I was kind of interested in reading about this study because I had never really thought about it much before. Andrew Howell at Grant MacEwan University (Canada) studied people's willingness to apologize (in general) and then compared them to a whole battery of personality assessments.
The obvious connections were that people with more compassion and more agreeableness apologize more. But what were more surprising were the effects of self-esteem. People with really low self-esteem are hesitant to apologize, even if they feel bad about what they did, because they direct the shame internally. They feel bad, but may also feel sorry for themselves, and therefore not apologize to others.
Those with really high self-esteem (i.e. egocentrics, narcissists, etc) were also less likely to apologize. Perhaps they felt entitled to do whatever they did and therefore didn't need to apologize for it.
So how can we use this information? First, think about how you feel when you do something that most people generally apologize for. If you apologize more than others, then your self-esteem is right in the sweet spot and you should feel good. But if you apologize less, think about which end of the tail you fall on. You may need to work on your self-esteem, or you may need to come off your pedestal.