| Literature DB >> 29954382 |
Hanne Søberg Finbråten1,2, Bodil Wilde-Larsson3,4, Gun Nordström4, Kjell Sverre Pettersen5, Anne Trollvik4, Øystein Guttersrud6.
Abstract
BACKGROUND: The European Health Literacy Survey Questionnaire (HLS-EU-Q47) is widely used in assessing health literacy (HL). There has been some controversy whether the comprehensive HLS-EU-Q47 data, reflecting a conceptual model of four cognitive domains across three health domains (i.e. 12 subscales), fit unidimensional Rasch models. Still, the HLS-EU-Q47 raw score is commonly interpreted as a sufficient statistic. Combining Rasch modelling and confirmatory factor analysis, we reduced the 47 item scale to a parsimonious 12 item scale that meets the assumptions and requirements of objective measurement while offering a clinically feasible HL screening tool. This paper aims at (1) evaluating the psychometric properties of the HLS-EU-Q47 and associated short versions in a large Norwegian sample, and (2) establishing a short version (HLS-Q12) with sufficient psychometric properties.Entities:
Keywords: Confirmatory factor analysis of categorical data; HLS-EU-Q47; HLS-Q12; Health literacy; Rasch modelling; Short version; Validation
Mesh:
Year: 2018 PMID: 29954382 PMCID: PMC6022487 DOI: 10.1186/s12913-018-3275-7
Source DB: PubMed Journal: BMC Health Serv Res ISSN: 1472-6963 Impact factor: 2.655
Item-fit indexes applying the one-dimensional approach to the various short versions
| HLS-Q12b | HL-SF12 [ | HLS-EU-Q16 [ | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Item | Loc. | Chi prob. | Infit |
| Com. | Loc | Chi prob. | DIF | ordered | Infit |
| Com. | Loc | Chi prob. | DIF | Ordered | Infit |
| Com. |
| 1 | |||||||||||||||||||
| 2 | −0.097 | 0.997 | 1.01 | 0.2 | 0.269 | − 0.041 | 0.699 | 0.99 | −0.1 | 0.278 | 0.133 | 0.606 | 1.03 | 0.5 | 0.276 | ||||
| 3 | |||||||||||||||||||
| 4 | −0.236 | 0.703 | 1.00 | 0.0 | 0.338 | ||||||||||||||
| 5 | −0.453 | 0.313 | Edu, h > l | 0.97 | −0.7 | 0.387 | |||||||||||||
| 6 | 0.137 | 0.348 | 1.05 | 1.0 | 0.183 | ||||||||||||||
| 7 | 0.053 | 0.705 | 1.03 | 0.7 | 0.239 | ||||||||||||||
| 8 | −0.865 | 0.087 | No | 0.94 | −1.1 | 0.376 | |||||||||||||
| 9 | |||||||||||||||||||
| 10 | 0.892 | 0.761 | 0.97 | −0.6 | 0.292 | 0.964 | 0.848 | 1.00 | −0.1 | 0.266 | |||||||||
| 11 | 1.084 | 0.001* | Age, y < o | 1.17 | 3.4a | 0.139 | |||||||||||||
| 12 | |||||||||||||||||||
| 13 | −0.082 | 0.332 | Gen m > f | 0.97 | −0.6 | 0.319 | |||||||||||||
| 14 | −0.625 | 0.275 | 1.00 | 0.0 | 0.260 | ||||||||||||||
| 15 | −0.842 | 0.025 | Gen, m > f | No | 1.06 | 1.2 | 0.207 | ||||||||||||
| 16 | −1.305 | 0.044 | 0.91 | −1.6 | 0.443 | ||||||||||||||
| 17 | |||||||||||||||||||
| 18 | 0.420 | 0.357 | 0.98 | −0.5 | 0.363 | 0.490 | 0.006 | 0.93 | −1.6 | 0.416 | 0.687 | 0.633 | 1.00 | 0.1 | 0.299 | ||||
| 19 | |||||||||||||||||||
| 20 | |||||||||||||||||||
| 21 | −0.793 | 0.002* | Edu, h > l | No | 0.95 | −0.9 | 0.347 | ||||||||||||
| 22 | |||||||||||||||||||
| 23 | −1.158 | 0.065 | 0.98 | −0.3 | 0.281 | −0.997 | 0.431 | 0.96 | −0.7 | 0.291 | −0.908 | 0.385 | 0.96 | −0.7 | 0.319 | ||||
| 24 | |||||||||||||||||||
| 25 | |||||||||||||||||||
| 26 | 0.526 | 0.129 | Age, y < o | 1.07 | 1.5 | 0.187 | |||||||||||||
| 27 | |||||||||||||||||||
| 28 | 1.068 | 0.265 | 1.04 | 0.9 | 0.176 | 1.360 | 0.039 | 1.07 | 1.4 | 0.232 | |||||||||
| 29 | |||||||||||||||||||
| 30 | 0.422 | 0.284 | 1.03 | 0.6 | 0.230 | 0.502 | 0.845 | Edu, h < l | 1.04 | 0.9 | 0.217 | ||||||||
| 31 | 1.167 | 0.166 | 0.98 | −0.4 | 0.349 | ||||||||||||||
| 32 | −1.135 | 0.618 | 0.98 | −0.5 | 0.337 | ||||||||||||||
| 33 | −0.298 | 0.652 | 0.97 | −0.5 | 0.321 | −0.110 | 0.820 | 1.03 | 0.6 | 0.240 | |||||||||
| 34 | |||||||||||||||||||
| 35 | |||||||||||||||||||
| 36 | |||||||||||||||||||
| 37 | 0.242 | 0.070 | Age, y > o | 1.06 | 1.2 | 0.220 | |||||||||||||
| 38 | 0.702 | 0.484 | 1.06 | 1.3 | 0.196 | ||||||||||||||
| 39 | 0.372 | 0.831 | 1.00 | 0.0 | 0.293 | 0.531 | 0.305 | 0.96 | −0.7 | 0.366 | |||||||||
| 40 | |||||||||||||||||||
| 41 | |||||||||||||||||||
| 42 | |||||||||||||||||||
| 43 | −0.728 | 0.375 | 0.95 | −0.9 | 0.426 | −0.621 | 0.236 | 0.94 | −1.1 | 0.385 | −0.452 | 0.450 | 1.00 | 0.0 | 0.322 | ||||
| 44 | 0.186 | 0.105 | 1.04 | 0.8 | 0.248 | ||||||||||||||
| 45 | −0.194 | 0.072 | 1.07 | 1.4 | 0.202 | ||||||||||||||
| 46 | |||||||||||||||||||
| 47 | |||||||||||||||||||
Note. This table shows the item-fit indexes when applying the one-dimensional approach to the various short versions. The HLS-EU-Q16 could not be deemed sufficiently unidimensional. The results are displayed for comparison purposes
Chi square probability (Chi prob), differential item functioning (DIF), item location estimate (Loc) and unordered response categories (ordered) were obtained from Rasch modelling using RUMM2030 software. ConQuest 4 software was used for the Infit measures
aA t–value > 1.96 and an infit-value > 1 indicate a poor fit with the Rasch model due to there being more variation in the data than expected given the model (item is under-discriminating)
*Item with a significant misfit (p-value below Bonferroni-adjusted 5%)
For items displaying uniform DIF, the relevant dichotomized person factor levels are indicated. For example, “Age, y > o” refers to the uniform DIF for the person factor age in favour of the y = younger respondents (47 years or younger) factor level as compared to o = older respondents (48 years or older) factor level. The “Highest completed education level” (Edu) factor has the l = low (primary and secondary school) and h = high (university or university college) levels, and the factor “Gender” (Gen) has the f = females and m = males levels
Ordered: “No” refers to items with unordered response categories
None of the items on the HLS-Q12 displayed DIF or unordered response categories
Com: communalities obtained from CFA using the LISREL software
bHLS-Q12 developed through the present study
Characteristics of study sample and the Norwegian population
| Sample | Populationa | |
|---|---|---|
| Age | ||
| mean ± sd | 47.0 ± 17.7 | 46.5 ± 19.0 |
| - median | 48 | 45 |
| - min−max | 16−91 | 16−105 |
| - missing | 0 | 0 |
| % | % | |
| 16–24 years | 13 | 15 |
| 25–39 years | 25 | 25 |
| 40–54 years | 25 | 26 |
| 55–66 years | 21 | 17 |
| 67–79 years | 14 | 12 |
| 80+ years | 2 | 5 |
| Gender | ||
| - males | 441 (49) | 2,567,434 (50) |
| - females | 459 (51) | 2,541,622 (50) |
| - missing | 0 | |
| Highest completed education | % | |
| - compulsory comprehensive school | 87 (10) | 26 |
| - upper-secondary school | 298 (33) | 38 |
| - university level, lower degreeb | 321 (36) | 23 |
| - university level, higher degreec | 191 (21) | 9 |
| - missing | 3 (< 1) | |
aNorwegian population 16 years and over in 2014 (Statistics Norway, 2017)
bEducation at university or university college for 4 years or less (Bachelor’s degree)
cEducation at university or university college for 5 years or more (Master’s degree and/or PhD)
Single-item characteristics of the HLS-EU-Q47 given various analytical approaches
| One-dimensional approach | Three-dimensional approach | Consecutive three-dimensional approach | 12-dimensional approach | Consecutive 12-dimensional approach | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| HD | CD | Item | Infit | CI |
| Ordered | DIF | Infit | CI |
| Ordered | DIF | Infit | CI |
| DIF | |||
| On a scale from very difficult to very easy, how easy would you say it is to: | |||||||||||||||||||
| HC | A | 1) find information about symptoms of illnesses that concern you? | 1.01 | 0.90 | 1.10 | 0.3 | Age, y > o | 0.98 | 0.90 | 1.10 | −0.4 | Age, y > o | 1.03 | 0.89 | 1.11 | 0.6 | |||
| “ | A | 2) find information on treatments of illnesses that concern you? | 0.99 | 0.90 | 1.10 | −0.3 | 0.95 | 0.90 | 1.10 | −1.0 | 0.99 | 0.90 | 1.10 | −0.2 | |||||
| “ | A | 3) find out what to do in case of a medical emergency? | 1.02 | 0.91 | 1.09 | 0.3 | 0.97 | 0.91 | 1.09 | −0.7 | 1.07 | 0.90 | 1.10 | 1.4 | |||||
| “ | A | 4) find out where to get professional help when you are ill? | 0.99 | 0.89 | 1.11 | −0.1 | 0.96 | 0.89 | 1.11 | −0.8 | 1.06 | 0.89 | 1.11 | 1.1 | |||||
| “ | B | 5) understand what your doctor says to you? | 0.96 | 0.90 | 1.10 | −0.7 | Edu, h > l | 0.91 | 0.90 | 1.10 | −1.7 | Edu, h > l | 0.95 | 0.90 | 1.10 | −0.9 | Edu, h > l | ||
| “ | B | 6) understand the leaflets that come with your medicine? | 1.06 | 0.90 | 1.10 | 1.3 | 1.04 | 0.90 | 1.10 | 0.9 | 1.03 | 0.90 | 1.10 | 0.6 | |||||
| “ | B | 7) understand what to do in a medical emergency? | 1.00 | 0.91 | 1.09 | 0.1 | 0.96 | 0.91 | 1.09 | −0.9 | 0.99 | 0.91 | 1.09 | −0.1 | Edu, h < l | ||||
| “ | B | 8) understand your doctor’s or pharmacist’s instruction on how to take a prescribed medicine? | 0.93 | 0.89 | 1.11 | −1.3 | No | 0.89 | 0.89 | 1.11 | −2.0b | No | 0.92 | 0.88 | 1.12 | −1.3 | |||
| “ | C | 9) judge how information from your doctor applies to you? | 0.96 | 0.89 | 1.11 | −0.6 | 0.94 | 0.89 | 1.11 | −1.1 | 0.96 | 0.89 | 1.11 | −0.7 | |||||
| “ | C | 10) judge the advantages and disadvantages of different treatment options? | 0.96 | 0.90 | 1.10 | −0.8 | 0.99 | 0.90 | 1.10 | −0.2 | 0.92 | 0.90 | 1.10 | −1.7 | |||||
| “ | C | 11) judge when you may need to get a second opinion from another doctor? | 1.09 | 0.91 | 1.09 | 1.8 | Age, y < o | 1.14 | 0.90 | 1.10 | 2.7a | Age, y < o Edu, h < l | 1.06 | 0.90 | 1.10 | 1.1 | Age, y < o | ||
| “ | C | 12) judge if the information about illness in the media is reliable? | 1.16 | 0.90 | 1.10 | 3.1a | 1.25 | 0.90 | 1.10 | 4.7a | 1.10 | 0.90 | 1.10 | 2.0a | |||||
| “ | D | 13) use information the doctor gives you to make decisions about your illness? | 0.92 | 0.90 | 1.10 | −1.6 | Gen, m > f | 0.93 | 0.90 | 1.10 | −1.4 | Gen, m > f | 0.93 | 0.90 | 1.10 | −1.5 | Age, y < o | ||
| “ | D | 14) follow the instructions on medication? | 0.98 | 0.88 | 1.12 | −0.3 | 0.97 | 0.88 | 1.12 | −0.5 | 0.90 | 0.87 | 1.13 | −1.6 | |||||
| “ | D | 15) call an ambulance in an emergency? | 1.07 | 0.90 | 1.10 | 1.4 | No | Gen, m > f | 1.07 | 0.90 | 1.10 | 1.4 | No | Gen, m > f | 0.96 | 0.89 | 1.11 | −0.7 | Age, y > o |
| “ | D | 16) follow instructions from your doctor or pharmacist? | 0.88 | 0.89 | 1.11 | −2.1b | 0.89 | 0.89 | 1.11 | −1.9 | 0.81 | 0.87 | 1.13 | −2.9b | |||||
| DP | A | 17) find information about how to manage unhealthy behaviour such as smoking, low physical activity and drinking too much? | 0.93 | 0.90 | 1.10 | −1.3 | Edu, h > l | 0.96 | 0.90 | 1.10 | −0.7 | Edu, h > l | 1.06 | 0.90 | 1.10 | 1.2 | Edu, h > l | ||
| “ | A | 18) find information on how to manage mental health problems like stress or depression? | 0.95 | 0.91 | 1.09 | −1.1 | 1.00 | 0.91 | 1.09 | 0.0 | 1.18 | 0.91 | 1.09 | 3.5a | |||||
| “ | A | 19) find information about vaccinations and health screenings that you should have? | 0.89 | 0.91 | 1.09 | −2.3b | 0.93 | 0.91 | 1.09 | −1.4 | 1.13 | 0.91 | 1.09 | 2.6a | |||||
| “ | A | 20) find information on how to prevent or manage conditions like being overweight, high blood pressure or high cholesterol? | 0.88 | 0.89 | 1.11 | −2.2b | 0.91 | 0.89 | 1.11 | −1.6 | 0.96 | 0.89 | 1.11 | −0.7 | |||||
| “ | B | 21) understand health warnings about behaviour such as smoking, low physical activity and drinking too much? | 0.94 | 0.89 | 1.11 | −1.2 | No | Edu, h > l | 0.94 | 0.90 | 1.10 | −1.1 | No | Age, y > o Edu, h > l | 0.90 | 0.89 | 1.11 | −1.7 | |
| “ | B | 22) understand why you need vaccinations? | 1.01 | 0.90 | 1.10 | 0.3 | Age, y > o | 1.03 | 0.90 | 1.10 | 0.6 | Age, y > o | 1.01 | 0.90 | 1.10 | 0.1 | Educ | ||
| “ | B | 23) understand why you need health screenings? | 0.94 | 0.89 | 1.11 | −1.0 | 0.97 | 0.89 | 1.11 | −0.5 | Age, y > o | 0.91 | 0.89 | 1.11 | −1.5 | ||||
| “ | C | 24) judge how reliable health warnings are, such as smoking, low physical activity and drinking too much? | 0.99 | 0.90 | 1.10 | −0.1 | 1.01 | 0.90 | 1.10 | 0.2 | 1.06 | 0.90 | 1.10 | 1.2 | Age, y > o | ||||
| “ | C | 25) judge when you need to go to a doctor for a check-up? | 0.98 | 0.91 | 1.09 | −0.4 | Age, y < o | 1.03 | 0.91 | 1.09 | 0.7 | Age, y < o Edu, h < l | 1.00 | 0.91 | 1.09 | 0.1 | Age, y < o Edu, h < l | ||
| “ | C | 26) judge which vaccinations you may need? | 1.03 | 0.91 | 1.09 | 0.7 | 1.05 | 0.91 | 1.09 | 1.0 | 1.06 | 0.91 | 1.09 | 1.2 | |||||
| “ | C | 27) judge which health screenings you should have? | 0.92 | 0.91 | 1.09 | −1.9 | Age, y < o | 0.94 | 0.91 | 1.09 | −1.4 | Age, y < o | 0.92 | 0.91 | 1.09 | −1.8 | Age, y < o | ||
| “ | C | 28) judge if the information on health risks in the media is reliable? | 1.03 | 0.90 | 1.10 | 0.6 | 1.05 | 0.90 | 1.10 | 1.0 | 1.02 | 0.90 | 1.10 | 0.4 | Age, y > o | ||||
| “ | D | 29) decide if you should have a flu vaccination? | 1.18 | 0.91 | 1.09 | 3.6a | Age, y < o | 1.24 | 0.91 | 1.09 | 4.7a | Age, y < o | 1.06 | 0.91 | 1.09 | 1.3 | Age, y < o | ||
| “ | D | 30) decide how you can protect yourself from illness based on advice from family and friends? | 1.06 | 0.91 | 1.09 | 1.3 | 1.12 | 0.91 | 1.09 | 2.5a | Edu, h < l | 1.00 | 0.91 | 1.09 | 0.0 | Age, y > o | |||
| “ | D | 31) decide how you can protect yourself from illness based on information in the media? | 0.98 | 0.91 | 1.09 | −0.3 | 1.01 | 0.91 | 1.09 | 0.3 | 0.93 | 0.91 | 1.09 | −1.5 | |||||
| HP | A | 32) find information on healthy activities such as exercise, healthy food and nutrition? | 0.96 | 0.90 | 1.10 | −0.7 | 0.96 | 0.90 | 1.10 | −0.8 | 0.95 | 0.90 | 1.10 | −1.0 | |||||
| “ | A | 33) find out about activities that are good for your mental well-being? | 0.97 | 0.90 | 1.10 | −0.6 | 0.93 | 0.90 | 1.10 | −1.3 | 0.93 | 0.90 | 1.10 | −1.5 | Gen, m < f | ||||
| “ | A | 34) find information on how your neighbourhood could be more health-friendly? | 1.04 | 0.90 | 1.10 | 0.8 | 1.01 | 0.90 | 1.10 | 0.2 | 0.98 | 0.90 | 1.10 | −0.4 | |||||
| “ | A | 35) find out about political changes that may affect health? | 1.10 | 0.90 | 1.10 | 1.8 | 1.08 | 0.90 | 1.10 | 1.5 | 1.06 | 0.89 | 1.11 | 1.0 | |||||
| “ | A | 36) find out about efforts to promote your health at work? | 1.02 | 0.91 | 1.09 | 0.3 | 1.02 | 0.91 | 1.09 | 0.5 | 1.02 | 0.91 | 1.09 | 0.3 | |||||
| “ | B | 37) understand advice on health from family members or friends? | 1.06 | 0.90 | 1.10 | 1.2 | Age, y > o | 1.07 | 0.90 | 1.10 | 1.4 | Age, y > o | 1.06 | 0.90 | 1.10 | 1.1 | Age, y > o | ||
| “ | B | 38) understand information on food packaging? | 1.12 | 0.91 | 1.09 | 2.5a | 1.16 | 0.91 | 1.09 | 3.3a | Age, y > o | 1.12 | 0.91 | 1.09 | 2.5a | Gen, m > f | |||
| “ | B | 39) understand information in the media on how to get healthier? | 0.97 | 0.90 | 1.10 | −0.7 | 0.97 | 0.90 | 1.10 | −0.7 | 0.96 | 0.90 | 1.10 | −0.8 | |||||
| “ | B | 40) understand information on how to keep your mind healthy? | 0.91 | 0.91 | 1.09 | −2.0b | 0.89 | 0.91 | 1.09 | −2.3b | 0.93 | 0.91 | 1.09 | −1.4 | Age, y < o | ||||
| “ | C | 41) judge how where you live affects your health and well-being? | 1.01 | 0.90 | 1.10 | 0.3 | Age, y < o | 0.97 | 0.90 | 1.10 | −0.5 | Age, y < o | 1.02 | 0.9 | 1.10 | 0.4 | |||
| “ | C | 42) judge how your housing conditions help you to stay healthy? | 0.99 | 0.90 | 1.10 | −0.2 | Age, y < o | 0.96 | 0.90 | 1.10 | −0.9 | Age, y < o | 0.99 | 0.9 | 1.10 | −0.3 | Edu, h < l | ||
| “ | C | 43) judge which everyday behaviour is related to health? | 0.92 | 0.89 | 1.11 | −1.5 | 0.90 | 0.89 | 1.11 | −1.8 | 1.15 | 0.89 | 1.11 | 2.5a | Age, y > o | ||||
| “ | D | 44) make decisions to improve your health? | 1.06 | 0.91 | 1.09 | 1.3 | 1.00 | 0.91 | 1.09 | 0.0 | 0.99 | 0.91 | 1.09 | −0.1 | |||||
| “ | D | 45) join a sports club or exercise class if you want to? | 1.12 | 0.90 | 1.10 | 2.3a | 1.06 | 0.90 | 1.10 | 1.3 | 1.01 | 0.90 | 1.10 | 0.2 | |||||
| “ | D | 46) influence your living conditions that affect your health and well-being? | 1.05 | 0.91 | 1.09 | 1.0 | 0.98 | 0.91 | 1.09 | −0.3 | 1.01 | 0.91 | 1.09 | 0.2 | Age, y > o | ||||
| “ | D | 47) take part in activities that improve health and well-being in your community? | 1.10 | 0.91 | 1.09 | 2.0a | 1.04 | 0.91 | 1.09 | 0.8 | 1.04 | 0.90 | 1.10 | 0.9 | |||||
Note. This table reports the item-fit indexes after applying the one-dimensional (subscale correlation fixed to 1), three-dimensional and 12-dimensional approaches (treating the subscales as correlated). The analyses of the ordering of response categories (ordered) and differential item functioning (DIF) are based on the one-dimensional and consecutive approaches (treating the subscales as orthogonal or uncorrelated) for the three health domains and the 12 subscales. Ordered: “No” refers to an item with unordered response categories
aA t–value > 1.96 and an infit-value > 1 indicate a poor fit with the Rasch model due to there being more variation in the data than was expected by the model (item is under-discriminating)
bA t–value <−1.96 and an infit-value < 1 indicate a poor fit with the Rasch model due to there being less variation in the data than was expected by the model (item is over-discriminating)
For items displaying uniform DIF, the relevant dichotomized person factor levels are indicated. For example, “Age, y > o” refers to a uniform DIF for the person factor age in favour of the y = younger respondents (47 years or younger) factor level compared to the o = older respondents (48 years or older) factor level. The “Highest completed education level” (Edu) factor has l = low (primary and secondary school) and h = high (university or university college) levels, and the “Gender” factor (Gen) has the f = females and m = males levels
cnon-uniform DIF (item 22). All other DIFs were uniform
A: access, B: understand, C: appraise, CD: cognitive domain, CI: confidence interval, D: apply, DP: disease prevention, HC: healthcare, HD: health domain, HP: health promotion
RUMM2030 was used for the analyses of the ordering of response categories and DIF. ConQuest 4 was used for all other analyses
Fig. 1Model fit of the HLS-EU-Q47 after applying various analysis approaches. Figure 1 shows the overall fit statistics for the one-dimensional approach (all subscale correlations fixed to 1), the consecutive approach (treating the three health domains as orthogonal or uncorrelated) and the two-, three- and 12-dimensional approaches (treating the theoretical subscales as correlated). A: access, B: understand, C: appraise, D: apply (cognitive domains). HC: health care, DP: disease prevention, HP: health promotion (health domains). Δ: change in parameter, AIC: Akaike’s information criterion, cv: critical value, D: deviance, df: degrees of freedom, ep: number of estimated parameters, LRT: likelihood ratio test. PSR: person separation reliability based on marginal maximum likelihood estimate/Warm’s mean weighted likelihood estimate
Unidimensionality, data-model fit and reliability applying Rasch modelling of the various short versions
| HLS-Q12a | HL-SF12 [ | HLS-EU-Q16 [ | ||||
|---|---|---|---|---|---|---|
| One-dimensional | Three-dimensional | One-dimensional | Three-dimensional | One-dimensional | Three-dimensional | |
| Unidimensionality | ||||||
| Proportion (%) of significant | 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 | |||
| | 0.50 | 0.39 | 0.46 | |||
| | 0.90 | 0.91 | 0.85 | |||
| | 0.80 | 0.87 | 0.82 | |||
| Total item chi square ( | 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 |
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
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
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
All the short versions are developed on the basis of the HLS-EU-Q47
aHLS-Q12 developed through the present study
Overall fit and reliability using confirmatory factor analyses of the various short versions
| HLS-Q12a | HL-SF12 [ | HLS-EU-Q16 [ | ||||
|---|---|---|---|---|---|---|
| GOF index (LISREL) | One-dimensional | Three-dimensional | One-dimensional | Three-dimensional | One-dimensional | Three-dimensional |
| SB scaled χ2 ( | 142.71 (54), | 112.96 (51) | 93.73 (54), | 83.71 (51) | 379.12 (104), | 283.57 (101) |
| SRMR | 0.059 | 0.056 | 0.047 | 0.045 | 0.080 | 0.070 |
| RMSEA (90% CI) | 0.086 | 0.078 | 0.066 | 0.064 | 0.118 | 0.103 |
| CFI | 0.951 | 0.966 | 0.975 | 0.979 | 0.923 | 0.949 |
| NNFI (TLI) | 0.940 | 0.955 | 0.969 | 0.973 | 0.911 | 0.939 |
| Log-likelihoods | ||||||
| -2ln(L)(ep) | 6857 (24) | 6787 (27) | 6718 (24) | 6696 (27) | 8105 (32) | 7851 (35) |
| AIC (ep) | 6905 (24) | 6841 (27) | 6766 (24) | 6750 (27) | 8169 (32) | 7921 (35) |
| BIC (ep) | 7014 (24) | 6964 (27) | 6874 (24) | 6872 (27) | 8313 (32) | 8078 (35) |
| Reliability | ||||||
| | 0.826 | 0.663/0.608/0.713 | 0.822 | 0.591/0.599/0.622 | 0.882 | 0.823/0.720/0.667 |
Note. The table shows goodness of fit (GOF) indexes, log-likelihood and reliability using confirmatory factor analysis (CFA) when treating the various short versions as one- and three-dimensional. CFA was performed using LISREL software
SB scaled χ2 :Satorra-Bentler scaled chi-square. SRMR (standardised root mean square residual) and RMSEA (root-mean-squared error of approximation): values < 0.05 indicate good model fit, and values < 0.08 indicate an acceptable model fit. CFI (comparative fit index) and NNFI (non-normed fit index [or TLI = Tucker and Lewis fit index]): values > 0.95 indicate good model fit (Hu and Bentler, 1999)
-2ln(L): likelihood function, AIC: Akaike’s information criterion, BIC: Bayesian information criterion, ep: number of estimated parameters. Lower values indicate a better overall fit
aHLS-Q12 developed through the present study