The top down approach is based on a small sample which is unrepresentative.
This is because it's based on 36 interviewed killers, 25 of which are serial and 11 of which are single or double killers.
However, not all offenders are killers and it's also not sensible to rely on killers to be honest and open within their interviews to construct a classification system based on them.
Therefore, the top down approach lacks population validity as it isn't applicable to crimes such as petty theft.