[SalesForce] Cannot update lightning component Map attribute

I'm having a problem with setting values during component event handling where the values are sent from a child component, during initialization, to the parent component. The values to be set are in a Map attribute, where the key is a string and the value is a string array.

I initially had a null related exception and already tried adding the 'default="{}"' to my parent component's attribute declaration:

<aura:attribute name="fieldValues"
                type="Map"
                default="{}"/>

This gets me over the first hurdle with a null related exception (which I subsequently found was covered in this question). However, when I try to update the map in the component's controller in an event handler I get a different error. The error is shown later, but first the context.

The handler declaration in the parent component is:

<aura:handler name="selectionChanged" event="c:filterSelectionChange" action="{!c.handleFilterSelectionChange}"/>

The handler code looks like this:

handleFilterSelectionChange: function (component, event, helper) {
    var field = event.getSource().get("v.field").fieldPath; // a value from the child component
    var value = event.getParam("value"); // a value from the event

    var fieldValues = component.get("v.fieldValues");

    fieldValues.set(field, value);

    component.set("v.fieldValues", fieldValues);
}

The "filterSelectionChange" event looks like this:

<aura:event type="COMPONENT">
    <aura:attribute name="value" type="String[]"/>
</aura:event>

This event is fired during the initialization of a child component. The child component includes the following:

<aura:handler name="init" value="{!this}" action="{!c.doInit}"/>

<aura:registerEvent name="selectionChanged" type="c:filterSelectionChange"/>

The child's controller's doInit looks like this:

doInit: function (component, event, helper) {
    var selection = helper.initSelection(component); // returns a string array value

    var selectionChangeEvent = component.getEvent("selectionChanged");

    selectionChangeEvent.setParams({
        value: selection
    });

    selectionChangeEvent.fire();
}

The error I get (which prevents the child from rendering) happens on the line:

fieldValues.set(field, value);

in the parent component's "handleFilterSelectionChange" event handler, see above, and is:

Uncaught Action failed: c:filter$controller$handleFilterSelectionChange [fieldValues.set is not a function]
Callback failed: apex://FilterController/ACTION$getFieldSet
throws at https://xxxx.visualforce.com/auraFW/javascript/a24vMs8Ru7Q5OyxXWeHeyg/aura_prod.js:38:15

Note that I am using Lightning-Out to render the component in a visual force page (though I don't believe that is specifically relevant to this issue).

You can also see (from the error's details) that this is triggered from the callback handler for a server-side controller query "getFieldSet". I know that this works as all the correct processing occurs prior to adding the management of this map of values. To be clear, this server-side action is handled thus in the parent component's controller:

doInit: function (component, event, helper) {
    var action = component.get("c.getFieldSet");

    action.setParams({
        objectType: component.get("v.objectType"),
        fieldSetName: component.get("v.fieldSet")
    });

    action.setCallback(this, function (response) {
        var state = response.getState();

        if (state === "SUCCESS") {
            component.set("v.fields", response.getReturnValue());
        } else {
            ...
        }
    });

    $A.enqueueAction(action);
}

Setting the "v.fields" attribute on the component triggers the rendering of the parent, which in turn creates and renders the children.

Do you know what I'm doing wrong? Is this a limitation due to triggering this flow in child component initialization? Is it linked to Lightning-Out or the handling in a callback for a server-side action (I doubt it)? Or have I used the wrong approach for managing the parent component's "fieldValues" map?

Any suggestions gratefully received.