JSF - Създаване на динамично меню с помощта на AJAX & selectOneListbox

Това, което бих искал да направя, е просто за обяснение:

bean

@ManagedBean
@ViewScoped
public class Articles {
    private String selectedMenu;

    @PostConstruct
    public void init() {
        if(selectedMenu==null || selectedMenu.trim().isEmpty()) {
            this.selectedMenu="0";
        }
    }

    public String getSelectedMenu() { return selectedMenu; }
    public void setSelectedMenu(String selectedMenu) { this.selectedMenu = selectedMenu; }
}

page

<h:selectOneListbox onchange="..?? ajax call that render on loadMenu and pass the value of the focused listbox to Articles Bean" id="category" size="0" >
    <f:selectItem itemLabel="first" itemValue="0" />
    <f:selectItem itemLabel="second" itemValue="1" />
    <f:selectItem itemLabel="third" itemValue="2" />
</h:selectOneListbox>

<h:panelGroup layout="block" id="loadMenu">
    <h:panelGroup rendered="#{articles.selectedMenu=='0'}">
        MENU 0
    </h:panelGroup>

    <h:panelGroup rendered="#{articles.selectedMenu=='1'}">
        MENU 1
    </h:panelGroup>

    <h:panelGroup rendered="#{articles.selectedMenu=='2'}">
        MENU 2
    </h:panelGroup>
</h:panelGroup>

Когато променя стойността на списъка, менюто трябва да се промени динамично (чрез извикване на някаква функция на сървъра). Мисля, че кодът по-горе изразява това, което търся.

Трябва да знам как да го извикам с помощта на опцията onchange. Възможно ли е?

наздраве

АКТУАЛИЗАЦИЯ

<h:panelGroup layout="block">
    <h:selectOneListbox styleClass="article_combo" size="0" id="selectedMenu" >
        <f:selectItem itemLabel="first" itemValue="0" />
        <f:selectItem itemLabel="second" itemValue="1" />
        <f:selectItem itemLabel="third" itemValue="2" />

        <f:ajax event="change" execute="@this" render="loadMenu" />
    </h:selectOneListbox>
</h:panelGroup>

<h:panelGroup layout="block" id="loadMenu">
    <h:panelGroup rendered="#{articles.selectedMenu=='0'}">
        MENU 0
    </h:panelGroup>

    <h:panelGroup rendered="#{articles.selectedMenu=='1'}">
        MENU 1
    </h:panelGroup>

    <h:panelGroup rendered="#{articles.selectedMenu=='2'}">
        MENU 2
    </h:panelGroup>
</h:panelGroup>