Children born in Mayo; Michael 1839, Patrick 1841, Margaret 1844, Andrew 1847. In Measham, Bridget 1850, John 1853. Catherine's name on birth cert. was Raven and Ragin. Barney Regan from the same address, lodger, on the 1841 census married Margaret at a later date. There is an amount of confusion over spellings as they could'nt read or write so could'nt correct mistakes the detail taker heard and wrote down. On the 1911 census my grandfather, Andrew's POB is written as Co. Mayo NK. There are various spellings of Dugan on early records, Dugin, Doogan, Dougan, Dughan. I was hoping some distant relative may have discovered more than I have been able to do purely from my computer. Thankyou, Andrew Dugan.
Various spellings are a part of family history especially where literacy was low.
We always have to accept that we must look at every possibility and then find proof for the link.
Catherine was born c1814 based on age 47 on 1861 UK census in Measham
You state that "Catherine's name on birth cert. was Raven and Ragin"
Birth certs are not available for that period in Ireland - where is this information from?
She shows that she was from Dareybrook on 1851 census - this could be DERRYBROCK
Derrybrock is north of Newport in west Mayo
but it is more likely to be DERRYNABROCK in east Mayo
Michael states he is from a place name transcribed as Rottradon on the same census return
It reads more as Bottradoo to me and could well be Ballindoo (Baile na dumha) in east Mayo
It is also known as Doocastle; This place is about 2 miles from Derrynabrock
The births of the eldest children are in Mayo on census returns
Ballindoo is in the parish of Kilturra close to the Sligo border
Have you located their baptisms in Ireland? or other source for them?
as this info would lead me to strongly believe the family were only Mayo based before emigrating
Best of luck in your searching as this is the time period most difficult to research in Irish records
Link to 2006 forum discussion on family you may or may not be aware of
Looking at the 1911 census return for Andrew I would consider NK to mean
not known