Background
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Unidimensionality: the items of a scale should measure only one latent variable (i.e., all EAT-10 items measure aspects of OD severity).
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Monotonicity: the scale items function hierarchically from easy to difficult, and the probability of a high item score should increase with increasing values of the latent variable (i.e., the probability of giving a score that reflects a swallowing problem increases with high EAT-10 total scores).
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Homogeneity: The rank order of the items from easy to difficult should be the same for all respondents, regardless of their level for the latent variable (i.e., the order of EAT-10 items according to the severity of the problem they express is the same for all respondents, regardless of their level on the scale, as reflected in the EAT-10 total score; the easiest problem to have is easiest for all respondents and vice versa).
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Local independency: the items of a scale must be conditionally independent given the latent variable (i.e., the rating of any one problem should depend only on the level of the scale, as reflected in the EAT-10 total score and not the rating of any other items).
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Absence of differential item function (DIF): the items should be conditionally independent of exogenous variables given the latent variable (i.e., the EAT-10 items should function equally for subgroups of respondents, for example male and female).
Method
Source of data and data cleaning
Analysis by the Rasch model
Person and item level fit to the Rasch model
The scoring structures
Overall fit to the Rasch model
Targeting
Improvement strategies
Sample size
Results
Verification of model and sample size
Overall fit to the Rasch model
Scale analysis | % Extr. | Fit residuals mean (SD) | Item-trait interaction | Reliability | Unidi-mensionality | |||
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Item | Person | χ2 (df) | P | PSI / α | Power of fit | T-test % | ||
Initial analyses | ||||||||
1. Full sample (N = 1144) | 42% | −0.66 (4.16) | − 0.30 (1.08) | 485.48 (40) | < 0.001 | 0.65 / 0.85 | Good | 2.27% |
2. Independent group (N = 594) | 53% | − 0.82 (2.13) | −0.37 (0.86) | 175.92 (30) | < 0.001 | 0.32 / 0.72 | Too low | 0.72% |
3. Dependent group (N = 550) | 30% | −0.19 (3.53) | −0.25 (1.17) | 293.28 (40) | < 0.001 | 0.74 / 0.87 | Good | 1.83% |
Analysis after reducing to three scoring categories (full sample,N = 1144) | ||||||||
4. Scoring structure: 00122a | 65% | −0.89 (3.21) | −0.25 (0.77) | 284.01 (40) | < 0.001 | 0.38 / 0.76 | Low | 1.73% |
5. Scoring structure: 01112 | 42% | −1.73 (4.72) | −0.35 (0.90) | 416.01 (40) | < 0.001 | 0.69 / 0.83 | Good | 1.21% |
6. Scoring structure: 01122 | 42% | −1.90 (4.34) | −0.38 (1.01) | 448.90 (40) | < 0.001 | 0.66 / 0.83 | Good | 2.27% |
7. Scoring structure: 01222 | 43% | −0.78 (4.26) | −0.26 (1.11) | 439.37 (40) | < 0.001 | 0.65 / 0.89 | Reasonable | 0.76% |
8. Scoring structure: 00112 | 65% | −0.56 (4.04) | −0.24 (0.74) | 225.24 (30) | < 0.001 | 0.49 / 0.76 | Low | 1.98% |
Optimal values < 15% | 0 (< 1.00) | 0 (< 1.00) | > 0.05 | > 0.70 | < 5% |
Item level fit to the Rasch model
Item-abbreviated | Loc | SE | FR | χ2 (df) | P | F (df) | P |
---|---|---|---|---|---|---|---|
Full sample | |||||||
1. Lose weight | −0.67 | 0.05 | 5.9 | 186.01 (5) | < 0.001 | 20.52 (5.655) | < 0.001 |
2. Go out meals | 1.00 | 0.07 | 0.9 | 5.93 (5) | 0.313 | 0.92 (5655) | 0.463 |
3. Liquids effort | 0.04 | 0.06 | −3.0 | 19.33 (5) | 0.002 | 4.64 (5655) | < 0.001 |
4. Solids effort | −0.29 | 0.06 | −3.5 | 37.34 (5) | < 0.001 | 8.96 (5655) | < 0.001 |
5. Pills effort | −0.51 | 0.05 | −0.1 | 9.35 (5) | 0.096 | 1.45 (5655) | 0.204 |
6. Painful | 0.10 | 0.06 | −5.7 | 62.73 (5) | < 0.001 | 25.20 (5655) | < 0.001 |
7. Pleasure eat | −0.36 | 0.06 | 1.6 | 28.77 (5) | < 0.001 | 4.51 (5655) | < 0.001 |
8. Stick throat | −0.11 | 0.06 | −1.5 | 32.71 (5) | < 0.001 | 7.39 (5655) | < 0.001 |
9. Cough | 0.52 | 0.06 | 5.1 | 31.30 (5) | < 0.001 | 5.33 (5655) | < 0.001 |
10. Stressful | 0.29 | 0.07 | −6.3 | 72.01 (5) | < 0.001 | 33.95 (5655) | < 0.001 |
Independent respondents | |||||||
1. Lose weight | −0.62 | 0.07 | 1.7 | 41.12 (3) | < 0.001 | 10.88 (3274) | < 0.001 |
2. Go out meals | 0.35 | 0.13 | 0.8 | 1.77 (3) | 0.622 | 0.54 (3274) | 0.656 |
3. Liquids effort | 0.42 | 0.12 | −2.3 | 12.37 (3) | 0.006 | 5.22 (3274) | 0.002 |
4. Solids effort | 0.02 | 0.09 | −2.0 | 15.31 (3) | 0.002 | 5.69 (3274) | 0.001 |
5. Pills effort | −0.47 | 0.08 | 0.4 | 4.76 (3) | 0.190 | 1.19 (3274) | 0.313 |
6. Painful | 0.06 | 0.10 | −3.6 | 30.93 (3) | < 0.001 | 21.86 (3274) | < 0.001 |
7. Pleasure eat | −0.28 | 0.09 | 0.0 | 11.88 (3) | 0.008 | 2.91 (3274) | 0.035 |
8. Stick throat | 0.27 | 0.10 | −1.0 | 12.80 (3) | 0.005 | 4.08 (3274) | 0.007 |
9. Cough | −0.24 | 0.09 | 1.9 | 16.06 (3) | 0.001 | 5.29 (3274) | 0.001 |
10. Stressful | 0.50 | 0.12 | −4.1 | 28.93 (3) | < 0.001 | 20.83 (3274) | < 0.001 |
Dependent respondents | |||||||
1. Lose weight | −0.61 | 0.06 | 5.9 | 122.30 (3) | < 0.000 | 19.71 (3379) | < 0.001 |
2. Go out meals | 0.96 | 0.08 | 0.9 | 1.90 (3) | 0.594 | 0.44 (3379) | 0.723 |
3. Liquids effort | 0.04 | 0.07 | −1.8 | 8.49 (3) | 0.037 | 3.14 (3379) | 0.025 |
4. Solids effort | −0.36 | 0.07 | −2.7 | 25.42 (3) | < 0.000 | 11.50 (3379) | < 0.001 |
5. Pills effort | −0.45 | 0.07 | −0.8 | 8.56 (3) | 0.036 | 3.05 (3379) | 0.029 |
6. Painful | 0.14 | 0.08 | −4.2 | 37.25 (3) | < 0.000 | 25.20 (3379) | < 0.001 |
7. Pleasure eat | −0.35 | 0.07 | 1.9 | 16.02 (3) | 0.001 | 3.43 (3379) | 0.017 |
8. Stick throat | −0.14 | 0.07 | −1.0 | 13.25 (3) | 0.004 | 5.32 (3379) | 0.001 |
9. Cough | 0.53 | 0.07 | 4.6 | 19.72 (3) | < 0.000 | 5.00 (3379) | 0.002 |
10. Stressful | 0.24 | 0.08 | −4.7 | 40.32 (3) | < 0.000 | 30.76 (3379) | < 0.001 |
Optimal value | <±2.5 | ≥0.05a | ≥0.05a |
Item (abbreviated) | Gendera | Ageb | Functional levelc | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Uniform | Non-uniform | Uniform | Non-uniform | Uniform | Non-uniform | |||||||
F(df) | p | F(df) | p | F(df) | p | F(df) | p | F(df) | p | F(df) | p | |
1. Lose weight | 0.35 (1) | 0.556 | 1.87 (5) | 0.097 | 0.06 (3) | 0.979 | 1.22 (15) | 0.250 | 0.63 (3) | 0.598 | 1.05 (15) | 0.405 |
2. Go out meals | 0.07 (1) | 0.789 | 1.22 (5) | 0.296 | 3.22 (3) | 0.022 | 1.22 (15) | 0.248 | 3.98 (3) | 0.008 | 0.62 (15) | 0.857 |
3. Liquids effort | 0.86 (1) | 0.353 | 1.44 (5) | 0.207 | 0.53 (3) | 0.664 | 0.98 (15) | 0.474 | 2.11 (3) | 0.097 | 0.56 (15) | 0.904 |
4. Solids effort | 0.21 (1) | 0.645 | 1.06 (5) | 0.381 | 0.27 (3) | 0.844 | 0.82 (15) | 0.661 | 1.04 (3) | 0.373 | 0.60 (15) | 0.879 |
5. Pills effort | 4.24 (1) | 0.040 | 0.03 (5) | 1.000 | 1.21 (3) | 0.304 | 1.46 (15) | 0.115 | 2.05 (3) | 0.105 | 0.83 (15) | 0.640 |
6. Painful | 2.48 (1) | 0.116 | 0.95 (5) | 0.449 | 0.63 (3) | 0.597 | 1.46 (15) | 0.114 | 1.35 (3) | 0.258 | 0.67 (15) | 0.819 |
7. Pleasure eat | 0.50 (1) | 0.481 | 0.14 (5) | 0.984 | 1.39 (3) | 0.245 | 0.31 (15) | 0.995 | 0.93 (3) | 0.426 | 1.15 (15) | 0.307 |
8. Stick throat | 2.85 (1) | 0.092 | 1.35 (5) | 0.243 | 0.19 (3) | 0.905 | 0.83 (15) | 0.640 | 0.57 (3) | 0.634 | 0.70 (15) | 0.786 |
9. Cough | 2.26 (1) | 0.133 | 0.65 (5) | 0.658 | 0.43 (3) | 0.731 | 0.85 (15) | 0.627 | 1.19 (3) | 0.312 | 1.33 (15) | 0.175 |
10. Stressful | 0.35 (1) | 0.555 | 1.62 (5) | 0.151 | 1.76 (3) | 0.153 | 0.66 (15) | 0.828 | 1.95 (3) | 0.121 | 0.19 (15) | 1.000 |
The scoring structures
Full sample | Independent group | Dependent group | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Item (abbreviated) | Category frequencies | Category frequencies | Category frequencies | ||||||||||||
0 | 1 | 2 | 3 | 4 | 0 | 1 | 2 | 3 | 4 | 0 | 1 | 2 | 3 | 4 | |
1. Lose weight | 497 | 72 | 50 | 23 | 19 | 229 | 19 | 19 | 8 | 3 | 268 | 53 | 31 | 15 | 16 |
2. Go out meals | 527 | 84 | 37 | 11 | 2 | 251 | 21 | 4 | 2 | 0 | 276 | 63 | 33 | 9 | 2 |
3. Liquids effort | 486 | 92 | 67 | 8 | 8 | 232 | 28 | 17 | 0 | 1 | 254 | 64 | 50 | 8 | 7 |
4. Solids effort | 393 | 145 | 100 | 13 | 10 | 195 | 52 | 27 | 4 | 0 | 198 | 93 | 73 | 9 | 10 |
5. Pills effort | 389 | 122 | 128 | 7 | 15 | 191 | 44 | 37 | 3 | 3 | 198 | 78 | 91 | 4 | 12 |
6. Painful | 449 | 114 | 83 | 9 | 6 | 216 | 41 | 18 | 2 | 1 | 233 | 73 | 65 | 7 | 5 |
7. Pleasure eat | 451 | 124 | 60 | 14 | 12 | 218 | 41 | 12 | 5 | 2 | 233 | 83 | 48 | 9 | 10 |
8. Stick throat | 348 | 181 | 125 | 1 | 6 | 165 | 80 | 33 | 0 | 0 | 183 | 101 | 92 | 1 | 6 |
9. Cough | 204 | 256 | 188 | 12 | 1 | 90 | 129 | 57 | 2 | 0 | 114 | 127 | 131 | 10 | 1 |
10. Stressful | 472 | 117 | 61 | 6 | 5 | 221 | 43 | 13 | 1 | 0 | 251 | 74 | 48 | 5 | 5 |
Thresholds | Thresholds | Thresholds | |||||||||||||
0/1 | 1/2 | 2/3 | 3/4 | 0/1 | 1/2 | 2/3 | 3/4 | 0/1 | 1/2 | 2/3 | 3/4 | ||||
1. Lose weight | 0.62 | −0.54 | −0.06 | −0.03 | 1.16 | −0.99 | −0.22 | 0.05 | 0.42 | −0.30 | 0.03 | −0.15 | |||
2. Go out meals | −1.22 | −1.31 | − 0.50 | 3.04 | 0.19 | 0.19 | −0.96 | 0.58 | −1.42 | −1.38 | − 0.18 | 2.97 | |||
3. Liquids effort | −0.58 | − 0.85 | 1.24 | 0.20 | − 0.47 | − 1.01 | 2.30 | − 0.82 | − 0.70 | − 0.85 | 0.99 | 0.56 | |||
4. Solids effort | − 1.20 | − 0.58 | 1.33 | 0.45 | − 1.05 | − 0.53 | 0.83 | 0.75 | − 1.24 | − 0.54 | 1.58 | 0.21 | |||
5. Pills effort | −0.75 | − 0.84 | 2.18 | −0.59 | − 0.36 | −0.61 | 1.47 | −0.49 | − 0.92 | −0.90 | 2.55 | −0.73 | |||
6. Painful | −1.08 | −0.83 | 1.32 | 0.59 | −0.70 | −0.24 | 1.04 | −0.10 | −1.19 | −1.01 | 1.45 | 0.74 | |||
7. Pleasure eat | −0.61 | 0.02 | 0.71 | −0.12 | −0.26 | 0.48 | −0.03 | − 0.18 | −0.73 | − 0.09 | 1.02 | − 0.21 | |||
8. Stick throat | −1.71 | −0.90 | 3.99 | −1.38 | − 1.90 | − 0.72 | 2.56 | 0.06 | − 1.59 | −1.00 | 3.82 | −1.23 | |||
9. Cough | −3.00 | −2.02 | 1.12 | 3.90 | −2.18 | −0.86 | 2.33 | 0.71 | −2.79 | −2.11 | 1.07 | 3.84 | |||
10. Stressful | −1.16 | −0.63 | 1.48 | 0.32 | −1.08 | −0.28 | 1.15 | 0.20 | −1.12 | −0.71 | 1.59 | 0.24 |
Targeting
Improvement strategies
Scale analysis | % Extr. | Fit residuals mean (SD) | Item-trait interaction | Reliability | Individual item-fit | |||
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Item | Person | χ2 (df) | P | PSI / α | Power of fit | Misfit items | ||
4.a. Remove item 6 | 42% | −1.58 (3.96) | −0.36 (0.95) | 382.42 (36) | < 0.001 | 0.61 / 0.79 | Reasonable | Item 1 / FR = 5.5a,b Item 3 / FR = −4.3a,b Item 4 / FR = −6.2a,b Item 8 / FR = − 3.2a,b Item 10 / FR = −6.4a,b Item 2,5,7,9 a,b |
4.b. Remove item 10 | 42% | −1.28 (3.53) | − 0.34 (0.93) | 299.55 (24) | < 0.001 | 0.53 / 0.74 | Reasonable | Item 1 / FR = 4.6a,b Item 3 / FR = − 4.5a,b Item 4 / FR = − 6.2a,b Item 8 / FR = − 3.1a,b Item 2,5,7,9a,b |
4.c. Remove item 4 | 43% | −1.02 (2.85) | −0.33 (0.87) | 230.68 (21) | < 0.001 | 0.40 / 0.66 | Low | Item 1/ FR = 3.5a,b Item 3 / FR = − 4.9a,b Item 8 / FR = − 2.6a,b Item 2,5,7 a,b |
4.d. Remove item 3 | 43% | −0.69 (2.15) | − 0.32 (0.85) | 196.29 (18) | < 0.001 | 0.24 / 0.55 | Too low | Item 7 / FR = − 2.8 a,b Item 8 / FR = − 2.6 a,b Item 1,2,5 a,b |
4.e. Remove item 7 | 45% | −0.39 (1.63) | − 0.28 (0.75) | 163.76 (10) | < 0.001 | 0.02 / 0.38 | Too low | Item 1,2,5,8 a,b |
Optimal values < 15% | 0 (< 1.00) | 0 (< 1.00) | > 0.05 | > 0.70 | FR < ±2.5, or non-significant fit statistics |