Display selected radio button from the JSON input in Angularjs

I want the radio button to be selected depending on the input json values.

my json is

       "inventoryType": {
                        "bulk": [
                            {
                                "totalUnits": 80,
                                "addedOn": "12-01-2013"
                            }
                        ]
                    }

or

        "inventoryType": {
                        "day": [
                            {
                                "from": "12-Jan-2013",
                                "to": "12-Jan-2014",
                                "unitsPerDay": "30"
                            },
                            {
                                "from": "13-Jan-2014",
                                "to": "12-Jan-2015",
                                "unitsPerDay": "20"
                            }
                        ]
                    },

These are the 2 different data "bulk" and "day" for inventory type.

If I get data for bulk I want the bulk radio button to be selected else the vice versa.

Html code

<label class="span1">                                     
<input type="radio" name="optionsRadios" id="optionsRadios1" ng-value="{{productServiceInventory}}" ng-model="bulk" >
<small>Bulk</small>
</label>
<label class="span1">
<input type="radio" name="optionsRadios" id="optionsRadios2" ng-value="{{productServiceInventory}}" ng-model="day" >
<small>Day</small>
</label>

here the value of {{productServiceInventory}} is passed in the controller

if($scope.productServiceData.inventoryType.day === undefined){
console.log("bulk");
$scope.productServiceInventory = "bulk";
}
else if($scope.productServiceData.inventoryType.bulk === undefined){
console.log("day");
$scope.productServiceInventory = "day";
}

but my radio button is not getting selected to the appropriate data..

Kindly help me in selecting the radio button on json fetch.

Thanks in advance..