Exploratory factor analysis (EFA)
The KMO test value of CPSS-10 in this study was 0.88, and Bartlett test of sphericity was significant (Chi-square = 1703.26,P < 0.01), which met the prerequisite for EFA. EFA results showed that eigenvalues of the first two components were greater than 1 (4.62 and 1.91), so the two factors structure is suitable. Factor 1 was composed of six negative items (called PHS subscale), accounting for 46.15% of the variance. Factor 2 was composed of four positive items (PSES subscale), explaining 19.13% of the variance (Table 1). There was no double loading in the pattern matrix, and the loading of all valid items was greater than 0.5. In addition, there was a correlation between PHS and PSES (r = 0.39, P < 0.05).
Table 1
Exploratory factor analysis (EFA) and reliability of CPSS-10
PSS-10 items (In the last month, how often have you…) | Factor loadings |
PHS | PSES |
Item 1 | …been upset because of something that happened unexpectedly? | 0.81 | -0.06 |
Item 2 | …felt that you were unable to control the important things in your life? | 0.85 | -0.06 |
Item 3 | …felt nervous and ‘stressed’? | 0.81 | -0.03 |
Item 4 | …felt confident about your ability to handle your personal problems? | 0.01 | 0.72 |
Item 5 | …felt that things were going your way? | -0.08 | 0.68 |
Item 6 | …found that you could not cope with all the things that you had to do? | 0.75 | 0.05 |
Item 7 | …been able to control irritations in your life? | 0.02 | 0.55 |
Item 8 | …felt that you were on top of things? | 0.11 | 0.79 |
Item 9 | …been angered because of things that were outside of your control? | 0.75 | 0.04 |
Item 10 | …felt difficulties were piling up so high that you could not overcome them? | 0.71 | 0.11 |
Eigenvalue | 4.62 | 1.91 |
% of variance explained | 46.15 | 19.13 |
Total% of variance explained | 65.28 |
Cronbach’s alpha coefficient of Factor 1 and 2 | 0.91 | 0.77 |
Cronbach’s alpha coefficient of the whole scale | 0.86 |
Inter-factor Pearson’s correlation (2-tailed) | 0.39 |
Note. PSS-10 10-item Perceived Stress Scale; PHS Perceived helplessness Subscale (First common factor); PSES Perceived Self-Efficacy Subscale (Second common factor). |
Confirmatory Factor Analysis
Table 2 showed the goodness of fit of the CFA model for CPSS-10. The one-factor CFA model had poor fit, Chi-square/df = 12.02, CFI = 0.77, TLI = 0.71, RMSEA = 0.18 (95%CI [0.12–0.15]), SRMR = 0.13. All indices of fit goodness did not meet the statistical criteria. However, the two factor of CFA model showed a good fit. The fitting index, Chi-square/df = 2.95, CFI = 0.96, TLI = 0.95, RMSEA = 0.07(95%CI [0.06,0.09]), SRMR = 0.04, all of them met criteria well. The results of model 3 in Table 2 showed that PSS-10 of bifactor model was preferred with fitting effect, Chi-square/df = 1.62, CFI = 0.99, TLI = 0.99, RMSEA = 0.07 (95%CI [0.06,0.09]), SRMR = 0.07, which was better than that of two-factor of CFA model (Chi-square = 73.385, P < 0.001). Figure 1 showed the schematic representations of one factor model (a), two factor model (b) and bifactor model (c) of CPSS-10.
Table 2
Comparison between confirmatory factor analysis and bifactor model
Model | Chi-square | df | Chi-square/df | CFI | TLI | RMSEA (95%CI) | SRMR |
Model1 | 420.55 | 35 | 12.02 | 0.77 | 0.71 | 0.18(0.16,0.19) | 0.13 |
Model2 | 100.46 | 34 | 2.95 | 0.96 | 0.95 | 0.07(0.06,0.09) | 0.04 |
Model3 | 40.44 | 25 | 1.62 | 0.99 | 0.99 | 0.04(0.01,0.06) | 0.07 |
Note. CFI Comparative fit index; SRMR standardized root-mean-square residual; RMSEA room-mean-square error of approximation; CI confidence interval; df degree of freedom; TLI tucker Lewis index. |
Model1: one-factor of CFA model |
Model2: two-factor of CFA model |
Model3: PSS-10 of the bifactor model |
Unidimensionality
Principal component analysis (PCA) showed that the residual explained 46.77% of the original variance (less than 50%). The ratio of the first factor eigenvalue to the second factor eigenvalue is 2.58 (e.g., < 3). Two factor structure of CPSS-10 was found in both EFA and CFA, as shown in Table 2. In addition, Martin-Loef-Test found that LR value = 365.186, P < 0.001, which indicated that CPSS-10 may not be an unidimensional scale. The bifactor model showed that PCU = 0.53 < 0.8, and ECV = 0.65 (which was less than 0.70), indicating there were not only general factor, but also specific factors. These above results confirmed the multidimensional of CPSS-10 from different aspects.
Reliability
In our study, the overall, PHS subscale, and PSES subscales Cronbach's alpha coefficient were 0.86, 0.91 and 0.77, respectively (Table 1). The overall reliability and PHS subscales were high, while the reliability of PSES subscale was only acceptable. After removing item 5 and item 7, the Cronbach's alpha coefficient increased, which were 0.863 (95%CI [0.833,0.886]) and 0.865 (95%CI [0.836,0.889]) respectively, while deleting any other item would reduce the Cronbach's alpha coefficient. This result indicated that the CPSS-10 could be further optimized (Table 3).
Table 3
Cronbach’s alpha and goodness of PSS-10
Item | Outfit | Outfit.z | Infit | Infit.z | Cronbach’s alpha after removing the item (95%CI) |
Item 1 | 0.838 | -1.615 | 0.856 | -1.677 | 0.840 (0.807,0.867) |
Item 2 | 0.717 | -2.405 | 0.807 | -2.274 | 0.838 (0.800,0.868) |
Item 3 | 0.778 | -1.781 | 0.850 | -1.726 | 0.838 (0.803,0.867) |
Item 4 | 1.068 | 0.644 | 0.991 | -0.046 | 0.856 (0.827,0.881) |
Item 5 | 1.038 | 0.420 | 0.952 | -0.482 | 0.863 (0.833,0.886) |
Item 6 | 0.810 | -2.074 | 0.853 | -1.764 | 0.839 (0.807,0.868) |
Item 7 | 1.204 | 1.784 | 1.077 | 0.768 | 0.865 (0.836,0.889) |
Item 8 | 0.064 | -3.318 | 0.220 | -6.569 | 0.845 (0.815,0.872) |
Item 9 | 0.807 | -2.100 | 0.860 | -1.623 | 0.838 (0.804,0.866) |
Item 10 | 0.819 | -1.585 | 0.903 | -1.089 | 0.837 (0.802,0.865) |
Note. PSS-10 10-item Perceived Stress Scale; CI confidence interval; Infit Information-weighted fit statistic; Outfit outlier-sensitive fit statistic. |
Multidimensional Graded Response Model (Mgrm) Analysis
Infit and outfit MNSQ values were used to evaluate the fitting of items. MNSQ of infit and outfit for MGRM were 0.807–1.077 and 0.717–1.204 respectively, which showed an overall good fitting effect of CPSS-10. However, the fitting effect of item 8 was poor with infit and outfit MNSQ value 0.064 and 0.220, respectively (Table 3).
CFA combined with MGRM analysis was used to test the CPSS-10 structure of the emergency medical team. The loads of all items were greater than 0.60, and no item showed disorder threshold (Table 4 and Fig. 2). Items 1, 2, 3, 6, 9, and 10 had higher loads on the coefficient λ1 (PHS subscale), while items 4, 5, 7, and 8 had higher loads on the coefficient λ2 (PSES subscale), which confirmed the stability of two-factor structure CPSS-10. MGRM showed that the correlation between PHS and PSES was 0.535. In addition, category probability curves of items 5 and 6 were provided, see Fig. 2A and 2B, which showed that the items could distinguish personnel ability and project difficulty. Other items of CPSS-10 showed similar category probability curves (Additional file 1: Figure S1).
Table 4
Confirmatory factor analysis combined with MGRM for 2-factor structure of CPSS-10
Item | \({\lambda }_{1}\left(se\right)\) | \({\lambda }_{2}\left(se\right)\) | \({a}_{1}\left(se\right)\) | \({a}_{2}\left(se\right)\) | \({b}_{1}\left(se\right)\) | \({b}_{2}\left(se\right)\) | \({b}_{3}\left(se\right)\) | \({b}_{4}\left(se\right)\) |
Item 1 | 0.79(0.06) | | 2.81(0.27) | | -1.14(0.21) | -0.23(0.03) | 1.45(0.31) | 2.51(0.66) |
Item 2 | 0.82(0.06) | | 3.23(0.32) | | -0.81(0.10) | 0.29(0.11) | 1.75(0.48) | 2.60(0.91) |
Item 3 | 0.80(0.07) | | 2.94(0.28) | | -0.77(0.16) | 0.08(0.03) | 1.60(0.34) | 2.30(0.57) |
Item 6 | 0.76(0.05) | | 2.59(0.24) | | -0.97(0.18) | 0.44(0.09) | 2.19(0.24) | 3.21(1.01) |
Item 9 | 0.77(0.06) | | 2.62(0.22) | | -1.09(0.25) | 0.21(0.05) | 1.87(0.29) | 2.75(0.68) |
Item 10 | 0.75(0.06) | | 2.54(0.24) | | -0.62(0.11) | 0.70(0.14) | 2.20(0.44) | 3.03(0.82) |
Item 4 | | 0.70(0.07) | | 2.06(0.18) | -0.98(0.21) | 0.72(0.17) | 1.95(0.29) | 2.43(0.39) |
Item 5 | | 0.62(0.08) | | 1.62(0.17) | -2.10 (0.28) | 0.27(0.14) | 1.92 (0.23) | 2.92(1.01) |
Item 7 | | 0.86(0.09) | | 1.72(0.17) | -0.88(0.17) | 0.90(0.17) | 2.04(0.26) | 2.73(0.38) |
Item 8 | | 0.58(0.08) | | 7.97(0.67) | -0.95(0.63) | 0.80(0.50) | 1.76(1.35) | 2.16(1.50) |
Note: λ indicate factor loadings; α is the item discrimination (slope) parameter; b1to b4 are item response category difficulty (threshold, location) parameters; Bolded items indicate the items chose for short form of CPSS-10; se standard error. |
Table 4 summarized the slope (α, discrimination) and difficulty (b1 to b4, threshold or location) parameters of 10 items in MGRM analysis. Item 8 and item 2 had high slopes (7.97 and 3.23), while item 1, item 3, item 6, item 9, and item 10 had medium slopes (2.54–2.94). Item 8 had the largest slope and item 2 had the second largest slope. Although item 8 was the most effective way to distinguish individual stress on CPSS-10, it had a very high slope compared with other items (e.g., > 4), and the results of MGRM showed a local dependence.
Expected Score And Item Information Function Of Cpss-10
As shown in Fig. 2C and 2D (e.g., items 5 and 6), the expected score (cumulative probability of category probability curves) increased with the increase of latent trait (\(\theta\)) of emergency medical team members. The item information function (IIF) of items 5 and 6 of CPSS-10 were shown in Fig. 2E and 2F. Generally, IIF reached the maximum when the potential trait (\(\theta\)) was between − 2 and 3. When the latent trait (\(\theta\)) was close to -3 or 3, the IIF was the smallest (close to zero). This result indicated that CPSS-10 showed better discrimination ability among emergency medical workers with medium ability level, rather than those with the lowest or highest ability level. Other expected score and item information function of CPSS-10 were showed in Supplementary information (Additional file 1: Figure S2 and S3).
Differential Item Functioning (Dif)
The DIF of CPSS-10 was determined by gender (male/female) and age (Younger:22–34; middle-age: 35–59). We used likelihood ratio Chi-square to test DIF. MGRM analysis found that DIF of item 2, 5, and 8 were all statistically significant across age groups. However, the DIF of item 2 and 5 were not statistically significant when Bonferroni adjustment was taken with α value (0.05/10 = 0.005). However, DIF of item 5 was still statistically significant among age groups. No significant DIF was found in gender (Table 5).
Table 5
DIF on age (adults and middle-aged) and gender (male and female) in CPSS-10 and CPSS-7
Item | DIF on age | DIF on gender |
CPSS-10 | CPSS-7 | CPSS-10 | CPSS-7 |
Wald\({\chi }^{2}\) | p | Wald\({\chi }^{2}\) | p | Wald\({\chi }^{2}\) | p | Wald\({\chi }^{2}\) | p |
PHS | | | | | | | | |
Item 1 | 0.571 | 0.450 | 1.206 | 0.272 | 0.098 | 0.755 | 0.054 | 0.816 |
Item 2 | 5.365 | 0.021 | | | 0.168 | 0.682 | | |
Item 3 | 2.689 | 0.101 | 3.344 | 0.067 | 0.599 | 0.439 | 0.835 | 0.361 |
Item 6 | 0.023 | 0.879 | 0.099 | 0.519 | 0.230 | 0.632 | 0.659 | 0.417 |
Item 9 | 2.809 | 0.094 | 1.267 | 0.260 | 1.210 | 0.271 | 0.694 | 0.405 |
Item 10 | 0.001 | 0.987 | 0.004 | 0.951 | 0.006 | 0.938 | 0.289 | 0.591 |
PSES | | | | | | | | |
Item 4 | 0.622 | 0.430 | 0.416 | 0.519 | 0.351 | 0.553 | 0.103 | 0.748 |
Item 5 | 10.365 | 0.001 | | | 0.618 | 0.432 | | |
Item 7 | 0.602 | 0.438 | 0.066 | 0.260 | 1.515 | 0.218 | 0.765 | 0.382 |
Item 8 | 3.948 | 0.047 | | | 0.162 | 0.687 | | |
Note: PHS Perceived helplessness Subscale; PSES Perceived Self-Efficacy Subscale; DIF Differential item functioning; Adults aged 22–34 years old; Middle-aged aged 35–59 years old. |
Revision Of Cpss-10 Scale
Item 5 was deleted according to DIF (corrected P < 0.005). Then items 2 and 8 were deleted for their discrimination beyond the interval [− 3.00, 3.00]. According to infit and outfit MNSQ values, the items with poor fitting were deleted. Finally, the CPSS-7 Version (composed of 7 items) was obtained. Cronbach's alpha coefficient of CPSS-7 was 0.82, and CPSS-7 was highly correlated with CPSS-10 (r = 0.98, P < 0.001). It was found that CPSS-7 was more effective in identifying stress perception than CPSS-10. In addition, no DIF difference was found in gender and age of CPSS-7 (Table 5).