Laravel Eloquent Select CASE?

Move your raw() call inside the SELECT statement:

->select('shares.id AS share_id', 'users.id AS user_id', 'shares.connected_user_id',    
  'shares.original_language_id', 'shares.image',
  'users.first_name', 'users.last_name', 'users.email',
  'locations.city', 'provinces.name', 'countries.code',
  'locations.lat', 'locations.lng',
  'shares.created_at',
  DB::raw('(CASE WHEN users.id = ' . $user . ' THEN 1 ELSE 0 END) AS is_user')
  )
->orderBy('shares.created_at', 'desc')

From: https://laravel.com/docs/5.4/queries#raw-expressions