 1.30). This suggested that the association between the mothers’ CREDs and religiosity was greater when the conformist learning cue was unclear (−1 SD: b = 0.67, 95% CI [0.48, 0.86], t = 6.91, p < .001) than when it was clear (+ 1 SD; b = 0.32, 95% CI [0.17, 0.47], t = 4.16, p < .001). The interaction with the fathers’ CREDs was not observed (b = −0.03, 95% CI [−0.13, 0.06], t = −0.72, p = .481, VIF = 1.41).

The results of the analyses based on the signal detection theory were consistent with our predictions (S6 Fig). First, d’ associated with the mothers’ CREDs (M = 0.69, 95% CI [0.57, 0.81], t (35) = 11.68, p < .001) and the fathers’ CREDs (M = 0.73, 95% CI [0.61, 0.84], t (35) = 12.58, p < .001) both differed from zero. It is unlikely that these averages would be expected to differ (95% CI [−0.11, 0.02], t (34) = −1.26, p = .216). Second, the conformist learning cue explained the index of C, which was associated with the mothers’ CREDs (b = 0.58, 95% CI [0.28, 0.89], t = 3.72, p < .001, R_adj² = .269) and the fathers’ CREDs (b = 0.61, 95% CI [0.31, 0.91], t = 4.03, p < .001, R_adj² = .303).