Abstract:Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study. The numerical results show that the underlying normal distribution can be substantially biased, even tho… Show more
“…Furthermore, McDonald's ordinal omega and the greatest lower bound to reliability were assessed [41][42][43]. Inter-item and item-total correlations were measured by polychoric correlations and Spearman's rho coefficients [44][45][46]. The normality of the data distribution was assessed by the Kolmogorov-Smirnov (Lilliefors) test.…”
Background: The Dermatology Life Quality Index (DLQI) is the most commonly used instrument for clinical evaluation of the impact on health-related quality of life (HRQOL) in dermatological research protocols. The DLQI's classical psychometric properties have been considered adequate in validation studies from several countries. However, the structure of the DLQI is a matter of discussion, especially concerning the dimensionality and informative properties of its questions according to the item response theory (IRT). Methods: Pooled data from studies in Brazil that utilized the DLQI to assess HRQOL in 14 dermatoses were reanalyzed. Classical psychometrical analysis, dimensionality assessment through parallel analysis and IRT (Samejima's ordinal model) analysis were performed. Results: The sample consisted of 1286 patients with a mean age of 47 years (SD = 16), and the proportion of women was 59% (765). The DLQI scores ranged from 0 to 29, with a median (p 25-p 75) of 5 (2-11). All items indicated significant correlations with the total DLQI score (rho > 0.54). The Cronbach's alpha result was 0.90 (CI 95% 0.89-0.91). Parallel analysis indicated a unidimensional factor structure. According to IRT analysis, items q6 (sports) and q7 (work/study) exhibited insufficient fit to the model (p < 0.01), while the items that indicated the best discrimination and information functions were q2 (embarrassment), q3 (shopping/gardening), q4 (clothing) and q5 (social/leisure). The ordination of the scores was confirmed for all items. Most items revealed non-uniform behavior according to sex, age and type of disease. Conclusions: The DLQI exhibits adequate psychometric reliability and a unidimensional structure for assessing HRQOL in Brazilian dermatological patients. The DLQI's performance varies in the assessment of HRQOL in heterogeneous samples.
“…Furthermore, McDonald's ordinal omega and the greatest lower bound to reliability were assessed [41][42][43]. Inter-item and item-total correlations were measured by polychoric correlations and Spearman's rho coefficients [44][45][46]. The normality of the data distribution was assessed by the Kolmogorov-Smirnov (Lilliefors) test.…”
Background: The Dermatology Life Quality Index (DLQI) is the most commonly used instrument for clinical evaluation of the impact on health-related quality of life (HRQOL) in dermatological research protocols. The DLQI's classical psychometric properties have been considered adequate in validation studies from several countries. However, the structure of the DLQI is a matter of discussion, especially concerning the dimensionality and informative properties of its questions according to the item response theory (IRT). Methods: Pooled data from studies in Brazil that utilized the DLQI to assess HRQOL in 14 dermatoses were reanalyzed. Classical psychometrical analysis, dimensionality assessment through parallel analysis and IRT (Samejima's ordinal model) analysis were performed. Results: The sample consisted of 1286 patients with a mean age of 47 years (SD = 16), and the proportion of women was 59% (765). The DLQI scores ranged from 0 to 29, with a median (p 25-p 75) of 5 (2-11). All items indicated significant correlations with the total DLQI score (rho > 0.54). The Cronbach's alpha result was 0.90 (CI 95% 0.89-0.91). Parallel analysis indicated a unidimensional factor structure. According to IRT analysis, items q6 (sports) and q7 (work/study) exhibited insufficient fit to the model (p < 0.01), while the items that indicated the best discrimination and information functions were q2 (embarrassment), q3 (shopping/gardening), q4 (clothing) and q5 (social/leisure). The ordination of the scores was confirmed for all items. Most items revealed non-uniform behavior according to sex, age and type of disease. Conclusions: The DLQI exhibits adequate psychometric reliability and a unidimensional structure for assessing HRQOL in Brazilian dermatological patients. The DLQI's performance varies in the assessment of HRQOL in heterogeneous samples.
“…Typically, the latent normality assumption has often been taken for granted by applied researchers (Foldnes and Grønneberg, 2020). If there are violations of latent normality, parameter estimates based on the incorrect latent normality assumption can provide substantially biased estimates (Jin and Yang-Wallentin, 2017;Foldnes and Grønneberg, 2020). It has shown that the latent normality assumption can be empirically tested (Maydeu-Olivares et al, 2009;Raykov and Marcoulides, 2015;Foldnes and Grønneberg, 2020).…”
Section: The Normality Assumption and The Latent Normality Assumptionmentioning
confidence: 99%
“…If the ordinal nature of variables would be taken seriously, more sophisticated modeling strategies for factor analysis that try to estimate more flexible distributions are required (Jin and Yang-Wallentin, 2017;Foldnes and Grønneberg, 2019). A particularly attractive distribution class is the factor copula model (Krupskii and Joe, 2013;Nikoloulopoulos and Joe, 2015;Ackerer and Vatter, 2017;Krupskii and Genton, 2018).…”
Section: The Normality Assumption and The Latent Normality Assumptionmentioning
“…5 , the relationship between and is displayed for the ordinalized bivariate Student’s t . The reader can also refer to Jin and Yang-Wallentin ( 2017 ) for some potential alternatives to the bivariate normal distribution assumption as un underlying stochastic model for ordinal data, where the authors study robustness against misspecification of the underlying distribution with respect to the polychoric correlation estimation. Fig.…”
Section: Conclusion and Further Researchmentioning
We consider a bivariate normal distribution with linear correlation $$\rho $$
ρ
whose random components are discretized according to two assigned sets of thresholds. On the resulting bivariate ordinal random variable, one can compute Goodman and Kruskal’s gamma coefficient, $$\gamma $$
γ
, which is a common measure of ordinal association. Given the known analytical monotonic relationship between Pearson’s $$\rho $$
ρ
and Kendall’s rank correlation $$\tau $$
τ
for the bivariate normal distribution, and since in the continuous case, Kendall’s $$\tau $$
τ
coincides with Goodman and Kruskal’s $$\gamma $$
γ
, the change of this association measure before and after discretization is worth studying. We consider several experimental settings obtained by varying the two sets of thresholds, or, equivalently, the marginal distributions of the final ordinal variables. This study, confirming previous findings, shows how the gamma coefficient is always larger in absolute value than Kendall’s rank correlation; this discrepancy lessens when the number of categories increases or, given the same number of categories, when using equally probable categories. Based on these results, a proposal is suggested to build a bivariate ordinal variable with assigned margins and Goodman and Kruskal’s $$\gamma $$
γ
by ordinalizing a bivariate normal distribution. Illustrative examples employing artificial and real data are provided.
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