Which of the following is true about collapsing categorical inputs?

The option stating that a single categorical input can decrease degrees of freedom is correct. When working with categorical variables, each level of the categorical input typically represents a separate category in a model, thus consuming degrees of freedom. By collapsing a categorical input, you effectively reduce the number of distinct levels in that variable, which leads to a decrease in the number of parameters estimated in the model. This reduction in levels helps to increase the degrees of freedom available for other parameters, resulting in a more robust estimation process.

In modeling, maintaining an appropriate balance of degrees of freedom is essential for avoiding overfitting, which can occur when a model has too many parameters relative to the number of observations. Collapsing categories judiciously can therefore enhance the model's performance by providing a more streamlined and manageable set of inputs.

Other answers may suggest concepts related to degrees of freedom and categorical variables, but they do not align with the benefits connected specifically to collapsing categorical inputs.