IntervalQuestionStat-package {IntervalQuestionStat}

Tools to Deal with Interval-Valued Responses in Questionnaires

Description

IntervalQuestonStat is an open source package for doing the statistical analysis of interval-valued responses collected through interval-valued scales in lots of different widely used questionnaires measuring many intrinsically imprecise human attributes in the R environment. In particular, this package implements the theoretical concepts, results, and ideas suggested by the SMIRE+CoDiRE (Statistical Methods with Imprecise Random Elements and Comparison of Distributions of Random Elements) Research Group (https://bellman.ciencias.uniovi.es/smire+codire/) from the University of Oviedo (Spain) taking into account some applied investigations and real-life studies.

Details

In Social and Educational Sciences and many other disciplines, interval-valued scales arise as a strong alternative to both traditional Likert-type or visual analogue scales in some questionnaires measuring people's behavior (attitudes, opinions, perceptions, feelings, etc.). This type of data can not be directly measured because it concerns inherently imprecise features. Likert-type and visual analogue scales force respondents to choose single-point answers linked to some items (statements or questions), so individual differences are almost systematically overlooked. In order to overcome the limitations of these scales in capturing uncertainty over respondents' answers, interval-valued scales allow them to select a real-valued interval and not being constrained to a single point.

This package provides S4 classes, methods, and functions for dealing with this type of data and it also includes some real-life data sets. In particular, it aims to provide the following functionality:

1. Definition of interval-valued objects and instances (see IntervalData-class, IntervalData, IntervalList-class, IntervalList, IntervalMatrix-class, and IntervalMatrix).

2. Calculation of basic operations with interval-valued data (see arithmetic and distance).

3. Calculation of some central tendency and variation measures (see mean, var and cov).

4. Visualization of interval-valued data (see plot).

5. Association of interval-valued responses and their corresponding equivalent Likert-type and visual analogue scales responses (see ivs2likert and ivs2vas).

6. Statistical analysis of reliability of questionnaire's responses (see cronbach).

7. Simulation of interval-valued responses in questionnaires (see simulIVS).

For a complete list of classes, methods and functions included in the IntervalQuestionStat package call help(package="IntervalQuestionStat") on the R console.

Acknowledgments: The initial development of this R package has been partially supported by the Principality of Asturias Grant AYUD/2021/50897 and also by the Spanish Ministry of Economy and Business Grant PID2019-104486GB-I00.

Author(s)

José García-García [e-mail],
with contributions from María Asunción Lubiano [e-mail].

References

• Aumann, R.J. (1965). Integrals of set-valued functions. Journal of Mathematical Analysis and Applications, 12(1):1-12. doi:10.1016/0022-247X(65)90049-1.

• Cronbach L.J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. doi:1001007/BF02310555.

• De la Rosa de Sáa, S.; Gil, M.Á.; González-Rodríguez, G.; López, M.T.; Lubiano M.A. (2015). Fuzzy rating scale-based questionnaires and their statistical analysis, IEEE Transactions on Fuzzy Systems, 23(1):111-126. doi:10.1109/TFUZZ.2014.2307895.

• Fréchet, M. (1948). Lés éléments aléatoires de nature quelconque dans un espace distancié. Annales de l'institut Henri Poincaré, 10(4):215-310.

• Gil, M.Á.; Lubiano, M.A.; Montenegro, M.; López, M.T. (2002). Least squares fitting of an affine function and strength of association for interval-valued data. Metrika, 56:97-111. doi:10.1007/s001840100160.

• Hankin, R.K.S. (2010).. A step-by-step guide to writing a simple package that uses S4 methods: a "hello world" example. Technical Report. Auckland University of Technology.

• Lubiano, M.A.; García-Izquierdo, A.L.; Gil, M.Á. (2021). Fuzzy rating scales: Does internal consistency of a measurement scale benefit from coping with imprecision and individual differences in psychological rating?. Information Sciences, 550:91-108. doi:10.1016/j.ins.2020.10.042.

• Minkowski, H. (1903). Volumen und oberfläche. Mathematische Annalen, 57:447-495.

• Moore, R.E.; Kearfott, R.B.; Cloud, M.J. (2009). Introduction to Interval Analysis. Society for Industrial and Applied Mathematics, USA. doi:10.1137/1.9780898717716.