Preheat oven to 325 degrees F (165 degrees C). Grease three 9 inch, round cake pans. Combine soda and buttermilk, and let stand a few minutes.
In a large bowl, cream sugar, 1/2 cup butter, 1/2 cup oil and shortening. Add egg yolks one at a time, beating well after each addition. Mix buttermilk mixture alternately with flour into creamed mixture. Stir in 1 teaspoon vanilla.
In a large glass or metal mixing bowl, beat egg whites until stiff peaks form. Fold 1/3 of the whites into the batter, then quickly fold in remaining whites until no streaks remain. Gently stir in 1 cup pecans and coconut.
Pour batter into prepared pans. Bake in the preheated oven for 25 to 30 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool.
To make the Cream Cheese Frosting: Beat together cream cheese, 1/2 cup butter or margarine, 1 teaspoon vanilla, and confectioners' sugar. Stir in 1 cup chopped pecans. Frost and fill cooled cake with cream cheese frosting.
