Live updated with form

Hi,

In my template I have a select field :

<flux:field>
    <flux:label badge="Required">Statut précédent</flux:label>
    <flux:select wire:model.live="form.type_dossier_status_id" variant="listbox" placeholder="Choisir le statut précédent...">
        @foreach ($this->statuses() as $item)
            <flux:select.option value="{{ $item->id }}">{{ $item->label }}</flux:select.option>
        @endforeach                    
    </flux:select>
</flux:field>

In my component, this field is related to a form :

...
class DossierStatusTypeAdmin extends Component
{
    ...
    public TypeDossierStatusForm $form;
    ...
}

...
class TypeDossierStatusForm extends Form
{
    ...
    public ?string $type_dossier_status_id = null;
    ...
}

But live update doesn't work. If I put the variable in the component and change input in blade wire:model.live="type_dossier_status_id" it works

Any idea ?