Programmatically add multiple values to an entity reference field

Question

I use the following code to load entities by their IDs.

$themes = entity_load('theme',array(7,8,9));
$thid = array();
foreach ($themes as $theme) {
  $thid[] = $theme->id; 
} 

Next, I should add those IDs to an entity reference field ($tests->field_theme).

How can I achieve this?