The matter will be governed by the laws of the state in which the judgment was entered. If the judgment was entered in Michigan the court would first have to find there is a change in circumstances and then evaluate eleven factors set forth by Michigan law. The court is always concerned with the best interests of the child. However, the court may or may not take the child's position into consideration. The court can meet with the child and discuss the matter, but they cannot disclose their position and will only say on the record that the child's position on the matter has been considered by the court. Usually, when a child is in the latter teenage years the court will give their opinion more consideration, as everyone realizes a child that age is going to be difficult to "force" into parenting time or custody situations.
Mr. Fox is correct in that the laws of the state where the judgment of divorce was entered control this outcome and, if that state is Michigan, most family court judges will give more weight to the child's preference, the older that child gets. Under the Child Custody Act, there are 11 factors which a court must consider before changing custody. One of those factors is "the child's reasonable preference". This preference is more meaningful, and carries more weight the older the child gets.
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