Quantifying the intangible benefit of an influencer’s credibility and its impact on brand loyalty in ROI calculations can be challenging, but not impossible. Here are some ways:

1. Survey customer sentiment: After a campaign, survey your customers about their attitudes towards your brand and the influencers you partnered with. Higher ratings and positive comments are signs of a strong connection.

2. Track Repeat Business: Credibility often leads to trust and this will drive recurring business. Measure the number of repeat purchases by customers who were directed from an influencer’s platform.

3. Monitor Social Media Engagement: Track and measure the interaction and engagement levels on the influencer’s social media posts about your products/services.

4. Use Coupon Codes: Unique codes assigned to each influencer can be used to track not only the direct sales from an influencer but also repeat purchases which might signify increased brand loyalty.

5. Lifetime Value (LTV): Look at the projected revenue a customer will bring over their lifetime. An increase here signifies greater loyalty.

Influencer marketing platforms, like Flinque, often include features that help you track these metrics, enabling a more holistic view of your ROI. However, the specific metrics that you focus on will depend on your campaign goals as well as the specific needs of your brand.

All these efforts demand time and expertise in deciphering big data analytics. ROI of an influencer’s credibility cannot be directly measured overnight, it’s more of a long-term game that requires consistent monitoring and evaluation over time. The key here is understanding the purpose and aligning your tracking methods with these intangible benefits. Comparatively, different platforms provide various tools, it’s about choosing the right one compatible with your demands. Remember, the kernel of success in influencer marketing lies in choosing the right influencer aligning with your brand ethos, as it’s their credibility propelling your brand’s loyalty.