Another way of looking at this is to consider state as a grouping variable. What we are trying to do is to fit a model so that all the units within one level of that variable (ie one state) share the same intercept but it may be different from that for other levels. There are two ways of doing this, either to specify parameters of the distribution of the intercepts (random model) or fit each one with its own parameter (fixed model). Put like perhaps we can see that we can either do one or the other but not both simultaneously.

Another way of looking at this is to consider state as a grouping variable. What we are trying to do is to fit a model so that all the units within one level of that variable (i.e. one state) share the same intercept but it may be different from that for other levels. There are two ways of doing this, either to specify parameters of the distribution of the intercepts (random model) or to fit each one with its own parameter (fixed model). Put like perhaps we can see that we can either do one or the other but not both simultaneously.