**4. Results**

The results shown in Figure 1 confirm the appropriateness of the indicators selected. Similarly, the reliability measures shown in Table 2 confirm the validity of the questionnaire used to assess the four latent dimensions proposed. The index of goodness-of-fit proposed by [61] as the geometric mean of the average communality and the average R<sup>2</sup> had a value of 0.451. This index is a working solution to the problem of the lack of optimization of scalar functions in PLS modelling and can provide an overall validation of the model.


**Table 2.** Reliability Measurements.

As shown in Table 2, the indicators used to verify the reliability of the measuring instruments and internal consistency (i.e. Cronbach's alpha and the composite reliability indexes) were in all cases more than 0.7 or very close to 0.7. Therefore, the reliability of the constructs was confirmed by their fulfilling the criterion proposed by [62]. In addition, the higher values of the composite reliability index in the PLS model have the advantage over Cronbach's alpha values of there being no need to assume that all indicators have the same weighting [63].

According to the criteria established by [63] to obtain convergen<sup>t</sup> validity, the values of the average variance extracted (AVE) for the four constructs were more than or very close to 0.5. In addition, the items are placed on the latent variable, where together they increase its quantitative load and the criterion proposed by these authors to test discriminant validity was also fulfilled. That is, a comparison of the amount of variance captured by the construct (AVEj) and the shared variance with other constructs (ρij) for the four latent variables (Table 3) showed that the values of the square root of the AVE of each construct were more than the estimated correlation between them (1):

$$
\sqrt{AVE\_j} \ge \rho\_{ij} \forall \ i \ne j,\tag{1}
$$


**Table 3.** Correlation Matrix of Latent Variables.

In the case of the predictive capacity of the structural sub-model (see Table 2), the estimated values of the R<sup>2</sup> statistic were more than 0.1 for all latent and significant variables. Therefore, the acceptability criterion proposed by [64] was fulfilled.

Table 4 shows the estimations of the direct and total effects between the latent variables of the study model. As shown, the dependency relationships in the proposed model were verified, and they also confirm the study hypotheses. These results are in line with those obtained by [58] for a sample of Spanish consumers. However, CSR-S had a weaker effect on Andalusian CPH than it did on Spanish CPH.

**Table**

**5.**

Tests

of

the


**Table 4.** Direct and Overall Effects Between Latent Variables.

With the aim of confirming the theoretical assumptions on which the hypotheses are based, Table 5 shows the estimations of the standardized regression coefficients of the constructs and their corresponding t-statistics using bootstrapping with 5000 samples. The estimated values confirm the statistical significance of the coefficients related to each of the proposed relationships. The signs of these values also confirm the primary and secondary study hypotheses.

 Hypotheses Direct 

Effects

Between

Latent

Variables.

of


Nots: see [64].

The results presented in Table 5 show the relevance to Andalusian clients of the three dimensions of the CSR initiatives (i.e. economic, environmental, and social) implemented by hotels. It is noteworthy that the relevance of the economic and environmental dimensions reached 99%.

The PLS model provides an assessment of the predictive capacity of our model, by indicating the variance explained by the predictor variables of the endogenous construct in the model. Although its predictive capacity was weak in the case of the social dimension, it was moderate or strong in the other two cases [65].
