So how can we interpret a nomogram once we have the data? Well going back to the love triangle example, say we have two actors (trying to be optimistic here) considering the role to play Anton, two actress (again, optimistic) for Jane, and finally, John Krasinski (haven’t quite given up on him, I’m WAY too optimistic now, I know) and another actor for the role of Randy. So then, after running the logistic regression, we can assignment points to each role based on those regression results. So we can assign 100 points to John Krasinski over that other actor, 30 points to Anton 1 over Anton 2, and 50 points to Jane 1 over Jane 2. So if our casting were to include John Krasinski, Anton 1, and Jane 1, we would have 100 + 30 + 50 = 180, or 180% chance to have that casting over any other combination. Or if we were to have John Krasinski, Anton 2, and Jane 1, we would have 100 + 0 + 50 = 150, or 150% chance to have that casting over any other combination. And how do we determine the points? Well, that’s a topic for another week. Until then, call me John, just sayin’ … if we meet in Chicago, I’ll treat you to some authentic Chicago deep-dish pizza …
And yes, it is real pizza! Jon Stewart doesn’t know what he’s talking about!
So we covered a lot of Anton and a lot of Randy lately (yeah, no, I’m not gonna even lie … that’s why I brought my trilogy straight up) but today I’m going to work through an example with the object of their affection, the love of their lives, the third side in their love triangle, the … well, hope you get the picture. And that person is Jane. Yes. Jane’s heart truly only belongs to one of them, to the one and only she is always devoted and to that one is … the one you find out about when you read the books! And how does she know if she’ll get to a dimension with that one and only? Well, she can look at a nomogram! Like this!
And what is that you may ask? Well, it’s basically a chart that can tell her the probability of her being with her one and only? And how does this chart tell her that? Well again, it depends on different parameters in the model that we got from logistic regression (like in Jane’s case, where does she live, what job does she have, and who is her one and only … again, you know what to do to find out). But wait … wait … wait … that’s not the most romantic model ever, you say? Well, maybe not but just think how romantic it can be once Jane is in the right dimension with her one true love!
Ah, that’s more like it! Until next time, you know where to find out who is Jane’s one true love 😉
So we all might have an idea of what interactions are but what do they mean in statistical terms? Well, they are something else we can put in regression models for one thing. For example, in my line of work, I put them in all the time, to see if, say, a certain type of medicine works better in boys or in girls. Or for example, is Randy (oh come on! no groaning!) more likely to capture the diabolical, evil, scheming, non-computer shop owning alter of Anton given whether he’s in a good or bad dimension and whom Anton is married to in that world. Well?, you say. Well?, I say. Well, what’s the answer?, you ask. Well, you know how to find out!, I say. But anyway, yeah, today’s post was short and sweet and we’ll let it at that until next time. What? What’s that? Again, I’m not telling ya, you know what to do to get the answer! But I will leave you with this pic of Lake Delton in Wisconsin Dells.
Ah, yes, nice, peaceful Wisconsin Dells. Where again you know what to do in order to get your answer …
So a little reminder. The probability of say, Randy finding Anton in a bad dimension is: exp(y)/[1+exp(y)]. And how do we get y? Well, we can use an algebra expression. Oh, come on! It won’t be that bad! Promise! So say in bad dimensions, Anton is less likely to own a computer store but he’s more likely to be found in warmer weather. So say we have the equation:
y = – 25 -2*(in computer store) + .5*(temperature)
If Randy sees Anton at a computer store when the temperature around the area is 40 degrees, than y = -25 -2*1 + .5*40 = -7 and so the probability becomes exp(-7)/[1+exp(-7)] = 0.0009, which is (wow!!) a small possibility that Anton is in a bad dimension. But if he’s not in a computer store and the temperature is say, 60 degrees, than y = -25 – 2*0 + .5*60 = 5 and exp(5)/[1+exp(5)] = 0.9933, which is a very, very, very, very high probability that Anton is in a bad dimension. So anyway, that’s the lesson for today, kids! And I was looking to leave you with a belated Canada Day/Happy Fourth of July pic and stumbled across this. Too yummy not to share.
By the way, you know what you could be reading while eating that yummy desse … okay, I’ll stop.