How to include Polymer paper-dropdown-menu in form submit - html

Question

When I submit this Polymer form with document.getElementById("form").submit(); firstName and lastName are included in the POST-data, but the title-value from the paper-dropdown-menu not. What is missing ?
<form is="iron-form" id="form" method="post" action="/edit">
<paper-dropdown-menu name="title" label="Title">
<paper-menu class="dropdown-content">
<template is="dom-repeat" items="{{titles}}" as="title">
<paper-item value="{{item.id}}">{{title.name}}</paper-item>
</template>
</paper-menu>
</paper-dropdown-menu>
<paper-input name="firstName" label="First name"></paper-input>
<paper-input name="lastName" label="Last name"></paper-input>
<paper-button raised onclick="submitForm()">Save</paper-button>
</form>
Edit:
Here my complete working example, thanks a lot to #Brandon for his answer:
<form is="iron-form" id="form" method="post" action="/api/edit">
<paper-dropdown-menu label="Title" selected-item="{{selectedItem}}" selected-item-label="{{selected}}">
<paper-menu class="dropdown-content">
<template is="dom-repeat" items="{{titles}}" as="title">
<paper-item value="[[title.id]]">[[title.name]]</paper-item>
</template>
</paper-menu>
</paper-dropdown-menu>
<input is="iron-input" name="title" type="hidden" value$="[[selectedItem.value]]">
<paper-input name="firstName" label="First name"></paper-input>
<paper-input name="lastName" label="Last name"></paper-input>
<paper-button raised onclick="document.getElementById('form').submit()">Save</paper-button>
</form>

Answer 1

This may solve your problem. Create a hidden input element and assign the selected item to the hidden element's value. This gives you the added benefit of the iron-input validators for multi-select for future forms.
<form is="iron-form" id="form" method="post" action="/edit">
<paper-dropdown-menu label="Title" selected-item-label="{{selected}}">
<paper-menu class="dropdown-content">
<template is="dom-repeat" items="{{titles}}" as="title">
<paper-item>{{title.name}}</paper-item>
</template>
</paper-menu>
</paper-dropdown-menu>
<input is="iron-input" name="title" type="hidden" value$="[[selected]]">
<paper-input name="firstName" label="First name"></paper-input>
<paper-input name="lastName" label="Last name"></paper-input>
<paper-button raised onclick="submitForm()">Save</paper-button>
</form>