Magento backend admin: Edit form with a multiselect field with product categories

Namespace_Module_Block_Adminhtml_Edit_Tab_XXXX.php

<?php
/* Set up: */

class Namespace_Module_Block_Adminhtml_News_Edit_Tab_Linking {

  protected function _prepareForm(){

     ...

        $fieldSet->addField('product_categories', 'multiselect',
            array(

                'name'     => 'product_categories[]',
                'label'    => 'Product Categories',
                'title'    => 'Product Categories',
                'required' => FALSE,
                'values'   => Mage::getModel('namespace_module/option_productcategories')->getOptionArray()
            ));

    ...

  }

}

ProductcategoriesGist.php

<?php

class Namespace_Module_Model_Option_Productcategories extends Varien_Object
{

    const REPEATER = '_';

    const PREFIX_END = '';

    protected $_options = array();

    /**
     * @param int $parentId
     * @param int $recursionLevel
     *
     * @return array
     */
    public function getOptionArray($parentId = 1, $recursionLevel = 3)
    {
        $recursionLevel = (int)$recursionLevel;
        $parentId       = (int)$parentId;

        $category = Mage::getModel('catalog/category');
        /* @var $category Mage_Catalog_Model_Category */
        $storeCategories = $category->getCategories($parentId, $recursionLevel, TRUE, FALSE, TRUE);

        foreach ($storeCategories as $node) {
            /* @var $node Varien_Data_Tree_Node */

            $this->_options[] = array(

                'label' => $node->getName(),
                'value' => $node->getEntityId()
            );
            if ($node->hasChildren()) {
                $this->_getChildOptions($node->getChildren());
            }

        }

        return $this->_options;
    }

    /**
     * @param Varien_Data_Tree_Node_Collection $nodeCollection
     */
    protected function _getChildOptions(Varien_Data_Tree_Node_Collection $nodeCollection)
    {

        foreach ($nodeCollection as $node) {
            /* @var $node Varien_Data_Tree_Node */
            $prefix = str_repeat(self::REPEATER, $node->getLevel() * 1) . self::PREFIX_END;

            $this->_options[] = array(

                'label' => $prefix . $node->getName(),
                'value' => $node->getEntityId()
            );

            if ($node->hasChildren()) {
                $this->_getChildOptions($node->getChildren());
            }
        }
    }

}