Update Multiselect field using PHP via SOAP

I'm creating a PHP application that adds and updates data in CRM (version 7.1). Here is the code snippet that I'm using for updating fields:

$update_data = array("personid"=>$person_id_in_crm, "interestedin"=>$product);
$update_var = new SoapVar($update_data , XSD_ANYTYPE, "person", "">http://tempuri.org/type");
$response = $client->update(array('entityname' => "person", 'records' => $update_var));

This works for all fields (text, drop-down, etc.), except multi-select ones - those are set to "NULL" after running this code. I have tried to set $product variable as array and as string, but the field is still not updated to "NULL".


Can you help with this, as I can't find what I'm doing wrong?