级联下拉列表不更新子下拉列表(Laravel livewire)

// Livewire组件
class MyComponent extends Component
{
    public $parentOptions;
    public $childOptions;
    public $selectedParentOption;

    public function mount()
    {
        // 初始化父级下拉列表的选项
        $this->parentOptions = [
            ['id' => 1, 'name' => 'Option 1'],
            ['id' => 2, 'name' => 'Option 2'],
            // ...
        ];
    }

    public function updatedSelectedParentOption($value)
    {
        // 当父级下拉列表的选项改变时，更新子级下拉列表的选项
        $this->childOptions = DB::table('child_table')
            ->where('parent_id', $value)
            ->get();
    }

    public function render()
    {
        return view('livewire.my-component');
    }
}

<!-- 视图 -->
<div>
    <select wire:model="selectedParentOption" wire:change="updatedSelectedParentOption($event.target.value)">
        <option value="">Select Parent Option</option>
        @foreach ($parentOptions as $option)
            <option value="{{ $option['id'] }}">{{ $option['name'] }}</option>
        @endforeach
    </select>
</div>

<div>
    <select wire:model="childOptions">
        <option value="">Select Child Option</option>
        @foreach ($childOptions as $option)
            <option value="{{ $option['id'] }}">{{ $option['name'] }}</option>
        @endforeach
    </select>
</div>