set admin bar to visible for authors, contributors, moderators and admins

Checking the capability of the users you can determine whether to show or not the admin bar.

add_action( 'after_setup_theme', 'remove_admin_bar' );

function remove_admin_bar() {
    if( ! current_user_can( 'administrator' ) || ! current_user_can( 'editor' ) || ! current_user_can( 'author' ) ) {
        show_admin_bar(false);
    }
}