Psychometric properties and CFA of the scales
The Social Disconnectedness Scale yielded a Cronbach’s alpha of .64 indicating moderate internal consistency. The item-test correlations exceeded the value of .27 indicating satisfactory reliability , with the exception of item 6 and item 7. The Perceived Isolation Scale attained a Cronbach’s alpha of .68 and item-test correlations > .25. The CES-D scale demonstrated acceptable internal consistency (α = .70) after the exclusion of item 6 and item 10, and item-test correlations > .20. The internal consistency of the LSNS-6 was .82 and item-test correlations were > .41).
According to Cornwell & Waite , the CFA on the 8 Social Disconnectedness items tested the expected two-factor structure (i.e., network size – 5 items - and social inactivity – 3 items). The model showed a χ2 (19) = 53.59, p < .0001. Although significant, this statistic should be used with caution because it is inflated by the large sample size. The CFI = .93 and the RMSEA = .07 (LO90 = .05; HI90 = .10) showed a moderate to good fit of the data. See Fig. 1 for details.
According to Cornwell & Waite  two factors were estimated through a CFA from the 9 items of subjective isolation, i.e., loneliness and lack of social support. The analysis yielded inadequate goodness of fit, χ2 (26) = 196.07, p < .0001, CFI = .65, RMSEA = .15. The errors of the 6 items of the lack of social support were correlated two by two (i.e., errors of items on family/or friends/ or partner correlated to each other). Thus, a second CFA was performed estimating two factors, the first on the 3 items of the lack of social support (from family, friends, and partner) calculated as the average of the original 6 items and the second factor on the 3 items of loneliness. The CFA showed good fit of the data, χ2 (8) = 12.31, p = .14, CFI = .98, and RMSEA = .042, (LO90 = .000, HI90 = .08). See Fig. 2 for details of the second CFA.
The LSNS-6 was checked with SEM and the expected two-factor structure emerged, χ2 (6) = 17,389, p = .006, CFI = .98, RMSEA = .06, (LO90 = .039, HI90 = .12). See Fig. 3 for details. According to Lubben et al.,  the cutoff for social isolated people identified 25.2% of the participants with a score lower than 12.
Relationships among measures
The three scales correlated each other (see Table 2) es expected. Other correlations emerged between Social Disconnectedness and Perceived Isolation and depression (positive), Perceived Isolation, physical (negative) and mental health (negative), the LSNS-6 and depression (negative). Physical and mental health correlated with each other (positive) and with depression (negative). Age correlated with subjective and objective isolation, and depression. Sex was significantly correlated with social disconnectedness and physical and mental health. Social Disconnectedness and Perceived Isolation were moderately correlated with each other, Perceived Isolation was weakly correlated with the LSNS-6, whereas Social Disconnectedness was highly correlated with the LSNS-6.
In both HRAs with physical health as outcome, sex was the only significant predictor (t < − 3.66, p < .0001) with women showing less physical health than men do (β = −.25 for both models). Neither objective isolation nor subjective isolation were significant predictors of physical health. Tables 3 and 4 show results of the HRAs respectively with mental health and depression mood as outcomes.
Women and participants with high perceived isolation scores showed low scores on their mental health and high scores on their depression mood. Age and not having a partner were significant predictors of depression mood.
It was tested whether subjective isolation served as a mediator between objective isolation and health. Table 5 shows the results. The findings yielded support for the full mediation between objective isolation, physical health, mental health, and depression (when the LSNS-6 was considered). Objective isolation was a significant predictor of subjective isolation, which was associated with physical and mental health and depression. There was also a partial mediation between social disconnectedness and depression. In this case, social disconnectedness was a significant predictor of both perceived isolation and depression and perceived isolation predicted an increase in depression.
Mental health and depression should serve as a mediator between subjective isolation and physical health. When depression was the mediator, there was a significant effect of subjective isolation on depression (β = 3.56, SE = .40, p < .001, LLCI = 1.95, ULCI = 4.22) and depression on physical health (β = −.07, SE = .02, p < .001, LLCI = -.09, ULCI = -.05). When perceived mental health was the mediator, there was a significant effect of subjective isolation on mental health (β = −.37, SE = .04, p < .001, LLCI = -.48 -.0003) and mental health on physical health (β = .39, SE = .05, p < .001, LLCI = .30, ULCI = .51). In both mediation analysis, the direct effects were not significant.
The findings yielded support for the moderation effect of the perceived isolation on the relation between social disconnectedness and mental health, F(3 301) = 7.89, p < .001. The interaction was significant, t(301) = 2.71, P = .007, β = .40 (SE = .15), and the main effect of perceived isolation as well, t(301) = − 4.26, p < .001, β = −.43 (SE = .10). The main effect of social disconnectedness was not significant. The Johnson-Neymar technique revealed two regions of significance defined by a lower bound of −.30 and an upper bound of 1.61. As shown in Fig. 4, this region implies that the regression of mental health on social disconnectedness is significant and negative at values of perceived isolation less than −.30 (corresponding to 104 of the 306 participants, 34%), not significantly different from zero at values of perceived isolation between −.30 and 1.61, and significant and positive at values of perceived isolation greater than 1.60 (corresponding to 5 participants, 1.63%). Given that the minimum and maximum values of the perceived isolation were − .60 and 2.65, respectively, both the upper and the lower region fell within the observed range of perceived isolation. However, given the fact that only 1.63% of participants had a value of perceived isolation higher than 1.60, hence this result will not be interpreted further. The lower bound of the region of significance (corresponding to 34% of participants) showed that the regression between social disconnectedness and mental health is negative if the values of perceived isolation are low. In other words, low values of social disconnectedness predicted high mental health but under the effect of low level of perceived isolation.
Results from the moderation analyses showed that the relations between subjective isolation and mental health/depression are not moderated by sex, t(302) = −.42, p > .05, β = −.07 (SE = .17), religious engagement, t(302) = − 1.88, p > .05, β = −.42 (SE = .22), marital status, t(302) = −.50, p > .05, β = −.09 (SE = .18), and education, t(302) = −.11, p > .05, β = −.04 (SE = .16).