My immediate guess is: You probably can't measure discrimination against homeless people from the view of the perpetrators.
My reason: To answer the above, the perpetrators need to be known. I assume no one would simply accept that they have some sort of discrimination against the homeless, thus leaving you with no participants to collect your data (levels of discrimination) from.
However, what might be somewhat possible is to explore the idea of how some people (e.g., bystanders and pedestrians) might be thinking about the homeless people; what are some of their biases and stereotypes about this population. You can do this by interviewing a number of people. You will then analyse the transcript of those interviews to explore themes related to discrimination.
Margarida - Since you want to measure the discrimination against homeless people not from the view of the victims but from the view of the perpetrators, You can use participant observation as a method for research. It is better to get the information from both victims as well as perpetrators as a participant observer in order to later make it a comparative study. Participant observation as a research technique is characterized by the effort of an investigator to gain entrance into and social acceptance by the alien group so as better to attain a comprehensive understanding of the group and sharing its activities. There are mostly four stages that most participant observation research studies are 1) establishing rapport or getting to know the people, 2) immersing oneself in the field, 3) recording data and observations, and 4) consolidating the information gathered. But the problem is that the researchers should be well trained to tackle issues by joining as a participant observer.
I agree with other respondents but I also suggest the possibility to interview people arrested acts against homeless people. I do not know if your scientific protocol allows this.
Your question is very interesting. I think it is going to be difficult measuring discrimination from the view of perpetrators because often the perpetrators may even not be aware their actions constitute discrimination. This can be however be best measured by a third party who is a non participant through careful observation.
el que discrimina a una persona sin hogar posiblemente lo haga desde la discriminación social, racial o económica. Por tanto estoy de acuerdo con las recomendaciones hechas anteriormente sobre la observación