Could be just a typo. Try writing:
is_user_logged_in()
Looks like just forgot the ()
UPDATE:
Because you don’t want to redirect on every page load you have to hook your redirect. I here an example (taken and slightly edited from the docs):
<?php
function daro_login_redirect( $redirect_to, $request, $user ) {
//is there a user to check?
if ( isset( $user->roles ) && is_array( $user->roles ) ) {
//check for admins
// edit this part accordingly to your login needs:
// maybe you can skip the else statement
if ( in_array( 'administrator', $user->roles ) ) {
// redirect them to the default place
return $redirect_to;
} else {
return home_url();
}
} else {
return $redirect_to;
}
}
add_filter( 'login_redirect', 'daro_login_redirect', 10, 3 );