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                                Distinctiveness of Psychological Constructs Table 3: χ2 difference tests and model fit indices for the models tested for the total group (THA and TKA)
  Five factor model Four factor model Two factor model One factor model
χ2 (df)
400.9 (160) 1121.8(164) 1220.4(169) 3081.9 (170)
P -value
<0.01 <0.01 <0.01 <0.01
Δχ2(df) 237.1 (4) $ 86.7 (5) # 271.1 (1) §
P -value
<0.01 <0.01 <0.01
TLI CFI
0.981 0.984 0.927 0.937 0.922 0.930 0.785 0.807
RMSEA
0.065 0.127 0.131 0.218
 $ five factor model compared to four factor model model # four factor model compared to two factor model § two factor model compared to one factor TLI= Tucker-Lewis Index, CFI= comparative fit index, RMSEA=root mean square error of approximation.
The five factor model including the standardized factor loadings and correlations
between factors is presented in Figure 1. In this five factor model a very strong
correlation was seen between the treatment credibility and treatment expectancy
factors, and a strong correlation between the optimism and hope factors. 5 Factorial Invariance testing (seeTable 4) showed that the baseline model was well-
fitting and thereby supported configural invariance. For the increasingly stringent models none of the subsequent null-hypotheses of measurement invariance were rejected using the recommendations of Cheung and Rensvold9 which state that the null hypothesis (invariance) is not rejected if the incremental change in CFI is equal to or smaller than 0.01.Thus, strict invariance could be supported.
Table 4: model fit indices of the multigroup models for factorial invariance testing across THA and TKA
 Factorial Invariance models
Baseline model (configural invariance) Weak Invariance
Strong Invariance
Strict Invariance
Χ2 (df) 640.1 (415) 653.6 (430) 672.4 (405) 718.6 (425)
P value
<0.01 <0.01 <0.01 <0.01
TLI CFI
0.986 0.985 0.987 0.985 0.983 0.982 0.983 0.981
RMSEA
0.055 0.054 0.060 0.062
  Because of the very strong correlation between treatment expectancy and treatment credibility, and between hope and optimism, three post-hoc analyses were performed. A four factor model with separate factors for hope, optimism and pessimism but in which expectancy and credibility items were forced to load on one factor (Additional figure 1) showed fit indices equal to the five factor model (TLI = 0.98, CFI =0.98, RMSEA = 0.06, χ2 (df) = 412.5 (164)) The Δχ2 test indicated that the four factor model fit significantly worse than the five factor model (Δχ2 (df) = 16.1 (4) p<0.01)).A four factor model with separate factors for treatment expectancy, treatment credibility and pessimism but in which optimism and hope were forced to load on one factor (Additional figure 2), had a slightly worse fit compared to the five factor model (TLI = 0.97, CFI = 0.97, RMSEA = 0.08, χ2 (df) = 568.7 (164)).The Δχ2
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