Descriptive statistics
The test of normality of the scale scores showed the distributions of all study variables were negatively skewed (Table 1). The -coefficient for the VI was very low, and for SF and MH were also below typically accepted standards. On the other hand, Cronbach’s alphas were adequate for the GH, RE, Physical and Mental components, and good for PF, RP and BP.

Table 1: Descriptive statistics and K-S test of normality of Persian SF-36 scales and summary measures

PF= Physical Functioning; RP=Role-Physical; BP= Bodily Pain; GH= General Health; VT= Vitality; SF= Social Functioning; RE = Role-Emotion; MH= Mental Health. D = Kolmogorov-Smirnov (K-S) test of normality. = Cronbach’s alpha. ** P<.01. * P<.05

Testing the Sf-36 factor structure models
Four CFA models were developed to confirm the factor structure of the Farsi SF-36. This analysis served to confirm Model A, the original US model, which is a comparison of the three competing models to ascertain the extent to which the Model A would demonstrate a superior fit to the three alternative models. Model B, the first alternative model was developed to load all items of the SF-36 into a single health construct. The second alternative model, Model C, was developed from the three summary measures of mental, physical and well-being (18). The third alternative model, Model D was then developed based on the eight factors that aggregate the 36 items of the SF-36.

Table 2 indicates how Model B provided a poor fit for this data. While a significantly greater model fit was observed for the original US model (Model A) and Model C and D; when compared to Model B, these models did not demonstrate a good fit. Models A, C and D however, provided a relatively better fit for this data. An examination of model fit statistics revealed mixed evidence for a good model fit, where all models did not fit the data well, according to the significant chi-square index, the relative chi-square per degrees of freedom and the RMSEA (17). The Comparative goodness-of-fit and Incremental Fit Index for these models indicated more than an acceptable model fit, but the goodness-of-fit index for all models was lower than the accepted criteria. Together, these results indicate that the one-factor did not provide a good fit for this data, and the three alternative models are the same, according to the fit indices, along with the fact that their overall fit did not appear across the model fit statistics.

Table 2: Factor loadings, communalities, mean and standard deviation of the scales of the Farsi SF-36, a two factor solution

Note. PF= Physical Functioning; BP= Bodily Pain; GH= General Health; RP=Role-Physical; RE = Role-Emotion; SF= Social Functioning, MH= Mental Health, VT= Vitality. h2= communality. Factor loading > 0.4. Cross-loaded items > 0.4.

Farsi SF-36 factor structure
A PCA of the eight scales was conducted with orthogonal and oblique rotations to explore the factor structure of the Farsi SF-36, and examined how many summary measures were extracted in the Iranian sample. The analyses demonstrated only one factor could be extracted with eigenvalues over 1, and explained a total 44.9% of the observed variance. The original two measure model and the three uncorrelated measures were examined and a scree-test was used to determine the proper number of several factor solutions. The results showed that the first two factors represented the main sources of variance in the data matrix. However, the results of orthogonal rotation showed the RP and VT had high factor loadings on both factors. The results of the oblimin rotation however, showed a better fit of the original measurement model because all eight scales were loaded on their appropriate factors. The explained variance by the two extracted factors was 56.7%.

The communality, eigenvalues and factor loadings for the two rotated factors using varimax and oblimin rotations are presented in Table 2, along with the means, and standard deviations for all eight scales.

One General Health Construct
A second order CFA based on the two factor model (Physical and Mental) and three factor model of adding General well-being, were loaded on a one general health conception. This analysis served to explore and determine the underlying latent trait in the SF-36 that aggregates the summary measures (Figure 2).

Table 3 shows how both models demonstrated an unacceptable fit of this data. The chi squares were significant, with p < 0.05, the relative chi square was higher than 2, and the RMSEA was higher than 0.05. However, the goodness-of fit indices were acceptable and confirmed both models.

Click here for Table 3: The Goodness of Fit Statistics for CFA Modified and non-modified two and three summary measure models of the Farsi SF-36

Note: Model E included the two summary measures belonging to one general factor (General Health), Model F included the three summary measures belonging to one general factor. CFI= Comparative Fit Index, GFI=goodness of fit index, IFI= Incremental Fit Index, NFI= Non Normed Fit Index, RMSEA=Root Mean Square Error of Approximation, ECVI= Expected Cross-Validation Index. ECVI for Saturated Model=0.18. * P< .05. ** P< .001

One strategy to improve the models was to add the correlations between error terms which were specified, when suggested, by high modification indices and also where theoretically defensible. In Model E, the correlated errors were added between RP items with GH, RE and MH, and between BP-VT. The correlated errors in model F were added between RP with PF, SF, RE and MH, and between MH-VT.

An examination of model fit statistics after modification revealed adequate evidence for a good model fit. However, in both Models the RP scale had the most error correlations with the other scales, but its pattern of correlated errors was different in the models with GH, RE and MH.

DISCUSSION

A comparative approach of the four factor structure models of the Farsi SF-36 is presented here.

Reliability
The Farsi SF-36 has shown satisfactory internal consistency reliability (>0.70) for all scales except VI, SF and MH, with the highest value for PF. Similar results for PF have been reported in other countries (19), which was to be expected given that the PF scale has 10 out of 36 items of the SF-36. Such a large set of items increases the Cronbach’s . A very low level of reliability has been reported for the VI in other studies conducted with older people and patients with chronic conditions (10, 20, 21). These studies determined whether the lower internal consistency of the SF-36 VI scale is due to the study sample or cultural differences, although this deserves further study. Additionally, the SF scale results for internal consistency reliability were below typically accepted standards in Iran, suggesting a decreased level of social abilities among older adults. The fact that this result was consistent with other studies (20, 22, 23) raises the question of whether only two items in the SF scale are adequate for assessing the concept of social functioning.

Factor structure
Both two and three factor models were confirmed in the Iranian older population, however a comparison of fit indices of the higher order two-factor model, Model A with two summary measures, and higher order three factor model, Model C with three summary measures, showed no differences between these two models. This result means it is not possible to show a preferred model for older people and suggests the instrument is conceptually equivalent with the original version. However, the question remains about how many scales could be extracted from this concept.

The two factor model (mental and physical) showed PF, RP, BP and GH to correlate with physical health component, and VI, SF, RE and MH with the mental dimension. These results are consistent with other studies (24) and confirmed the Farsi SF-36 met the psychometric standards hypothesized in the original model for physical and mental health.

The results of testing a three second-order factor are consistent with the study conducted across nine countries (18) and Rasch validation of the SF-36 in Korea (25). The third factor, interpreted as general well-being in this data, was the result of clustering GH and VI, as in previous studies, and interpreted for the mixed factor content of GH and VI (18). The reason for such a divergent result between this and previous studies that confirmed the two-factor model may be the difference in separating elderly from the other population group. Another reason for this divergent result is that cultural value plays a role in the interpretation of these differences, and Iranian elderly tend to put more value on items related to well-being compared with other population groups and cultures. Therefore the three-factor model makes the Farsi SF-36 particularly suitable for use in the assessment of older adults, as its three scales make it more appropriate to identify older people’s needs. Such data makes it possible to develop a more precise care plan, since the more factors indicate a greater identification of the underlying latent trait. The three factor model will be achieved by slightly modifying items on the VI scale and developing items for the well-being scale.

CONCLUSION

The Farsi SF-36 has generally accepted psychometric properties, with empirical evidence showing that developing items for the third factor of well-being would be useful to better identify the needs of older people.

Acknowledgement
The authors of this paper acknowledge their gratitude to Dr Emma Caukill and all of the participants in this research project.