lightning:input type="date" not binding with my object

Question

I'm currently creating a Lightning Component for a custom object in SalesForce, for some reason the data is not binding to this input. Even when I select a date from the date picker nothing shows up on the input field. I have read/write access to the field as I see it in a previous VF page I created for this object. All other fields are binding correctly, just not the dates.

<force:recordData aura:id="applicantRecord" targetRecord="{!v.applicant}" targetFields="{!v.applicantFields}" targetError="{!v.error}" layoutType="FULL" mode="EDIT"/>

<lightning:recordEditForm objectApiName="Applicant__c">
    <div class="slds-grid">
        <lightning:input label="First Name" value="{!v.applicantFields.FirstName__c}"/>
        <lightning:input label="Last Name" value="{!v.applicantFields.LastName__c}"/>
        <lightning:input type="email" label="Email" value="{!v.applicantFields.Email__c}"/>
    </div>
    <div class="slds-grid">
        <lightning:inputField fieldName="PlacementState__c" value="{!v.applicantFields.PlacementState__c}"/>
    </div>
    <div class="slds-grid">
        <lightning:input type="checkbox" label="Ref1" checked="{!v.applicantFields.Reference1__c}" labelClass="uiLabel-top"/>
        <lightning:input type="checkbox" label="Ref2" checked="{!v.applicantFields.Reference2__c}"/>
        <lightning:input label="Bill Rate" value="{!v.applicantFields.BillRate__c}"/>
        <lightning:input label="Pay Rate" value="{!v.applicantFields.PayRate__c}"/>
    </div>
    <div class="slds-grid">
        <lightning:input type="date" label="Start Date" value="{!v.applicantFields.StartDate__c}"/>
        <lightning:input type="date" label="End Date" value="{!v.applicantFields.EndDate__c}"/>
    </div>
    <lightning:button label="Save" onclick="{!c.save}"/>
    <div>
        {!v.error}
    </div>
</lightning:recordEditForm> 

Answer 1

Issue was two things.

1. As Jayant pointed out, lightning:inputField should be used rather than lightning:input.

2. layoutType=FULL still requires the fields to be on the Page Layout of the object otherwise the data won't show when it's pulled with Lightning Data Service.