Disclosed are binder compositions for glass fiber, comprising a polycarboxylic acid such as polyacrylic acid and a crosslinking agent. The crosslinking agent comprises a polyhydroxy component formed from a reaction of an epoxidized vegetable oil with an amine and optionally with a phenolic compound. The molar ratio of the amine to the epoxidized vegetable oil at the beginning of said reaction may be greater than 1: 1. Also disclosed are methods of preparing the binders and fiber-containing compounds made with such binders.