Is Homicide Victims dataset repeated? I am studying an example where a Poisson model is applied to the Homicide Victims dataset. The dataset contains survey results of 1308 people who where asked about the number of homicide victims they knew. The dataset includes the response of a person (the number of homicide victims he/she knows) and his/her race. The response has minimum and maximum values of 0 and 6. The goal is to model the response using a Poisson model and assess the goodness of fit of the model.
I have two questions.

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*Is the dataset repeated? I understand that a repeated measure is a study where for each predictor variable there are repeated number of observations. In this case, I can redesign the dataset as a seven by two table (response and race) where each cell contains the number of people who know a specific number of homicide victims and have a specific race. It is important to identify if the data is repeated or not to make sure that the results of the Deviance and Pearson's Chi-Square tests are valid.

*The results of the Deviance and Pearson Chi-Square tests are as follows:
Deviance Test: Deviance = 844.7073, df = 1306, p-value = 1 and
Pearson's Chi-Square Test: Chi-Square=2279.873, p-value = 0.
So, in this case I am not sure why the p-values are critically different.


Agresti takes this data from the General Social Survey (GSS), and perhaps he treats it as a simple random sample(?) which is fine if he's simply using it as an illustration. However, the GSS is not a simple random sample; it's a multiple-stage cluster sample. You can find details here.
It is likely that respondents in the same cluster are not independent. If one respondent knows someone who was the victim of a homicide, it's likely that another respondent from the same cluster also knows someone who was the victim of a homicide, possibly the same victim.
I'm not sure that I follow your concern about repeated observations, but there is a problem here with using the chi-squared test as the standard test is not appropriate for data generated under a multi-stage cluster sample. P-values are likely to be too small. Several strategies exist for adjusting the chi-squared test. An early approach utilizes the Wald test. Rao and Scott introduce two additional approaches which are generally preferable. See here and here. All of these approaches are included in the survey package in R. See here.
