Laravel通过连接（内部连接）字段和急切加载进行雄辩的分组

I want to achieve grouping on joined fields using Laravel's eloquent ORM with eager loading.

I have 2 models defined as follows:

class User extends Model{
  public $table = 'user';
  public function department(){
    return $this->belongsTo('models/Department','department_id','belongs_to_department_id');
  }
}
class Department extends Model{
  public $table = 'department'; 
}

I'm trying to join both the tables, and group by 'id' of department with eager loading

$User::with('department')->groupBy('department_id');

I'm getting error "department_id column not found". I'm expecting to run the following MySql query:

select * from user inner join department inner join user.belongs_to_department_id=department.department_id group by department.department_id;