In an essay identifying the causes of independence movements in Latin America and the Caribbean, the student would likely include Enlightenment ideas. These ideas promoted concepts of liberty, equality, and self-governance, which inspired many independence movements throughout the region.
The other options, such as the absence of slavery, religious persecution, and decentralized government, were not primary factors driving independence movements in the same way that Enlightenment ideals were.
So, the correct answer is Enlightenment ideas.