Sheriff Michelle LaJoye-Young told media the three children were primary school age and younger.
There's no word at this point on the relationships between the victims. Authorities said evidence collected at the second scene suggests some of the children were killed in a wooded area there before all four were found dead at the home.
Police say there is not a public safety concern at this time, and there are no suspects on the loose.
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Sheriff LaJoy-Young said in a statement: "I can confirm that we have had a shooting and that there are four deceased individuals on the scene". They were found at a home in rural Northern Kent County.
They added that Moore had a history of mental illness and was previously admitted to a mental health facility.
WOOD-TV reported that LaJoye-Young said authorities discovered the victims at a property near Cedar Springs, a community about 30 miles north of Grand Rapids. She described the situation as "horrific" and that her "heart goes out to the families involved here and the community".