Is it a good idea for a daemon to split logging between stderr and stdout based on severity levels?

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http://serverfault.com – Usually log messages are written to stderr. I'm wondering if it is a good idea/practice to split log messages so that errors and warnings go to stderr while debug/informational/notice messages go to stdout instead? Or is this irrelevant given that many dedicated logging processes only read from stdin anyway, which requires source log messages in stderr and stdout be combined and redirect to logger's stdin. (HowTos)