I am trying to let the user choose in a combobox in the datagrid, but can not find the correct approach. I have tried using both binding and x:bind. What would be the best approach? I would imagine the following code to be correct, but I am missing something.

ViewModel

public partial class CustomerModel : ObservableObject
 {
     private ObservableCollection<DataType> _objects;
     public ObservableCollection<DataType> Objects
     {
         get => _objects;
         set => SetProperty(ref _objects, value);
     }
     public ObservableCollection<string> _test;



     private ObservableCollection<string> _field;
     public ObservableCollection<string> Field
     {
         get => _field;
         set => SetProperty(ref _field, value);
     }


     public CustomerModel()
     {
         Objects = new();
         Field = new ObservableCollection<string> { "Test", "Test" };
     }


     public class DataType : ObservableObject
     {
         public int ID { get; set; }
         public string Name { get; set; }
         public string Caption { get; set; }
         public bool Numeric { get; set; }
        

         public DataType()
         {

         }
       
     }
 }

.xaml

 <controls:DataGrid
     x:Name="dataGrid1" KeyDown="dataGrid1_KeyDown"
     ItemsSource="{x:Bind Model.Objects}" AutoGenerateColumns="False" >
     <controls:DataGrid.Columns>
         <controls:DataGridComboBoxColumn Header="Field" ItemsSource="{x:Bind Model.Field}" Tag="Field"/>
     </controls:DataGrid.Columns>
 </controls:DataGrid>