Wiązanie DataGridComboBoxColumn

Usiłuję powiązać ObservableCollection T do DataGridComboBoxColumn DataGrid.
Definicja DataGrid to:

<DataGrid AutoGenerateColumns="False" ItemsSource="{Binding Model, IsAsync=True}">

     <DataGrid.Columns>
         <DataGridTextColumn  Header="Column Entry"  IsReadOnly="True" Binding="{Binding ColumnName}"/>
         <DataGridComboBoxColumn Header="Road Type" ItemsSource="{Binding RoadTypes}"/>
    </DataGrid.Columns>

</DataGrid>

To jest ViewModel i model

public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();
        var viewModel = new ViewModel();
        DataContext = viewModel;
    }
}

public class ViewModel : ViewModelBase
{
    private ObservableCollection<Model> _model;

    public ViewModel()
    {
        var list = new List<Model>();
        var roadTypes = new ObservableCollection<RoadType>
                            {
                                new RoadType
                                    {
                                        Code = 1,
                                        Id = 1,
                                        Name = "Name1"
                                    },
                                new RoadType
                                    {
                                        Code = 1,
                                        Id = 1,
                                        Name = "Name1"
                                    }
                            };

        Model = new ObservableCollection<Model>
                    {
                        new Model
                            {
                                ColumnName = "Col1",
                                RoadTypes = roadTypes
                            },
                        new Model
                            {
                                ColumnName = "Col1",
                                RoadTypes = roadTypes
                            }
                    };
    }

    public ObservableCollection<Model> Model
    {
        get { return _model; }
        set
        {
            _model = value;
            RaisePropertyChanged(() => Model);
        }
    }
}

public class RoadType
{
    public int Id { get; set; }
    public int Code { get; set; }

    public string Name { get; set; }
}

public class Model : ObservableObject
{
    private ObservableCollection<RoadType> _roadTypes;
    public string ColumnName { get; set; }

    public ObservableCollection<RoadType> RoadTypes
    {
        get { return _roadTypes; }
        set
        {
            _roadTypes = value;
            RaisePropertyChanged(() => RoadTypes);
        }
    }
}

DataGrid wyświetla także kolumnę tekstową, ale nie wyświetla wartości ComboBox.
Co jest nie tak?

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