<dxe:ComboBoxEdit Grid.Row="1" HorizontalAlignment="Left" Margin="69,3,0,0" Name="comboBoxEdit_inst" 
                          VerticalAlignment="Top" Width="265" Height="23" 
                          ItemsSource="{Binding ElementName=rb_strucDomainDataSource, Path=Data}" DisplayMember="name" 
                          AutoComplete="True"  SelectedIndexChanged="comboBoxEdit_inst_SelectedIndexChanged" />

     private void comboBoxEdit_inst_SelectedIndexChanged(object sender, RoutedEventArgs e)
        {
            comboBoxEdit_inst.IsPopupOpen=true;
        }

<dxe:ComboBoxEdit HorizontalAlignment="Left" Margin="118,53,0,0" 
                          Name="comboBoxEdit" VerticalAlignment="Top" Width="214" DisplayMember="name"
                          ItemsSource="{Binding ElementName=rb_spec_groupDomainDataSource, Path=Data}">
            <dxe:ComboBoxEdit.StyleSettings>
                <dxe:CheckedComboBoxStyleSettings />
            </dxe:ComboBoxEdit.StyleSettings>
        </dxe:ComboBoxEdit>