Who was the model for the Statue of Liberty?

Various sources cite different models for the face of the statue. One indicated the then-recently widowed Isabella Eugenie Boyer, the wife of Isaac Singer, the sewing-machine industrialist. "She was rid of the uncouth presence of her husband, who had left her with only his most socially desirable attributes: his fortune and... his children. She was, from the beginning of her career in Paris, a well-known figure. As the good-looking French widow of an American industrialist she was called upon to be Bartholdi's model for the Statue of Liberty." (Ruth Brandon, Singer and the Sewing Machine: A Capitalist Romance, p. 211) Another source believed that the "stern face" belonged to Bartholdi's mother, with whom he was very close. (Leslie Allen, "Liberty: The Statue and the American Dream," p. 21) National Geographic magazine also pointed to his mother, noting Bartholdi never denied nor explained the resemblance. (Alice J. Hall, "Liberty Lifts Her Lamp Once More," July 1986.)
https://en.wikipedia.org/wiki/Statue_of_Liberty

Nobody knows for certain, but most sources indicate that the statue of liberty's face at least was modeled after the sculptor's mother.

"The Statue of Liberty, the most famous symbolic statue of a woman, was modeled after Marie Bartholdi, the sculptor's mother."
http://www.factmonster.com/ipka/A0101054.html

"Frédéric-Auguste Bartholdi knew he wanted to build a giant copper goddess; he used his mother as the model."
https://en.wikipedia.org/wiki/Fr%C3%A9d%C3%A9ric_Auguste_Bartholdi

I can't find that the National Park Service offers any information.

The Roman goddess Libertas or Liberty was quite accustomed to being depicted in art prior to Bartholdi's statue. Here's detail of an 1872 statue in Florence by the sculptor Fredi, which bears a remarkable resemblence to Bartholdi's later face and pose:
endex.com/gf/buildings/liberty/worldstatues/SOLsantacroce/SCroce040227.0860.x1.jpg webpage no longer exists

Most authoritative sites list the face model being Bartholdi's mother Charlotte.
National Park Service is one of many:
http://www.nps.gov/stli/forkids/index.htm

Site with original clay model along with (small) painting of his mother:
endex.com/gf/buildings/liberty/nytc/solnytc1943.htm webpage no longer exists

A smaller secondary role was apparently played by his future wife Jeanne-Emilie Baheux de Puysieux as a fill-in model and body model:
endex.com/gf/buildings/liberty/libertyquestions.htm#solq17 This page also has a better picture of his mother's painting.

There are a number of sites, and one book, that list the inspiration as Isabelle Boyer, the widow of sewing machine magnate Isaac Singer, whom Bartholdi met in Luxembourg in 1878, and with whom he might possibly have had an affair. However, there's zero detail to this. The book is about her family, and it might have been a legend started by them after the fact due to a rumored resemblence. In any event, if he did indeed meet her in 1878, 3 years after the clay model was completed, he would not have had time to alter the actual statue's face, which was completed early that year, for showing at the Paris Exposition. Barring other evidence, it appears her claim is merely legend.

So other than simply classical inspirations, any real depictions appear to be his mother's head on his future wife's body.
https://en.wikipedia.org/wiki/Oedipus_complex