So we covered mixed effects models and GEE models and I thought about covering something today about these things that go into them known as time varying covariates. I came upon this subject while realizing it’s Thursday and I needed something for my Friday blog and I was running out of time, (no pun intend- … okay, pun intended there), so I just googled some stuff on statistical applications in physics. After all, I need to give physics some fair play if I want APS to feature an Order of The Dimensions movie premiere and someday at one of their March meetings and … yeah, they’re still not listening. That’s okay. But anyway I came across astrophysics and quantum statistical mechanics, leading me to the Schrödinger equation leading me to the time-dependent Schrödinger equation which looks like this and I’d love to explain what all that is but I’m pretty sure Michio Kaku or Brian Greene will do a better job of that again at my movie premiere coinciding with the APS March … again, they’re not listening.
But anyway, although I cannot explain the entire Schrödinger equation, I could tell you a little something about time-varying covariates, which are basically things that can change over time. Like in the clinical trial data I work with, the patients’ sex and what treatment they are on theoretically stay the same over time but their blood sugar or hormone levels, say, could change over the course of the trial. Or like in my trilogy (oh come on! You knew it was coming!), we have Anton Zelov … our deep, dark sexy Russian spy with his deep, dark, sexy Russian accent — yeah, I can’t really do the accent even in real life so you’ll just have to imagine it on your own. So I guess his gender and ethnicity (ethnicity being Russian — sorry, a deep, dark, sexy Russian and all) would again be again be fixed over time, while, say, where his location would depend on where in time and in what dimension he is in the story. So in a sense, location would be a time-varying covariate. Meaning he could be in Moscow … or Zurich … or Miami … or wherever, depending on the timeline of the story. Even his different alters are at different locations at different times in the story. Like his good alter could be in Houston one second and then Atlanta another second at then back at Indiana … or what — did I get that right? I hope — have to go back and check before I confuse myself even. But anyway, that’s all for today’s topic. And what to end with, you think? Well, I did mention Houston which is about a three-hour drive from San Antonio which is where the next APS March meeting which would be all the more perfect since come on, Anton? Antonio? Eh? Eh? And … they’re still not listening. That’s okay. They might … someday. Until then – remember the Alamo!
So today we’re covering another fun, exciting, okay a topic from my dissertation concerning the general location model. And what does this model do? Well, it’s like a model with two components, a component which describes the distribution of your categorical data, and a component that describes the distribution of your continuous data based on the categorical data. And what kind of example can I give you to stop you from shaking your head no?
Well, good question! I thought about this and then thought about my heroine, Jane. Now, as you may recall (or maybe not which is why I provide you with the link here) in some dimensions, Jane is a physics student and in others, she is an art student. Now, she’s actually quite smart in all the dimensions, but lets just say she doesn’t quite apply herself to her physics studies when she’s an art major. Kind of like maybe I didn’t apply myself hard enough when I was at the University of Wisconsin-Madison and that’s why I only got my Masters there when I was aiming for a PhD. Wait … was that aloud? Ah, well. It’s all good though as I eventually did get my PhD from UIC. As you can see from the proof right here. But enough about me.
So lets say in the dimensions where Jane is a physics student, her physics midterm scores were probably in the nineties and in the dimensions where she is an art student, maybe they’re in their eighties. Okay, so that’s not the most thrilling, heart stopping story I ever told, but you get the picture. Guess I’m still in vacation mode. So anyway, join me next time when hopefully I’ll get my act together and think of another (okay, at least a little bit more) exciting topic to share. Methinks maybe another reference to the deep, dark sexy Russian spy, Anton Zelov may help, non? We’ll see. But for now, I leave you with the women’s soccer team at the University of Wisconsin-Madison doing the #ALSIceBucketChallenge.
and a bunch of challenges from the UIC swim team. So something from both my grad school alma maters. Go Badgers and Flames! But don’t worry, Northwestern, my dear undergrad alma mater, got your back and saving you for something good. Go Cats!! And let it be known that actually I’ll always be a Wildcat girl.
So we talked about coverage rates and we talked about standardized biases so now I thought I would talk about the root mean squared error (RMSE). And the root mean squared error is basically another way you can see if your estimated value, like the one you get from your simulations is anywhere close to your true value. And like its name implies, first you square the differences between your estimated values and the true value, then you take the mean of those squared differences, then you take the square root of mean of those squared differences. I know — maybe not the most intriguing stuff but lets use it in an exciting example. And I thought I would use the example of the probability that Tina would be in a justified dimension again but then I thought something more exciting might be needed to grab your attention. Something really big, really huge, out of this world, out of this dimension, if you will. Something that would make you grab on to your seats and then get up from your seats and say, “Damn, that Irene sure knows how to write. I have to go and get her trilogy right now! Yes, I have to! I just have to! Yes, damn, she’s good! Yes!” Something like that. And then I got writer’s block. I thought about maybe giving an example involving my recent trip to Boston and Cape Cod like about something neat I learned at the Joint Statistical Meetings or how it took my colleagues, Peter and Julia, and me forever going around and around … and around … to find this celebrity hub called Strega where we dined for lunch (and yet could not find a single celebrity there to pitch my trilogy to). By the way, GPS around the Boston harbor? Works even worse than usual. Or like how my publicist Jessi whom I vacationed with in Cape Cod used to do her best Joey Tribbiani impersonation from our balcony every time she saw the cute poolboys Filip or Stefan below. Or how I almost got in trouble in the airport because … um, never mind … not gonna pull an Amanda Seyfried here as I don’t have that much star power … yet anyway. Damn … I had a great trip! But damn … can’t find a good example in any of those tidbits. So instead I conducted another simulation with our previous example and got an estimate for the probability of Tina being in a justified dimension as 12.54% and an RMSE of 0.54%, which is fairly small, so again we can deduce that our estimate is quite close to the true value of 12%. Well, that’s all for now but join me next time for more statistics-y/physics-y/trilogy related stuff. Until then …
What can I say? That’s stuck in my head now. Thanks for that, Jessi!
PS: Also, want to thank Julia just for the yummiest salmon I ever had at Strega during JSM. Next time, it’ll be my treat. When we’re there for an APS March meeting. Coinciding with an Order of The Dimensions movie premiere. Yes, I’m serious. Yes, it’s gonna happen. Yes, I have a backup plan to treat Julia sooner too.
Out of This Dimension 