Passenger and Immigration Lists is an index to immigration records published in other sources. The original three volumes were published in print by Gale in 1983 and supplements are published annually. The earliest volumes rely on scores of published passenger lists. The "source number", a numerical code, can be used to identify the original source (you can then go to the bibliography for the full citation). Glancing through the source bibliography, I'm seeing a wide mix of genealogical and historical journals cited. I've attached an image of the source code key from volume 2 of the first edition (1983) as an example.
Later volumes might rely on just one source; for example, the 2017 supplement includes "immigrants from Russia and Italy who arrived in the Americas in the nineteenth century. Their names are drawn from a digital database in the U. S. National Archives that was originally extracted from ship passenger lists in the U. S. Customs Service and cumulated by the Center for Immigration Research" (page ix)
Chasing down the original record for Anne Guion in PIL is not possible from the Ancestry record (below), as it doesn't include which volume it draws from. The annotation is misleading and useless. But under "source bibliography" we see BOYER, CARL, 3RD, editor Ship Passenger Lists, New York and New Jersey (1600-1825). Newhall, CA: the editor, 1978. 333p. 4th pr. 1986. Reprint. Family Line Publications, Westminster, MD, 1992
The library has this in print. The book reprints an article from Seacord's Biographical Sketches and Index of the Hugenot Settlers of New Rochelle, 1687-1776.
Seacord's article includes a list of nine sources but not footnoted.
All this for the following quote "Jacques Guion and his wife Anne Vigneau were members of the French Church in New York City in 1701. Apparently his father was also named Jacques. His wife was in New Rochelle as early as 1705."
Here's an attempt at a citation but it could definitely be better.
Ancestry.com. Passenger and Immigration Lists Index [database]. Citing Carl Boyer (ed.), Ship Passenger Lists, New York and New Jersey (1600-1825). (Newhall, CA: the editor, 1978; 4th pr. 1986. Reprint. Family Line Publications, Westminster, MD, 1992), page 150. Excerpt from Morgan H. Seacord. Biographical Sketches and Index of the Hugenot Settlers of New Rochelle, 1687-1776. (New Rochelle, NY: 1941), pages 9-54.
||Anne Vigneau Guion|
||New York, New York|
||Guion, Anne Vigneau|
|Source Publication Code:
||Contains passenger listings mentioned in Lancour, A Bibliography of Ship Passenger Lists, 1538-1825 (1963), nos. 72-76, 78B, 79, 81-83, 83 note, 85, 87A, 88, 89, 98(1), 100, 102(1A), 104-106, 107A, 110-111, 111 corr., 112-114. Includes index to ship names, place names, and about 10,000 personal names, with variant surname spellings. Tepper, in nos. 9120, 9135, 9143, 9144, and 9151, has similar lists.|
||BOYER, CARL, 3RD, editor Ship Passenger Lists, New York and New Jersey (1600-1825). Newhall, CA: the editor, 1978. 333p. 4th pr. 1986. Reprint. Family Line Publications, Westminster, MD, 1992.|