During survey completion, some data were not collected due to refusal of the respondents, negligence of the investigators, or issues with the questionnaire itself but were resolved by multiple imputation methods. The goal of using descriptive statistics was to gain an understanding from the personal characteristic data of the participants. Absolute and relative frequencies were determined for categorical data, and the mean and standard deviation (SD) were determined for continuous data.

The current study determined the test-retest reliability of the Chinese version of the scale by evaluating participants. Residents were revisited 3 days later by a different assessor who they had not met previously, and the scale was assessed again. Using the comprehensive Cohen κ statistic, including 95 % confidence intervals, the personal items and the administrator rating were compared under continuous testing. The κ value is expressed as a number between 0 and 1, where 0 indicates no agreement and 1 indicates complete agreement; therefore, κ values of ≥ 0.81 indicate almost perfect agreement, those between 0.80 and 0.61 indicate substantial agreement, and those between 0.60 and 0.41 indicate moderate agreement [33].

The internal consistency reliability was tested by using McDonald’s ω (hierarchical), Cronbach’s α, and McDonald’s ω total for each competency [34]. The α value is expressed as a number between 0 and 1; thus, an α value of ≥ 0.91 indicates excellent reliability, and a value between 0.90 and 0.71 indicates acceptable reliability [35]. Two types of item analysis were used, including (1) within-item relevance and (2) item-to-total correlation, to analyse the homogeneity of the research tool. Finally, the correlation between the subscale and the total scale was analysed. Cronbach’s α coefficient was used to measure the internal consistency reliability between the Chinese version of the PaArticular Scales and its subscales.

The Kaiser-Meyer-Olkin (KMO) and Bartlett sphericity tests were both performed to determine whether the data collected from the questionnaire were suitable for factor analysis. According to the principle of varimax rotation, EFA was used to assess the validity of the Chinese version of the PaArticular Scales. The original English version of the PaArticular Scales has good criterion validity and internal consistency reliability [15]. EFA was used to determine the essential structure of multivariate observations. The factors were first selected based on a screening index of an eigenvalue > 1.0 [36]. The factors were selected again based on a scree plot, clinical experience, and the original factor structure of the scales [3740]. Finally, the items were selected, provided that the minimum variance of each factor was 5 %.

Convergent construct validity was evaluated by comparing the Pearson correlation coefficients of the Chinese version of the PaArticular Scales to both the WHOQoL-BREF and WHODAS 2.0–36 items, which have been used previously among elderly residents in LTC facilities. These comparisons are valuable because alterations in activity and participation are accompanied by alterations in participants’ QoL [41, 42]. The point-biserial correlation coefficient was used to calculate the correlations among the Chinese version of the WHOQoL-BREF, the Chinese version of the WHODAS 2.0–36 items, and the Chinese version of the PaArticular Scales total score to establish concurrent validity. All data were statistically analysed using the SPSS 22.0 software package (IBM, Armonk, NY, USA).

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