Our 443 respondents (egos) are preponderantly pro-vaccination (ƒ = 319; 72.0%), females (ƒ = 335; 75,6%), have higher education (ƒ = 285; 64.3%), and a monthly income between the national minimum and median salary (ƒ = 193; 43.6%). They are relatively young (Median = 34.0 years old, Range = 56.0) and embedded in personal networks of durable relationships (Mdn = 23.0 years; R = 77.0). Their personal networks have rather only one component (Mdn = 1.0, R = 9.0), with a low degree of centralization (Mdn = 0.3, R = 0.7), and moderate density (Mdn = 0.4, R = 1.0). Overall, in their social contexts, the interviewees are surrounded by females (ƒ = 2,717; 61.3%) and by contacts who reportedly have pro-vaccination opinions (ƒ = 2,895; 65.4%). Further, people with higher education are slightly prevalent in egos’ networks (ƒ = 2,226; 50.3%).
Looking at the 4,430 alters in our dataset, their median age is similar to the one of the egos (Mdn = 40.0; R = 72.0), which may express an age selection effect. Given the high number of pro-vaccines alters in each network (Mean = 6.5, Std. Dev. = 3.0, Mdn = 7, R = 10), the number of ties to peers that are in favor of COVID-19 vaccination (M = 2.9, SD = 2.2, Mdn = 3.0, R = 9.0) is higher than the one to peers that are against (M = 1.0, SD = 1.5, Mdn = 0.0, R = 9.0). Further, alters have, on average, 4.2 ties (SD = 2.5, Mdn = 4.0, R = 9.0), and display low scores of betweenness (M = 2.1, SD = 4.8, Mdn = 0.0, R = 34.0). We emphasize that in each personal network, the maximum number of alter-alter ties is nine (all personal networks have ten alters). Detailed descriptive statistics about the variables of interest are available in Tables 1–2. We also compute the distribution of our variables of interest by the egos as a grouping variable; see Fig. 1 (descriptive statistics on each personal network are available in the Supplementary Material).
Table 1
Descriptive statistics. Numeric variables of interest
Egos | | | | | | |
| Age | Betweenness | Constraint | Centralization | Density | Components |
Mean | 36.47 | 24.07 | 0.32 | 0.31 | 0.47 | 1.67 |
Std.Dev | 11.20 | 8.90 | 0.04 | 0.15 | 0.20 | 1.28 |
Min | 19.00 | 0.00 | 0.10 | 0.00 | 0.00 | 1.00 |
Q1 | 28.00 | 19.00 | 0.30 | 0.22 | 0.33 | 1.00 |
Median | 34.00 | 25.00 | 0.33 | 0.31 | 0.44 | 1.00 |
Q3 | 44.00 | 30.00 | 0.35 | 0.40 | 0.58 | 2.00 |
Max | 75.00 | 45.00 | 0.38 | 0.73 | 1.00 | 10.00 |
MAD | 11.86 | 8.90 | 0.03 | 0.13 | 0.19 | 0.00 |
IQR | 16.00 | 11.00 | 0.05 | 0.18 | 0.25 | 1.00 |
CV | 0.31 | 0.37 | 0.13 | 0.47 | 0.43 | 0.76 |
Skewness | 0.66 | -0.56 | -1.89 | 0.06 | 0.57 | 3.07 |
SE.Skewness | 0.04 | 0.12 | 0.12 | 0.12 | 0.12 | 0.12 |
Kurtosis | -0.17 | 0.24 | 5.40 | -0.17 | 0.24 | 12.56 |
N.Valid | 443.00 | 443.00 | 443.00 | 443.00 | 443.00 | 443.00 |
Pct.Valid | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
Alters | | | | | | |
| Age | Betweenness | Ties to anti-vaccination peers | Ties to pro-vaccination peers | Degree | Ego alter tie duration (years) |
Mean | 41.71 | 2.14 | 1.04 | 2.90 | 4.19 | 22.82 |
Std.Dev | 15.05 | 4.82 | 1.48 | 2.23 | 2.49 | 14.99 |
Min | 18.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 |
Q1 | 30.00 | 0.00 | 0.00 | 1.00 | 2.00 | 8.00 |
Median | 40.00 | 0.00 | 0.00 | 3.00 | 4.00 | 23.00 |
Q3 | 52.00 | 1.50 | 2.00 | 4.00 | 6.00 | 33.00 |
Max | 90.00 | 34.00 | 9.00 | 9.00 | 9.00 | 78.00 |
MAD | 16.31 | 0.00 | 0.00 | 2.97 | 2.97 | 19.27 |
IQR | 22.00 | 1.50 | 2.00 | 3.00 | 4.00 | 25.00 |
CV | 0.36 | 2.25 | 1.43 | 0.77 | 0.59 | 0.66 |
Skewness | 0.57 | 3.17 | 1.81 | 0.74 | 0.32 | 0.34 |
SE.Skewness | 0.04 | 0.04 | 0.04 | 0.04 | 0.04 | 0.04 |
Kurtosis | -0.29 | 10.74 | 3.49 | 0.00 | -0.74 | -0.66 |
N.Valid | 4430.00 | 4430.00 | 4212.00 | 4212.00 | 4430.00 | 4430.00 |
Pct.Valid | 100.00 | 100.00 | 95.08 | 95.08 | 100.00 | 100.00 |
Table 2
Descriptive statistics. Categorical variables of interest
| Opinions about COVID-19 vaccination |
| Egos | Alters |
Very good & good | 319 | 72.01% | 2,895 | 65.35% |
Very bad & bad | 87 | 19.64% | 1,055 | 23.81% |
Missing | 37 | 8.35% | 480 | 10.84% |
Total | 443 | 100.00% | 4,430 | 100.00% |
| Sex |
| Egos | Alters |
Male | 108 | 24.38% | 1,713 | 38.67% |
Female | 335 | 75.62% | 2,717 | 61.33% |
Missing | 0 | 0.00% | 0 | 0.00% |
Total | 443 | 100.00% | 4,430 | 100.00% |
| Higher education studies |
| Egos | Alters |
Yes | 285 | 64.33% | 2,226 | 50.25% |
No | 158 | 35.67% | 2,204 | 49.75% |
Missing | 0 | 0.00% | 0 | 0.00% |
Total | 443 | 100.0% | 4,430 | 100.00% |
| Income | | |
| Egos | | |
Less than minimum wage | 78 | 17.61% | | |
In-between minimum & median wage | 193 | 43.57% | | |
In-between median wage & median wage plus one minimum wage | 145 | 32.73% | | |
More than median wage plus one minimum wage | 27 | 6.09% | | |
Missing | 0 | 0.00% | | |
Total | 443 | 100.00% | | |
We report in Table 3, the results of the multilevel logistic regression models fitted to predict alters’ opinion about COVID-19 vaccination. And specifically, to detect evidence of possible assortativity effects in personal networks.
Table 3
Multilevel logistic regression models explaining alters’ opinion about vaccination
| Model 0 (‘intercept’) | Model 1 (‘attributes’) | Model 2 (‘network’) | Model 3 (‘full’) |
| Log-odds (95% CI) | OR (p) | Log-odds (95% CI) | OR (p) | Log-odds (95% CI) | OR (p) | Log-odds (95% CI) | OR (p) |
alter sex | | | 0.08 (-0.12; 0.27) | 1.08 (0.435) | | | 0.11 (-0.08; 0.31) | 1.12 (0.260) |
alter edu | | | 0.46 (0.25; 0.67) | 1.58 (< 0.001) | | | 0.44 (0.23; 0.65) | 1.55 (< 0.001) |
alter age | | | 0.15 (0.04; 0.26) | 1.16 (0.005) | | | 0.16 (0.04; 0.28) | 1.17 (0.008) |
ego sex | | | 0.08 (-0.27; 0.42) | 1.08 (0.658) | | | 0.06 (-0.29; 0.41) | 1.06 (0.739) |
ego edu | | | -0.28 (-0.61; 0.05) | 0.75 (0.094) | | | -0.28 (-0.62; 0.06) | 0.75 (0.102) |
ego income | | | 0.18 (-0.01; 0.38) | 1.20 (0.069) | | | 0.19 (-0.01; 0.39) | 1.21 (0.065) |
ego age | | | 0.05 (-0.11; 0.20) | 1.05 (0.561) | | | 0.04 (-0.12; 0.20) | 1.04 (0.612) |
ego covid | | | 2.14 (1.80; 2.48) | 8.48 (< 0.001) | | | 2.12 (1.77; 2.46) | 8.30 (< 0.001) |
ego alter duration | | | | | 0.05 (-0.05; 0.15) | 1.05 (0.324) | 0.00 (-0.12; 0.12) | 1.00 (0.997) |
assortativity | | | | | 0.30 (0.21; 0.38) | 1.34 (< 0.001) | 0.27 (0.19; 0.36) | 1.31 (< 0.001) |
alter betw | | | | | 0.07 (-0.03; 0.17) | 1.07 (0.156) | 0.10 (0.00; 0.20) | 1.10 (0.058) |
comp | | | | | 0.03 (-0.18; 0.25) | 1.04 (0.758) | 0.09 (-0.09; 0.27) | 1.10 (0.312) |
dens | | | | | 0.05 (-0.19; 0.28) | 1.05 (0.696) | 0.09 (-0.10; 0.28) | 1.10 (0.345) |
centraliz | | | | | 0.03 (-0.18; 0.24) | 1.03 (0.809) | 0.03 (-0.14; 0.20) | 1.03 (0.736) |
Intercept | 1.46 (1.28; 1.65) | 4.32 (< 0.001) | -0.69 (-1.17; -0.20) | 0.50 (0.005) | 1.47 (1.28; 1.66) | 4.36 (< 0.001) | -0.66 (-1.16; -0.17) | 0.51 (0.008) |
Num. obs. | 3,588 | | 3,588 | | 3,588 | | 3,588 | |
Num. groups: ego_id | 401 | | 401 | | 401 | | 401 | |
ICC | 0.414 | | 0.260 | | 0.412 | | 0.265 | |
AIC | 3616.287 | | 3462.61 | | 3576.006 | | 3428.7 | |
BIC | 3628.658 | | 3524.464 | | 3625.489 | | 3527.665 | |
Log Likelihood | -1806.144 (df = 2) | | -1721.305 (df = 10) | | -1780.003 (df = 8) | | -1698.35 (df = 16) | |
Var (SD): ego_id (Intercept) | 2.323 (1.524) | | 1.153 (1.074) | | 2.305 (1.518) | | 1.183 (1.088) | |
We find that alters with a higher level of education (Model 1, OR: 1.58, 95% CI: 1.28, 1.95, p < .001; Model 3, OR = 1.55, 95% CI: 1.26, 1.91, p < .001) and older alters (M1, OR: 1.16, 95% CI: 1.05, 1.29, p = .005; M3, OR = 1.17, 95% CI: 1.04, 1.32, p = .008) are more likely to have a positive opinion on Covid19 vaccination. The only significant effect among the network-based covariates is the assortativity variable which is consistently positive (M2, OR: 1.34, 95% CI: 1.24, 1.46, p < .001; M3: OR: 1.31, 95% CI: 1.21, 1.43, p < .001). This indicates that alters with similar opinions cluster together. Namely, people are more likely to have a positive attitude if their neighbors, on average, have a more positive attitude than the average attitude in the network. We also find that ego’s opinion about vaccination makes a statistically significant contribution in predicting alters’ opinions (M1, OR: 8.48, 95% CI: 6.03, 11.94, p < .001; M3: OR: 8.30, 95% CI: 5.87, 11.73, p < .001). This positive association suggests a possible ego-alter contagion effect or, alternatively, a social selection effect in the sense that egos tend to select alters with the same opinion.
Table 4
(Standard) logistic regression models explaining alters’ opinions about vaccination.
| Model 0 (‘intercept’) | Model 1 (‘attributes’) | Model 2 (‘network’) | Model 3 (‘full’) |
| Log-odds (95% CI) | OR (p) | Log-odds (95% CI) | OR (p) | Log-odds (95% CI) | OR (p) | Log-odds (95% CI) | OR (p) |
alter sex | | | 0.05 (-0.13; 0.23) | 1.05 (0.568) | | | 0.09 (-0.09; 0.28) | 1.10 (0.318) |
alter edu | | | 0.43 (0.25; 0.62) | 1.54 (< 0.001) | | | 0.41 (0.22; 0.60) | 1.51 (< 0.001) |
alter age | | | 0.14 (0.04; 0.23) | 1.15 (0.006) | | | 0.14 (0.03; 0.25) | 1.15 (0.013) |
ego sex | | | 0.02 (-0.19; 0.23) | 1.02 (0.845) | | | -0.00 (-0.22; 0.21) | 1.00 (0.988) |
ego edu | | | -0.24 (-0.44; -0.04) | 0.79 (0.021) | | | -0.23 (-0.43; -0.02) | 0.80 (0.030) |
ego income | | 0.02 (-0.10; 0.14) | 1.02 (0.719) | | | 0.02 (-0.10; 0.14) | 1.02 (0.731) |
ego age | | | -0.03 (-0.13; 0.07) | 0.97 (0.549) | | | -0.04 (-0.15; 0.06) | 0.94 (0.424) |
ego covid | | | 0.72 (0.50; 0.94) | 2.05 (< 0.001) | | | 0.67 (0.44; 0.89) | 1.95 (< 0.001) |
ego alter duration | | | | 0.04 (-0.05; 0.12) | 1.04 (0.412) | 0.01 (-0.09; 0.12) | 1.01 (0.793) |
assortativity | | | | | 0.28 (0.20; 0.35) | 1.32 (< 0.001) | 0.26 (0.18; 0.33) | 1.30 (< 0.001) |
alter betw | | | | | 0.08 (-0.01; 0.18) | 1.09 (0.081) | 0.10 (0.00; 0.19) | 1.10 (0.050) |
comp | | | | | 0.05 (-0.06; 0.16) | 1.05 (0.358) | 0.08 (-0.03; 0.19) | 1.08 (0.175) |
dens | | | | | 0.07 (-0.04; 0.18) | 1.07 (0.225) | 0.09 (-0.02; 0.21) | 1.10 (0.107) |
centraliz | | | | | 0.03 (-0.06; 0.13) | 1.04 (0.491) | 0.04 (-0.06; 0.14) | 1.04 (0.467) |
prop vacc ex alter | 1.01 (0.93; 1.10) | 2.74 (< 0.001) | 0.82 (0.72; 0.92) | 2.71 (< 0.001) | 1.01 (0.93; 1.10) | 2.75 (< 0.001) | 0.84 (0.73; 0.94) | 2.31 (< 0.001) |
Intercept | 1.27 (1.18; 1.36) | 3.56 (< 0.001) | 0.56 (0.23; 0.88) | 3.27 (< 0.001) | 1.28 (1.19; 1.37) | 3.61 (< 0.001) | 0.61 (0.28; 0.94) | 1.84 (< 0.001) |
Num. obs. | 3,588 | | 3,588 | | 3,588 | | 3,588 | |
AIC | 3428.97 | | 3377.527 | | 3380.57 | | 3338.17 | |
BIC | 3441.34 | | 3439.38 | | 3430.053 | | 3437.136 | |
Log Likelihood | -1712.485 (df = 2) | | -1678.763 (df = 10) | | -1682.285 (df = 8) | | -1653.085 (df = 16) | |
Deviance | 3424.97 | | 3357.527 | | 3364.57 | | 3306.17 | |
We assess the robustness of our results (Table 3) by fitting standard logistic regression models, without any multilevel structure (Table 4). In these models, the additional variable proportion of alters that are pro-vaccination (excluding the alter of reference), i.e., prop vacc ex alter, control for the average opinion of all other alters in the network. Interestingly, the two families of models (the multi-level logistic and standard logistic regression models) qualitatively yield the same results for almost all effects. The only qualitative difference in the standard logistic regression models, compared to the multilevel models, is that in the “joint” model (M3, in Table 4), alters whose ego has a higher level of education are less likely to have a positive opinion (M1, OR: 0.79, 95% CI: 0.65–0.96, p = .021; M3, OR: 0.80, 95% CI: 0.65–0.98, p = .030). While this might seem strange at first glance, we have to take into account that all alter data is reported by ego. The negative effect of ego’s education could reveal a social prejudice that higher educated people think more often that their alters have a negative attitude toward vaccination. Thus, it might be a sign that egos with different levels of educations have a different understanding of what constitutes a positive opinion. Similarly, in the multi-level logistic regression models (Table 3), ego’s education also has a negative effect. However, this is not statistically significant (M1, OR: 0.75, 95% CI: 0.54, 1.05, p = .094; M3, OR: 0.75, 95% CI: 0.54, 1.06, p = .102).
In Table 4, the additional control variable prop vacc ex alter (proportion of alters that are pro-vaccination, excluding the alter of reference), giving the average opinion among the alters in the same network (minus the alter of reference), has a strongly positive effect on the attitude of the alter of reference. While this was expected (in fact, everything else would be a surprise), it underlines the need to control for the average opinion in the network. Note that the multilevel models control for varying average opinion via the random ego-level intercepts.