See 1:05:35 into it (yes, the whole talk is long!)
Now, Temple Grandin is not a doctor, not a nurse practitioner, not a physicians assistance. She's not even an EMT.
But she does have experience talking with a range of families. And since a lot of medication for depression and anxiety is trial and error in a respectful sense anyway, I think this is pretty good advice. And I'll add that I've read elsewhere that it's usually a pretty good idea to phase down in a series of steps rather than cold turkey. Even if the medication doesn't seem to have been working, just that your body may have gotten used to it.
Temple is recommending this 1/4 to 1/2 starting dose just for three categories: SSRI Antidepressants, Tricyclic Antidepressants, and Atypical Antipsychotics. Her slide says that other drugs usually require standard doses.