With an electric mixer, beat together the cream cheese and brown sugar until smooth. Beat in the eggs one at a time. Blend in the raspberry pie filling, yogurt, flour, cinnamon, ginger, rum flavoring, and vanilla extract. Pour the filling into a 9" springform pan coated with nonstick cooking spray.
Bake 1 hour 10 minutes. Remove from the oven and run a knife around the sides to loosen. Let stand at room temperature for 30 minutes.
Chill the cake in the refrigerator, uncovered, until cold. Then cover with foil and chill at least 4 hours (or up to 3 days).