{% set subcategoryParam = craft.request.getParam('subcategory') %}
{% set subcategories = craft.categories.group('partnerAreas').find() %}

<form action="{{ craft.request.url }}">

  {% for subcategory in subcategories %}
    <input type="checkbox" value="{{ subcategory.slug }}" id="{{ subcategory.slug }}" name="subcategory" {{ subcategory.slug in subcategoryParam ? 'checked'}}>
    <label class="label__checkbox" for="{{ subcategory.slug }}">
      {{ subcategory.title }}
    </label>
  {% endfor %}

  <button type="submit">
    Search
  </button>
</form>

{% set subcategoryParam = craft.request.getParam('subcategory') %}
{% set selectedSubcategories = craft.categories.slug(subcategoryParam) %}
{% set entries = craft.entries({
  section: listingType,
  relatedTo: {
    targetElement: selectedSubcategories,
    field: 'involvementAreas.area'
  }
}) %}