PHP creating a recursive DomDocument

I am attempting to create the following XML from a database table. Here is the XML

<groups>
     <group id="1" name="DEBUG"/>
     <group id="2" name="ORSP">
          <group id="3" name="PRE">
               <group id="4" name="TRANS"/>
               <group id="5" name="OPP"/>
          </group>
          <group id="6" name="POST">
               <group id="7" name="DGM"/>
          </group>
     </group>
</groups>

Here is the simple table to the database

GROUP_ID | GROUP_NAME | GROUP_PARENT 
1            DEBUG       NULL 
2            ORSP        NULL 
3            PRE         2 
4            TRANS       3 
5            OPP         3 
6            POST        2 
7            DGM         6

Here is my current code. I am trying to return a DomElement however I can never get the above XML. Using strings I am able to produce the XML. Any advice is welcomed.

public function process(){
        $xml = '<groups>';
        $xml .= $this->getAllGroups();
        $xml .= '</groups>';

        return $xml;
    }

    public function getAllGroups($groupID=null){
        $where = null;
        $placeholder = array();
        $xml = null;

        if (is_null($groupID)){
            $where = " GROUP_PARENT IS NULL ";
        }
        else {
            $where = " GROUP_PARENT=?";
            $placeholder=array($groupID);
        }

        $sql = "SELECT
                    GROUP_ID,
                    GROUP_NAME
                FROM
                    GROUPS
                WHERE
                    $where";
        $data = $this->dbh->executeSql($sql,$placeholder);
        foreach ($data["records"] as $row) {
            $groupID = $row["GROUP_ID"];
            $groupName = $row["GROUP_NAME"];

            $xml .= "<group id='$groupID' name='$groupName'>";
            $xml .= $this->getAllGroups($groupID);
            $xml .= "</group>";
        }
        return $xml;
    }