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In a saucepan, heat cranberry juice cocktail and sugar to boiling over medium-high heat. Add cinnamon stick, ginger root, cloves and anise. Reduce heat to low. Simmer uncovered 15 minutes. In a heatproof container, strain mixture through a fine-mesh strainer; discard spices. Stir rum and liqueur into container. Pour cocktail into mugs. Garnish with an orange slice, cranberries, a cinnamon stick and star anise if desired.
For a less sweet version, substitute cranberry juice for the cranberry juice cocktail or omit the sugar.