Journal of Aging Research Social resources .22 (t = 2.42) .29 (t = 2.23) Social provisions .16 (t = 2.06) .36 (t = 3.12) Self-eﬃcacy 2 R = .30 .31 (t = 3.03) Physical health 2 R = .33 Mental health 2 R = .31 Figure 2: Test results for the support-eﬃcacy model with cente- narians residing in private homes; model ﬁt: Satorra-Bentler χ2 (N = 126; df = 3) =5.14; P = .16; CFI = .97; RMSEA = .08; SRMR = .03(using F1ML). Nonsigniﬁcant paths deleted; parameter estimates are from the standardized solution. Test of Indirect Eﬀect for Social Resources on Physical Health (.07; t = 1.93; P = .053; two-tailed). Test of Indirect Eﬀect for Social Provisions on Physical Health (.09; t = 1.66; P = .097; two-tailed). Endogenous variables were controlled for sex, mental status, ADLs, education, and economic suﬃciency. Muthe´n [57]; this model’s ﬁt was not signiﬁcantly diﬀerent from the model with the path regressing physical health on social provisions: Δχ2 (1 df ) = 2.50, P = .11. The ﬁnal model (see Figure 2) depicts the most par- simonious, best ﬁtting model to our data following the support-eﬃcacy conceptualization for centenarians residing in private dwellings. Direct eﬀects for social resources on physical health (β = .16; P < .05) and social provisions on mental health (β = .36; P < .05) were found in the previous model, whereas in this best-ﬁtting model for centenarians in private homes, no direct eﬀects for social resources on mental health or social provisions on physical health were found. However, consistent with Antonucci and colleagues [13], indirect eﬀects operating through self-eﬃcacy were found both for social resources (.07; P = .053; two-tailed test) and social provisions on physical health (.09; P = .097; two- tailed test), whereas no indirect eﬀects were found for either predictor on the outcome mental health. 3.2. Centenarians in Assisted Living Facilities. In the base model, signiﬁcant predictors of physical health and self- eﬃcacy were found; no predictors were found for mental health. Physical health was predicted by social resources (β = .34; P ≤ .003) and self-eﬃcacy by social provisions (β = .58; P ≤ .02). Based on these results we tested a model deleting the path of social provisions predicting physical health, social resources predicting self-eﬃcacy, and the predictors of mental health except controls. This model ﬁt the data adequately: MLR χ2 (5, N = 55) = 8.93; P = .11; CFI = .91; RMSEA = .12; SRMR = .06. However, in addition to the higher value for RMSEA, one of the modiﬁcation indices looked promising for the regression of mental health on self-eﬃcacy, so we tested a model including this path. This model ﬁt the data well: MLR χ2 (4, N = 55) = 5.29, P = .26, CFI = .97; RMSEA = .08; SRMR = .04. The nested model chi-square test was signiﬁcant (Δχ2 = 6.90, 1 df, P = .01). We selected the latter model over the former because the Chi-square and the CFI, RMSEA, and SRMR Social resources .24 (t = 1.79) .57 (t = 2.35) Social provisions Self-eﬃcacy 2 R = .47 .25 (t = 1.84) .30 (t = 2.00) Physical health 2 R = .48 Mental health 2 R = .41 5 Figure 3: Test results for the support-eﬃcacy model with centenar- ians residing in assisted living facilities; model ﬁt: Satorra-Bentler χ2 (N = 55; df = 4) =5.29; P = .26; CFI = .97; RMSEA = .08; SRMR = .04(using F1ML). Parameter estimates are from the standardized solution; endogenous variables were controlled for sex, mental status, ADLs, education, and economic suﬃciency. indices suggested that it was the better ﬁtting model than the nested model with more degrees of freedom (see Figure 3). In addition, we conducted the tests of indirect eﬀects from social provisions to both physical and mental health. The indirect eﬀect on physical health was not signiﬁcant (P = .18), whereas the indirect eﬀect from social provisions on mental health through self-eﬃcacy reached signiﬁcance for a hypothesized eﬀect (P = .05; one-tailed test). 3.3. Centenarians in Nursing Homes. The base model used in previous analyses could not be tested because the covariance coverage fell below 10 percent (i.e., all variables and pairs of variables have data for at least ten percent of the sample). Inspection of our individual variables led us to delete our measure for economic suﬃciency. In addition, when this model was run, diﬃculties were encountered estimating appropriate standard errors (nonpositive deﬁnite matrix) based on the control variable sex. Of the 105 centenarians living in nursing homes, 92 were female and 13 male. Thus, further models for centenarians in nursing homes excluded economic suﬃciency and the control variable, sex. No further estimation diﬃculties were encountered. In the tested base model, neither exogenous predictor, social resources (β = .20; P > .05) nor social provisions (β = −.13; P > .05) signiﬁcantly predicted self-eﬃcacy. However, both self-eﬃcacy (β = .60; P = .01) and social provisions (β = −1.09; P = .008) signiﬁcantly predicted mental health, whereas only social provisions approached statistical signiﬁcance predicting physical health (β = .77; P = .14). Regarding the magnitude of the standardized beta for social provisions, Jo¨reskog [62] noted that it is possible for a standardized coeﬃcient to be greater than one (e.g., 1.04, 1.40, or 2.08) and that it does not necessarily imply error in the model. However, he did point out that such a ﬁnding likely points to multicollinearity in the data. Our measure of ADLs was negatively and highly correlated with social provisions (r = −.85) in this model. Thus, we deleted ADLs from the analysis and found that indeed social provisions signiﬁcantly predicted physical health (β = .43; P = .02), neither measure of social resources predicted self-eﬃcacy, and only self-eﬃcacy predicted mental health