Hey @FicoMike0. Diversity of credit mix doesn't change when you close an account. That metric looks at all accounts on your credit reports, open and closed. What is gained/lost with an [only] installment loan is the bonus awarded from the Amount of Debt slice of the FICO pie when it is opened and eventually closed. Diversity of credit mix would be satisfied upon opening the loan, then remain for ~10 years following the closure of the loan until it falls off of one's reports. Presumably at some point during that decade another loan would be opened in most cases, thus allowing diversity of credit mix to be maintained.
