Can I fit you into a pretty equation?

Discrete Choice Analysis. 

It is currently all the rage in human behavioral models. Using it, we researchers hope to fit people's discrete choices (discrete means separate or distinct, as opposed to continuous) into nice equations. The equations are called utility functions. Each distinct choice (e.g., blue pen vs. red pen vs. pencil) is associated with a utility function that is determined by various explanatory variables that have been shown to be significant to your choice set (e.g., gender, income, education level, price of blue pen, stated preference toward the color blue on a scale from 1-5). Then a probability that you will choose the blue pen over the other options is computed.

The first assumption of Discrete Choice Analysis is that people will act rationally and will choose the item with the highest probability. So, there may be a problem there, huh? Given discrete choice analysis I would assume that most people would stay home on snowy days... but perhaps their utility functions are vastly different than mine. . .

BUT, Somewhere along the way I am put into a class of people with the same explanatory variable values as I have (someone with the same income, education, gender, household structure, occupation, etc) who has answered a survey at some point in time and indicated they prefer a blue to red and further have bought 20 blue pens this year and only 2 red. Statistically I should be more likely to purchase a blue pen than a red pen?? 

Ah, well, it's close enough most of the time and afterall we do have predict driver decisions. (Believe me your transportation models have gotten much better as a result of discrete choice analysis). It is used to predict mode splits (car vs. bus vs. carpool vs. train) and travel routes and has afforded opportunities to do analysis on possible changes to the system (new roads, new lanes, new buses, fare increases) and policy decisions (gas tax, congestion pricing, toll roads, etc). It's predecessor was the gravity model (and yes it's a Newtonian equation), but that may be for another post.

If you're interested in seeing a plan in the works, take a look at http://www.slideshare.net/nashvillempo/nashville-mpo-2035-plan-policy-initiatives
It is Nashville's long range plan (Transportation and Land Use) put on every college students' favorite medium: slideshow!

So you tell me: Can we fit you in to a pretty equation and predict what choices you will make? If you had the data available what choices would you like to build models for? 

I'll leave you with a picture of my personal favorite form of transportation:

You were expecting a bicycle weren't you? hehe.

"What do you do?"

"What do you do?"

We all ask it and we all have had and will continue to have to answer it. I know I have to answer it ALOT, and I still seem to lack the ability to answer the question both accurately and concisely. First you have to gauge what the person is asking: do they want to know what you do for work, fun, etc... And while what we all do for fun is probably more interesting than work (see exhibit below):

Fun

Work

Note the rainbow jacket in the Fun picture!! And the beer!! And Brian dressed as a pink rhinoceros!! Versus the fake smile in the Work picture.. And the messy hair.. I know the Powerpuff mug in the Work picture could skew things, but focus on all those papers and that awful simulation running in the background. Yep I think I've rightly convinced you that Fun is more fun than Work, right?

But, most of the time the question for me entails what I do for work. So, then you have to decide whether they really want to know what you do, or if they are being polite and don't really care. That certainly affects the way in which I should structure my answer. Then you have to decide how much detail 1) they want to know and/or 2) they would understand.

 So, I find myself dreading the question and taking a deep breath before I have to answer it. Perhaps it is a symptom of being in graduate school. Technically, 'what I do' has to be proposed in a 15-20 page paper to my committee, so maybe there is no one sentence that could properly capture what I do. The shortest answer I can give is, "I am getting a PhD in Transportation Engineering," (although it's really civil engineering, but I don't want people to think that I am a civil engineer because I'm not. So, I stretch the truth a bit to more accurately reflect my course of study; and, my friend Jenny tells me it would be unethical to sell myself as a Civil Engineer to which I agree wholeheartedly). Here's Jenny working,

I felt I needed to add that because 1) she's probably the hardest worker in our office and 2) she seems to have mastered the art of telling people what she does; I've seen it in action; don't deny it, Jenny!

Most people have no idea what transportation engineering means. And rightly so. There are so many facets of transportation engineering and transportation studies that it would be impossible to even know all of them that exist. If the person happens to be an engineer themselves and happens to have taken transportation classes during their undergraduate course of study they might think I design the geometric aspects of roadways or do signal timing (and then sometimes I get asked when I'm going to fix certain freeway exits or intersection light timings, which has already been covered by xkcd: http://xkcd.com/277/).

So I try to explain that transportation studies have become more interdisciplinary and that we (and 'I' in particular) try to model human behavior by using census data and travel surveys/diaries in order to better predict traffic patterns in order to make the best policy decisions when considering new infrastructure or modifying existing infrastructure (aka construction). It's a bit like social science meets mathematical modeling meets engineering.
 And while I wish everyone were this excited at this point in my explanation:

Bethany

Although now that I look more closely at the picture above it might be terror rather than excitement. Either way, it's still a reaction. And instead the general response more closely resembles: 

Confusion?/Boredom?

And as if the above mentioned weren't enough disciplines, I also am trying to model wireless communications (computer science) and incorporate measures of risk and uncertainty in designing such networks. So, most people (and felines) are now:

and I'm starting the miss the two years of my life where I could just say, "I teach highschool math." Because that was easy (not the teaching part, just the talking about it part). So sometimes I just find myself saying, "I do math."

We all have to start somewhere, and I have chosen here

I have been trying to decide if I really wanted to keep a blog. I finally decided that for me it may be worth it since I have been  unable to actually keep a journal for the last 6 or more years due to time limitations, the deterioration of my handwriting (I completely attribute the deterioration to graduate school), and apparently the decline in my ability to spell correctly (it took me forever to get 'deterioration' correct of my own volition in that last sentence). So whether or not it's worthy of being read will remain to be seen. Also a part of my decision hinged on the question: what on earth would I write about? So I made this list of things I love and would probably love to talk about:

BRIAN! (Not to be confused with Jesus)

MATH!

RAINBOWS!

BUBBLES!

RAINBOWS AND BUBBLES!

FAMILY

KITTIES!

Just to name a few.... And of course I'll add the obligatory not necessarily in that order... Except for Brian!

Although I doubt he'd like the thought of me blogging about him, so you might have to accept blogs drawn from my other likes. Especially math because I do it a lot.

So that could get me off to a pretty good start with the things I love and I'm sure the time will come where I'll talk about some things I severely dislike because that's just the way the world works, right?

So today I'll talk about an idea my friend Bethany and I came up with that we think should appear in PhD comics (if you don't read it you should go here now and read the archives, too: http://www.phdcomics.com/comics.php). Bethany and I carpool together since I now live such that all routes to school are scant of bicycle infrastructure (boo poor Nashville infrastructure). I found myself yawning one day as we walked from the car to the engineering building with increasing frequency relative to the distance to the building. Then upon entering the building the yawns turned into sighs with intensity that was indirectly proportional to the distance to my office (as the distance to my office decreased, the sigh increased). Right now I'm having a hard time imaging how both of those things would look together on one of PhD comics' famous graph pictures (e.g., http://www.phdcomics.com/comics/archive.php?comicid=125), but I'm getting started with something of this nature (plot produced in Matlab) using reverse logarithmic (frequency of yawns) and exponential (intensity of sighs) scales. 

  

I wanted to make the plot in Matlab for two reasons:

1. to make sure that I could still plot logarithmic and exponential functions so that the results were what I wanted (some of the mad PreCalculus skills I picked up from teaching it at CCA) and I think the results were successful for the most part. I faked some things though that I would have known how to do at the drop of a hat while I was teaching:
1. the y scale is really multiplied by 100, but I manually changed the axis for this picture;
2. I actually computed both the logarithmic and exponential functions on an increasing X matrix from 0 to 600 but then plotted them on the reverse axis as it appears from 600 to 0)
2. I also wanted to make sure that it was a pretty smooth line rather than one I drew in paint that would have been a little wavy at best.

Why I chose these functions: 

Exponential for intensity of sighs: The exponential function takes the form y=e^x (or y=exp(x) in several computer languages) where e (Euler's constant) is about equal to 2.718...... (Note that ^ sign means: raised to the xth power) The function reflects the property that when x increases constantly, y increases proportionally (i.e., demonstrates a percentage increase). It also has the wonderful property that the derivative (or slope of the tangent line, remember slope is rise/run) of e^x is e^x. For example when x=0, then the function e^0 = 1 and also the slope of the tangent line to e^x at x=0 is 1.

 In other words: as wikipedia states: (http://en.wikipedia.org/wiki/Exponential_function)

• The slope (rise/run) of the graph at any point is equal to the height (y-value) of the function at that point.
• The rate of increase of the function at x is equal to the value of the function (y) at x 

And those are awesomely beautiful properties for a function to have. Especially when you're trying to do very complex Calculus as a student.

From personal experience, I knew that a characteristic of an exponential plot was that as x gets bigger, the y increases more quickly and continues to infinity (think of all the times you have heard the phrase 'exponential growth', although most of the time the phrase is used incorrectly and should actually be 'geometric growth', but that will have to be the topic of a separate blog posting). I truncated the function for real world illustrative purposes, but I figured that the intensity of the sigh would grow quickly within the short walk from the building's door to my office's door, and would only be bounded by the limitation that I had finally reached my office.

The Logarithmic Function for number of yawns: 
The logarithmic function ln(x) is the inverse of the exponential function. So when y=ln(x) then x=exp(y). I won't go any further than that explanation other than to say that this leads to the neat results that :
ln(e)=1 so
ln(e^x)=x and
ln(e^891)=891 and
ln(e^zebra)=zebra.
Catch my point?

And while that is cool, I chose the function because it has the opposite property of the exponential function in that it starts at negative infinity, rises really fast and then that increase slows down to a crawl. Frequency of yawn I thought would be completely limited by the amount of oxygen your body could take in at one time. Also, all of us grad students know that the cycle of dread starts with one giant thought of everything that needs to be done and then other things trickle in.  I thought the logarithmic function would catch that beautifully.

To wrap up:

So, my plot is probably not perfect. I wasn't quite sure what to use as units of intensity, so I chose the Richter scale as hyperbole. Also, I should probably truncate the intensity of the sigh function on the left hand side to start from 100 m away to more accurately reflect entering the building, but I really didn't want to rework Matlab code anymore. I wanted to go have dinner with my mom at Cabana instead (mmmmmm.... Lobster Brie Macaroni!)

This was a wonderful way to spend an hour or so instead of reading more about Human Behavior in Travel Demand Modeling, which is my current research task... I do not really like literature reviews, but I do realize that they are helpful in trying to figure out which model I should implement within my research. They also keep reviewers at bay, I hear. Yay Academia.