An internal combustion engine has a crankcase and a crankcase ventilation system having a switchable shut-off valve, and sensors that detect different operating parameters of the engine, including a load variable of the engine. An estimated load parameter is determined based on the different detected operating parameters using a dynamic model, and a corrective value of a characteristic value is determined as a function of a deviation between the estimated load variable and the detected load variable. To implement a diagnosis, diagnosis switching cycle(s) are controlled, in which the shut-off valve is set to a closed switched position for a first time and set to an open switched position for a second time. A diagnosis value representative of a shut-off valve being in a correct or incorrect state is determined based on a change to the corrective value in response to the one or the plurality of diagnosis switching cycles.