First, your code ignores the binary nature of the response, and the fact that you have multiple observations with the same
name. Without knowing details of the variables and the data collection, it is impossible to be sure what is the appropriate model to use.
name refers to the subjects, and you are measuring the same subjects in different weeks, this is longitudinal data, and you should probably use a mixed effects model.
model <- glmer(response ~ week + x1 + x2 + (1 | name),
family=binomial indicates that
response is a binary variable. The
(1 | name) indicates that the data are repeated measures on the same subjects. The model has a random effect for subjects.
Now to answer your question, it depends what you mean by a prediction. You have different values of the covariates
x2 for each week/subject combination, so you naturally have a different prediction for each row of your data. Just use
predict() to get these values. The order of the resulting output is the same as the order of the rows in your data frame.
If you are expecting one value per
name, then I assume you want to estimate effects due to the subject rather than predictions. You can get that with
ranef(model). However, these will be conditional on the
x2 being zero. You can estimate subject effects conditional on other values of
x2; a common approach is to set them to their median values.