Table 1.

Methodological Considerations.

Challenge	Alternative method used
UCLA-LS structure
1. The structure of the UCLA measure is unclear	1. Several structures were considered alongside a three-factor ESEM model
Sample
2. Unbalanced age groups may lead to biased measurement invariance findings	2. Analyses were based on 100 random samples of balanced groups
Measurement invariance testing
3. The chi-square difference test used to compare nested models is sensitive to sample size	3. A CFI difference of .01 was used to compare the nested models
4. The accuracy of CFI difference with polychoric data and WLSMV is not well established	4. Items were treated as continuous and MLR was used to account for skewed data
5. Model modification in the search for partial measurement invariance based on modification indices can be biased	5. Where full measurement invariance was not achieved, alignment was considered
6. Alignment is not implemented yet for ESEM models and modification indices are not available for multiple imputation	6. Model modifications for the ESEM model were based on post-hoc pairwise comparisons using Wald tests
7. RMSEA can be overestimated in models with small samples and degrees of freedom	7. RMSEA was not considered in baseline models with degrees of freedom < 20
8. Breaking a continuous variable such as age into discrete groups has several theoretical and methodological limitations	8. Local structural equation modeling was employed where the age invariance of the measures was considered through a continuous moderator

Note. UCLA-LS = University of California Los Angeles, Loneliness Scale; ESEM = Exploratory Structural Equation Modeling; CFI = comparative fit index; WLSMV = weighted least squares mean and variance adjusted; MLR = robust maximum likelihood; RMSEA = root mean square error of approximation.