使用绑定数据和转换器对datagrid列进行排序

I'm trying to sort data in datagrid, but when I click on the header of the column which has binding with the converter, nothing happens. I use MVVM pattern. Example is attached below. In the example, the grid shows column (Type) which displays type of person and therefore I use converter (class TypeValueConverter). When I use this converter, the grid doesn't sort column Type.I'm trying to sort data in datagrid, but when I