Add custom field in registration page. Display in profile and update.

/******************** Add new field in registration form **************************/
    //1. Add a new form element...
add_action( 'register_form', 'myplugin_register_form' );
function myplugin_register_form() {
    $usertype = ( ! empty( $_POST['usertype'] ) ) ? trim( $_POST['usertype'] ) : '';?>
        <p>
            <label for="first_name"><?php _e( 'User Type', 'mydomain' ) ?><br />
            <input type="radio" name="usertype" id="usertype" value="eventmanager" />Event Manager
            <input type="radio" name="usertype" id="usertype" value="subscriber" />Subscriber          
        </p>
        <?php
    }
    //2. Add validation. In this case, we make sure User type is required.
    add_filter( 'registration_errors', 'myplugin_registration_errors', 10, 3 );
    function myplugin_registration_errors( $errors, $sanitized_user_login, $user_email ) {       
        if ( empty( $_POST['usertype'] ) || ! empty( $_POST['usertype'] ) && trim( $_POST['usertype'] ) == '' ) {
            $errors->add( 'usertype_error', __( '<strong>ERROR</strong>: You must select User Type.', 'mydomain' ) );
        }
        return $errors;
    }
    //3. Finally, save our extra registration user meta.
    add_action( 'user_register', 'myplugin_user_register' );
    function myplugin_user_register( $user_id ) {
        if ( ! empty( $_POST['usertype'] ) ) {
            update_user_meta( $user_id, 'usertype', trim( $_POST['usertype'] ) );
        }
    }


/************* Display extra fields user profile****************/
add_action ( 'show_user_profile', 'my_show_extra_profile_fields' );
add_action ( 'edit_user_profile', 'my_show_extra_profile_fields' );   
function my_show_extra_profile_fields ( $user ){ ?>
    <h3>Extra profile information</h3>
    <table class="form-table">
        <tr>
            <th><label for="twitter">User Type</label></th>
            <td>
                <input type="text" name="usertype" id="usertype" value="<?php echo esc_attr( get_the_author_meta( 'usertype', $user->ID ) ); ?>" class="regular-text" /><br />
            </td>
        </tr>
    </table>
<?php }
/************* Update user profile fields ****************/
add_action ( 'personal_options_update', 'my_save_extra_profile_fields' );
add_action ( 'edit_user_profile_update', 'my_save_extra_profile_fields' );
function my_save_extra_profile_fields( $user_id )    {
if ( !current_user_can( 'edit_user', $user_id ) )
        return false;
        /* Copy and paste this line for additional fields. Make sure to change 'twitter' to the field ID. */
        update_usermeta( $user_id, 'usertype', $_POST['usertype'] );
    }
/**********************************************************/