Yii2 kartik dependent dropdown在使用ajax加载下拉值后，未使用ajax更改所选值

use kartik\depdrop\DepDrop;
use yii\helpers\Url;

echo $form->field($model, 'category_id')->widget(DepDrop::classname(), [
    'options' => ['id' => 'category-id'],
    'pluginOptions' => [
        'depends' => ['parent-category-id'],
        'placeholder' => 'Select...',
        'url' => Url::to(['/controller/action']),
    ]
]);

use yii\helpers\ArrayHelper;
use yii\helpers\Json;
use yii\web\Response;

public function actionGetSubcategories($id)
{
    Yii::$app->response->format = Response::FORMAT_JSON;
    
    $subcategories = Subcategory::find()
        ->where(['category_id' => $id])
        ->all();
    
    $output = [];
    foreach ($subcategories as $subcategory) {
        $output[] = [
            'id' => $subcategory->id,
            'name' => $subcategory->name,
        ];
    }
    
    return ['output' => $output, 'selected' => ''];
}

$('#parent-category-id').on('change', function(){
    var parentId = $(this).val();
    
    $.ajax({
        url: '/controller/get-subcategories',
        type: 'GET',
        data: {id: parentId},
        dataType: 'json',
        success: function(response) {
            var subcategories = response.output;
            var selected = response.selected;
            
            var $subcategoryDropdown = $('#category-id');
            $subcategoryDropdown.empty();
            
            $.each(subcategories, function(index, subcategory) {
                $subcategoryDropdown.append($('<option/>', {
                    value: subcategory.id,
                    text: subcategory.name,
                    selected: (subcategory.id == selected)
                }));
            });
            
            $subcategoryDropdown.trigger('change');
        }
    });
});