Multiple groups of radio buttons in custom dialog box?

I am creating a custom dialog box, and I am trying to add two sets of radio buttons with four choices each. I have them appearing as I want with the script below, but I want the two sets of radio buttons to operate independently of each other.  As it is right now, you can only select one button in the entire dialog box.

Code

description:
{
name: "Exhibit Stamping",
elements:
[
{
type: "view",
elements:
[
{
type: "cluster",
name: "Type:",
elements:
[
{
type: "view",
char_width: 8,
align_children: "align_top",
elements:
[
{
type: "view",
alignment: "align_left",
elements:
[
{
type: "radio", item_id: "PEx",
group_id: "ExType", name: "Paintiff's Exhibit"
},
{
type: "radio", item_id: "Ex",
group_id: "ExType", name: "Exhibit"
},
]
},
{
type: "view",
alignment: "align_right",
elements:
[
{
type: "radio", item_id: "DEx",
group_id: "ExType", name: "Defendant's Exhibit"
},
{
type: "radio", item_id: "JEx",
group_id: "ExType", name: "Joint Exhibit"
},
]
}
]
}
]
},
{
type: "cluster",
name: "Position:",
elements:
[
{
type: "view",
char_width: 8,
align_children: "align_top",
elements:
[
{
type: "view",
alignment: "align_left",
elements:
[
{
type: "radio", item_id: "ulLo",
group_id: "ExLoc", name: "Upper-left"
},
{
type: "radio", item_id: "blLo",
group_id: "ExLoc", name: "Bottom-left"
},
]
},
{
type: "view",
alignment: "align_right",
elements:
[
{
type: "radio", item_id: "urLo",
group_id: "ExLoc", name: "Upper-right"
},
{
type: "radio", item_id: "brLo",
group_id: "ExLoc", name: "Bottom-right"
},
]
}
]
}
]
},
]

},
{
type: "gap",
height: 10
},
{
type: "ok_cancel",
ok_name: "Ok",
cancel_name: "Cancel",
}
]
}