2.5. Perception Index: Statistical Analysis and Structural Equation Modeling

The Likert data related to the consumers’ visual perceptions of beef were subjected to polychoric correlation analysis, to ensure that the relationships among Likert variables were >0.3. The Kaiser–Meyer–Olkin measure of sample adequacy (MSA) test was used to verify that variables were pertinent. Likert responses with MSA values < 0.5 were discarded [34]. Factorial analysis was used to develop a consumer acceptance index into a single variable (“visual beef consumer perception index”) [35]. The analysis was developed to apply a maximum likelihood method to factor extraction and used a “varimax” rotation to guarantee factor independence. The construct identified was subjected to the Cronbach’s alpha coefficient, and the factor was validated to ensure it met the criterion of alpha > 0.6 [34]. The visual beef consumer perception index was validated and applied to structural equation modeling (SEM), as indicated by Beaujean [36]. The quality of the model was ensured by the absence of negative variance in the errors, correlations higher than 1, high standard errors, and factorial loadings (FL) > 1. The model was validated to have a root mean square error of approximation (RMSEA) ≤ 0.1, and comparative fit index (CFI) and Tucker–Lewis index (TLI) values ≥ 0.9 [34,36].

All data analysis was performed during index development using a psych [37] and lavaan package [38], in the software R-Project.