What is the most effective or most utilized method of appeal used by the author to put forth his or her story, logos[logic/reason],pathos[emotion] and ethos[authority figures for ehtical support]?

Certainly I think that pathos is mixed with ethical support to give the reader a very unique understanding of the Walls family. Consider the title of the book. The title of the book and a major theme within it, the Glass Castle represents Rex's hope for a magical, fantastic life in which he can provide for his family and please his children. Rex lays out plans for the Glass Castle, including detailed dimensions for each of the children's rooms, but he never actually builds the castle. For a long time Jeannette believes that he will but she gives up on the hope after the hole they dig for the foundation of the Glass Castle is filled with garbage. Though the physical structure is not erected, the symbol the Glass Castle represents remains with Jeannette in her childhood and helps her to believe that her father will do what he promises. When she discovers that this is not always true and realizes that the Glass Castle will never actually be built, she has reached adulthood.