Editable datatable using suggestionbox

[hdu]

I would like to put input fields inside a datatable. The datatable is bound to an PersonLevel entity list. The input fields use rich:suggestionbox and when a value is selected it should return a Level entity that will be bound to the PersonLevel.level property. That's how it should work in theory, but it doesn't (type mismatch error). If I don't put in the a4j:support for selecting the suggestionbox it overwrites the Level.name property which is not the desired behaviour. What is the proper way of implementing this?

<rich:dataTable var="_personLevel" value="#{personHome.personLevelsList}">
     <rich:column>
          <h:inputText id="levelInput" value="#{_personLevel.level.name}"/>
          <h:graphicImage value="/img/dropdown.png" onclick="#{rich:component('levelSuggestion')}.callSuggestion(true)"/>
          <rich:suggestionbox id="levelSuggestion" for="levelInput" fetchValue="#{_level.name}"
               var="_level" suggestionAction="#{levelLookup.lookup}">
               <a4j:support event="onselect">
                    <f:setPropertyActionListener target="#{_personLevel.level}" value="_level"/> 
               </a4j:support>
               <h:column>
                    <h:outputText value="#{_level.name}"/>
               </h:column>
          </rich:suggestionbox>
     </rich:column>
</rich:dataTable> 

@Entity
public class PersonLevel {
     private int id;
     private Level level;
...
}

@Entity
public class Level {
     private int level;
     private String name;
}