The General Data Protection Regulation (GDPR), which took effect on May 25, 2018, is a set of regulations governing the use of personal data across the EU. This is forcing some affiliates to obtain user data through opt-in consent (updated privacy policies and cookie notices), even if they are not located in the European Union. This new regulation should also remind you to follow FTC guidelines and clearly disclose that you receive affiliate commissions from your recommendations.
Cost per action/sale methods require that referred visitors do more than visit the advertiser's website before the affiliate receives a commission. The advertiser must convert that visitor first. It is in the best interest of the affiliate to send the most closely targeted traffic to the advertiser as possible to increase the chance of a conversion. The risk and loss are shared between the affiliate and the advertiser.
Analytics are limited. Unlike with conversions made directly on your WordPress site, you’ll be limited in terms of what you can learn about the people making purchases through your affiliate links. While Amazon does provide you with details about clicks and sales, you won’t get deep insights into who the consumer was and what they did on your site before they got to that point that you would with Google Analytics.