How can I use knockout’s $parent/$root pseudovariables from inside a .computed() observable?

The pseudovariables are only available in the context of data binding. The view model itself ideally should not know about or have any dependencies on the view that is displaying it.

So, when adding computed observables in the view model, you have no knowledge of how it will be bound (like what is going to be $root). A view model or part of a view model could even be bound separately to multiple areas of the page at different levels, so the pseudo-variables would be different depending on the element that you are starting with.

It depends on what you are trying to accomplish, but if you want your child to have an isSelected computed observable that indicates whether this item is the same as the selected item on the parent view model, then you will need to find a way to make the parent available to the child.

One option is to pass the parent into the constructor function of your child. You do not even need to add the pointer to the parent as a property of the child and can just use it in your computed observable directly.

Something like:

var Item = function(name, parent) {
   this.name = ko.observable(name);  
   this.isSelected = ko.computed(function() {
       return this === parent.selectedItem();        
   }, this);
};

var ViewModel = function() {
   this.selectedItem = ko.observable();
   this.items = ko.observableArray([
       new Item("one", this),
       new Item("two", this),
       new Item("three", this)
       ]);
};

Sample here: http://jsfiddle.net/rniemeyer/BuH7N/

If all you care about is the selected status, then you can tweak it to pass a reference to the selectedItem observable to the child constructor like: http://jsfiddle.net/rniemeyer/R5MtC/

If your parent view model is stored in a global variable, then you could consider not passing it to the child and using it directly like: http://jsfiddle.net/rniemeyer/3drUL/. I prefer to pass the reference to the child though.