Accessing this from within an object's inline function

A common way is to assign the this you want to a local variable.

init: function() {
   var _this = this;
   this.testObject.submit(function() {
        console.log(_this.testVariable); // outputs testVariable 
   });
}

You could also do this using ES6 arrow functions:

init: function(){
    this.testObject.submit( () => {
        console.log(this.testVariable);
    }
}

Arrow functions capture the this value of the enclosing context, avoiding the need to assign this to a new variable, or to use bound functions.