Dynamic fit index cutoffs for treating likert items as continuous

Area of Science:

• Psychometrics
• Statistical modeling
• Quantitative psychology

Background:

• Empirical factor analyses frequently use Likert-type responses, often treated as continuous data.
• Traditional model fit index cutoffs were developed for continuous data, creating a methodological disconnect.
• Existing guidelines may inaccurately assess model fit when applied to Likert-type responses.

Purpose of the Study:

• To address the disconnect between traditional factor analysis guidelines and the common use of Likert-type responses.
• To extend the dynamic fit index (DFI) framework to effectively accommodate Likert-type data characteristics.
• To improve the sensitivity of model fit assessment for Likert-type responses in factor analysis.

Main Methods:

• An illustrative simulation study was conducted to assess the impact of treating Likert-type responses as continuous.
• The dynamic fit index (DFI) framework was extended to incorporate data characteristics like Likert scale points and response distributions.
• Two simulation studies were performed using 5-point Likert-type responses to evaluate the extended DFI method.

Main Results:

• Treating 5-point Likert responses as continuous can significantly reduce the sensitivity of traditional fit index cutoffs to misspecification.
• The extended DFI method demonstrated improved performance compared to traditional cutoffs and DFI based on multivariate normality.
• The proposed DFI extension consistently maintained over 90% sensitivity to misspecification with 5-point Likert-type responses.

Conclusions:

• Applying traditional factor analysis cutoffs to Likert-type data can lead to inaccurate conclusions about model fit adequacy.
• The extended dynamic fit index (DFI) framework provides a more reliable method for assessing model fit with Likert-type responses.
• This research offers a crucial methodological advancement for researchers utilizing Likert-type data in factor analysis.