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Table 3 Unidimensionality, data-model fit and reliability applying Rasch modelling of the various short versions

From: Establishing the HLS-Q12 short version of the European Health Literacy Survey Questionnaire: latent trait analyses applying Rasch modelling and confirmatory factor analysis

  HLS-Q12a HL-SF12 [26] HLS-EU-Q16 [11]
One-dimensional Three-dimensional One-dimensional Three-dimensional One-dimensional Three-dimensional
Unidimensionality
 Proportion (%) of significant t-tests (lower CI-prop) 8.78% (0.07)   8.01% (0.07)   10.44% (0.09)  
 PSI 0.767   0.759   0.830  
 PSIb 0.687   0.668   0.703  
Fractal indexes   na   na   na
c 0.50   0.39   0.46  
A 0.90   0.91   0.85  
r 0.80   0.87   0.82  
Total item chi square (df), probability 112.61 (108), 0.361   130.21 (108), 0.072   208.90 (144), 0.00034  
Log-likelihoods
 Deviance (ep) 18,590 (37) 18,556 (42) 18,707 (37) 18,696 (42) 22,964 (49) 22,815 (54)
 AIC (ep) 18,664 (37) 18,640 (42) 18,781 (37) 18,780 (42) 23,062 (49) 22,923 (54)
Reliability
 PSR (MLE) 0.762 0.537/0.517/0.575 0.758 0.501/0.497/0.564 0.825 0.713/0.619/0.545
  1. Note. The table shows the results of the tests of unidimensionality based on paired t-tests of person-location estimates for subsets of items. It also reports fractal indexes, c, A and r. The person separation index (PSI) and fractal indexes were estimated for the complete dataset (HLS-Q12 n = 696, HL-SF12 n = 680, HLS-EU-Q47 n = 670). Significant t-tests ≤5% (or lower confidence interval [CI] proportion ≤ 5%), small drops in PSI (b after adjusting for violations of local independence due to subtest structure), high values of A and r, and low values of c could indicate unidimensionality. Analyses were performed by using RUMM2030 software
  2. Log-likelihoods and person separation reliability (PSR) were estimated for the one- and three-dimensional approaches to the short versions by using ConQuest4 software. Lower values of deviance and AIC indicate a better fit
  3. AIC: Akaike’s information criterion, ep: number of estimated parameters, na: not applicable, PSR (MLE): person separation reliability based on a marginal maximum likelihood estimate
  4. All the short versions are developed on the basis of the HLS-EU-Q47
  5. aHLS-Q12 developed through the present study