Edit in JSFiddle

var subModel = Backbone.Model.extend({
    constructor:function(){ //extend this constructor, not Model
        this.goo = 'boo';
        Backbone.Model.apply(this, arguments); //add in Model instance properties
    }
});

myModel = new subModel();

console.log(myModel.goo); //logs boo
console.log(myModel.cid); //logs c1, cid is a Model instance property