public function actionDependedSelect($name, $parentId = null, $selectedId = null)
    {
        echo \backend\next\helpers\CategoryHelper::dependedSelect($name, $parentId, $selectedId);
    }

// --------------------

class CategoryHelper
{
    /**
     * TODO: adjust interface to match Html::dropDownList().
     *
     * @param string     $name
     * @param mixed|null $parentId
     * @param mixed|null $selectedId
     *
     * @return string
     */
    public static function dependedSelect($name, $parentId = '', $selectedId = '')
    {
        if (!$parentId) {
            $parentId = null;
        }

        if (!$selectedId) {
            $selectedId = null;
        }

        $category = Category::findOne($parentId);

        $html = '';
        if ($category) {
            $html = self::dependedSelect($name, $category->parent_id, $parentId);
        }

        /** @var Category[] $categories */
        $categories = Category::find()
            ->withI18n(Language::EN)
            ->select([
                'name',
                'lv_category.id',
            ])
            ->where([
                'parent_id' => $parentId,
            ])
            ->indexBy('id')
            ->column();

        if ($categories) {
            $html .= '<select name="'.e($name).'">';
            $html .= '<option value=""></option>';
            $html .= Html::renderSelectOptions($selectedId, $categories);
            $html .= '</select>';
        }

        return $html;
    }
}

// ---------------------
<script>
    function getCategoryId() {
        return $('#categories')
            .find('select')
            .map(function(idx, elem) {
                return elem.value;
            })
            .filter(function(idx, elem) {
                return elem;
            })
            .get()
            .pop();
    }

    $('#categories').on('change', 'select', function () {
        var categoryId = this.value;

        $('#categories').find('select').attr('disabled', 'disabled');

        $.get("<?= $this->createAbsoluteUrl('nextCategory/dependedSelect') ?>", {
            name: 'category_id',
            parentId: categoryId,
            selectedId: categoryId,
        }).done(function (data) {
            $('#categories').html(data);
            $('#categoryform-parentid').val(getCategoryId());
        });
    })
<script>