Measuring quality of life with fuzzy numbers: in the perspectives of reliability, validity, measurement invariance, and feasibility

Jointly Modeling Rating Responses and Times with Fuzzy Numbers: An Application to Psychometric Data

In several research areas, ratings data and response times have been successfully used to unfold the stagewise process through which human raters provide their responses to questionnaires and social surveys. A limitation of the standard approach to analyze this type of data is that it requires the use of independent statistical models. Although this provides an effective way to simplify the data analysis, it could potentially involve difficulties with regard to statistical inference and interpretation. In this sense, a joint analysis could be more effective. In this research article, we describe a way to jointly analyze ratings and response times by means of fuzzy numbers. A probabilistic tree model framework has been adopted to fuzzify ratings data and four-parameters triangular fuzzy numbers have been used in order to integrate crisp responses and times. Finally, a real case study on psychometric data is discussed in order to illustrate the proposed methodology. Overall, we provide initial findings to the problem of using fuzzy numbers as abstract models for representing ratings data with additional information (i.e., response times). The results indicate that using fuzzy numbers leads to theoretically sound and more parsimonious data analysis methods, which limit some statistical issues that may occur with standard data analysis procedures.

Postselection Inference in Structural Equation Modeling

Most statistical inference methods were established under the assumption that the fitted model is known in advance. In practice, however, researchers often obtain their final model by some data-driven selection process. The selection process makes the finally fitted model random, and it also influences the sampling distribution of the estimator. Therefore, implementing naive inference methods may result in wrong conclusions-which is probably a prime source of the reproducibility crisis in psychological science. The present study accommodates three valid state-of-the-art postselection inference methods for structural equation modeling (SEM) from the statistical literature: data splitting (DS), postselection inference (PoSI), and the polyhedral (PH) method. A simulation is conducted to compare the three methods with the commonly used naive procedure under selection events made by L₁-penalized SEM. The results show that the naive method often yields incorrect inference, and that the valid methods control the coverage rate in most cases with their own pros and cons. Real world data examples show the practical use of the valid inference methods.

Testing Measurement Invariance with Ordinal Missing Data: A Comparison of Estimators and Missing Data Techniques

Ordinal missing data are common in measurement equivalence/invariance (ME/I) testing studies. However, there is a lack of guidance on the appropriate method to deal with ordinal missing data in ME/I testing. Five methods may be used to deal with ordinal missing data in ME/I testing, including the continuous full information maximum likelihood estimation method (FIML), continuous robust FIML (rFIML), FIML with probit links (pFIML), FIML with logit links (lFIML), and mean and variance adjusted weight least squared estimation method combined with pairwise deletion (WLSMV_PD). The current study evaluates the relative performance of these methods in producing valid chi-square difference tests ([Formula: see text]) and accurate parameter estimates. The result suggests that all methods except for WLSMV_PD can reasonably control the type I error rates of [Formula: see text] tests and maintain sufficient power to detect noninvariance in most conditions. Only pFIML and lFIML yield accurate factor loading estimates and standard errors across all the conditions. Recommendations are provided to researchers based on the results.

Mining latent information in PTSD psychometrics with fuzziness for effective diagnoses

The options of traditional self-report rating-scale, like the PTSD Checklist Civilian (PCL-C) scale, have no clear boundaries which might cause considerable biases and low effectiveness. This research aimed to explore the feasibility of using fuzzy set in the data processing to promote the screening effectiveness of PCL-C in real-life practical settings. The sensitivity, specificity, Youden's index etc., of PCL-C at different cutoff lines (38, 44 and 50 respectively) were analyzed and compared with those of fuzzy set approach processing. In practice, no matter the cutoff line of the PCL-C was set at 50, 44 or 38, the PCL-C showed good specificity, but failed to exhibit good sensitivity and screening effectiveness. The highest sensitivity was at 65.22%, with Youden's index being 0.64. After fuzzy processing, the fuzzy-PCL-C's sensitivity increased to 91.30%, Youden's index rose to 0.91, having seen marked augmentation. In conclusion, this study indicates that fuzzy set can be used in the data processing of psychiatric scales which have no clear definition standard of the options to improve the effectiveness of the scales.