# Can a continuous cause have a discrete effect?

Say we have a continuous temperature as an input and a few climate categories as an output. For example, if the temperature is between 22.93 and 27.65 degrees it is comfortable. If it is over 27.65, it is uncomfortable.

Does this sort of model automatically convert temperature into a discrete variable because the result is discrete? Or should the temperature still be treated as continuous, but won't that be illogical?

• Consider an analogy: how much arsenic a person eats. For all practical purposes, that can be treated as a continuous cause. The next day, the person is either dead or alive. That's a discrete effect. Nov 8, 2018 at 4:44
• @jbowman I think in this case there would be a thousand other variables like person's health, weight, genetics, etc. If all other variables are controlled for, wouldn't there be a precise threshold of arsenic that separates the outcomes of life and death? 2 discrete inputs 2 discrete outputs? or maybe I'm being too philosophical about it... Nov 8, 2018 at 4:52
• The input / cause is how much arsenic the person eats, not how much the person needs to eat in order to die. You are confusing the threshold with the thing being thresholded; a category mistake (wisegeek.com/what-is-a-category-mistake.htm). Nov 8, 2018 at 4:58
• @jbowman I think that hits the nail on the head there. Except now I'm wondering if input and cause are the same categories. Probably not at all. Because I'm sure eating above a certain threshold of arsenic would cause death. But now my intuition tells me that input would in fact be the quantity of arsenic, which is continuous. Nov 8, 2018 at 5:13

A continuous cause can have a discrete effect, as you've pointed out.

Does this sort of model automatically convert temperature into a discrete variable because the result is discrete?

What do you mean by "automatically convert"? Mathematical objects such as the variables you describe don't generally have things automatically happen to them.

Or should the temperature still be treated as continuous, but won't that be illogical?

Seems quite reasonable to me that temperature is continuous. In fact if you've defined temperature as a continuous variable, the fact that it's treated as continuous is almost tautological.

• What I mean is now it would seem the temperature is either within 22.93 to 27.65 interval or above 27.65 so it can have one two values as far as the model goes. The continuity within those values now seems irrelevant, or is it still relevant within the model? Nov 8, 2018 at 4:01
• @ArthurTarasov if you are trying to answer the question "is the temperature comfortable", then yes, you only need to know whether the temperature is above or below a certain value, but that doesn't change the fact that temperature is continuous. In real life, temperature or weight or length doesn't suddenly "become" a binary variable whenever I need to test if something is above/below a threshold. Nov 8, 2018 at 4:04
• What is blowing my mind is whether it makes sense to consider a continuous variable as a valid input to a model with discrete output or whether the continuous variable has to be converted into a set of discrete values before it can become an input for a model with discrete output. Nov 8, 2018 at 4:13
• There is no rule that the "discreteness" of the input and outputs of a model must be the same. Nov 8, 2018 at 4:16

This isn't a model. This is just recoding a variable.

Now, if you measured the temperature in a room and had a variety of subjects rate the room on a "comfortable" scale, you could then create a model where the temperature in the room predicted how comfortable subjects were in the room.