List categories which contain products with specific product attribute

Question

I'm trying to get a list of categories (ID, Name). However, only categories that contain products with a certain product attribute value can be listed.

I've already tried the following;

<?php
        $categories = Mage::getModel('catalog/category')
        ->getCollection()
        ->addAttributeToFilter('product_supplier', '5');

        foreach($categories as $category) {
            echo $category->getName().'<br>';
        }

And;

<?php
        $category = Mage::getModel('catalog/category');
        $catTree = $category->getTreeModel()->load();
        $catIds = $catTree->getCollection()
        ->addAttributeToFilter('product_supplier', '5')
        ->getAllIds();
        $cats = array();
        if ($catIds){
            foreach ($catIds as $id){
                $cat = Mage::getModel('catalog/category');
                $cat->load($id);
                $cats[$cat->getId()] = $cat->getName();
            }
        }

But, I keep getting the error: Call to a member function getBackend() on a non-object

I found out that this error occurs when the collection tries to filter on the category, so i guess it thinks i i meant to filter by the category attribute product_supplier. I really don't know what to try next.

Suggestions?

=> My solution so far:

$catIds = array();
$validCategories = array();

//get the filtered product collection
$productCollection = Mage::getModel('catalog/product')->getCollection()
   ->addAttributeToSelect('*')
   ->addAttributeToFilter('product_supplier', '5');

// Loop through products, throw category id's into array
foreach($productCollection as $product) {
    $catIds = array_merge($catIds,$product->getCategoryIds());
}

/**
 * Loop through category id's, load categories and get name, 
 * create the final array
 */
foreach ($catIds as $x => $catId) {
    $cat = Mage::getModel('catalog/category')->load($catId);
    $validCategories[$cat->getId()] = $cat->getName();
}

Answer 1

I haven't tested this, but here is my idea.
You should start from the product collection because you cannot filter a category collection by a product attribute.

//get the filtered product collection
$productCollection = Mage::getModel('catalog/product')->getCollection()
   ->addAttributeToSelect('*')
   ->addAttributeToFilter('product_supplier', '5');

//get a list of all categories
$categories = Mage::getModel('catalog/category')->getCollection()->addAttributeToSelect('*');

//match products to categories
$productCollection->addCountToCategories($categories);
$validCategories = array();
//check which category has a product count higher than 0
foreach ($categories as $category) {
    if ($category->getProductCount()) {
        $validCategories[$category->getId()] = $category->getName();
    }
}