Posts tagged with interaction terms
My father used to tell me that when people complimented him on his tie, it was never because of the tie—it was because of the suit. If he wore his expensive suit, people would say “Nice tie!” But they were just mis-identifying what it was that they thought was nice. Similarly if you’re interviewing candidates and accidentally doing your part to perpetuate the beauty premium to salaries, you aren’t going to think “She was really beautiful, therefore she must be more competent”. You might just notate that she was a more effective communicator, got her point across better, seemed like more of a team player, something like that.
Achen (2002) proposes that regression in the social sciences should stick to at most three independent variables. Schrodt (2009) uses the phrase “nibbled to death by dummies”.
I understand the gripes. These two men are talking about political analysis, where the “macro” variables are shaky to begin with. What does it mean that the Heritage Foundation rated two countries
9 points apart on corruption or freedom? Acts of corruption are individual and localised to a geography. Even “ethnofract”, which seems like a valid integral, still maps
∼10⁷ individual variation down to
10⁰. But this is statistics with fraught macro measures trying to answer questions that are hard to quantify in the first place—like the Kantian peace or center–periphery theories of global political structure.
What about regressions on complexes in more modest settings with more definitive data measurements? Let’s say my client is a grocery store. I want to answer for them how changing the first thing you see in the store will affect the amount purchased of the other items. (In general trying to answer how store layout affects purchases of all items … this being a “first bite”.) Imagine for my benefit also that I’m assisted or directed by someone with domain knowledge: someone who understands the mechanisms that make X cause Y—whether it’s walking, smelling, typical thought patterns or reaction paths, typical goals when entering the store, whatever it is.
I swear by my very strong personal intuition that complexes are everywhere. By complexes I mean highly interdependent cause & effect entanglements. Intrafamily violence, development of sexual preference, popularity of a given song, career choice, are explained not by one variable but by a network of causes. You can’t just possess an engineering degree to make a lot of money in oil & gas. You also need to move to certain locations, give your best effort, network, not make obvious faux pax on your CV, not seduce your boss’ son, and on and on. In a broad macro picture we pick up that wealth goes up with higher degrees in the USA. Going from G.E.D. to Bachelor is associated with
tripling ± 1 wealth.
I think this statistical path is worth exploring for application in any retail store. Or e-store or vending machine (both of which have a 2-D arrangement). Here as the prep are some photos of 3-D stores:
And for the 2-D case (vending machine or e-store) here are some screen shots from Modcloth, marked up with potential “interaction arrows” that I speculated.
Again, I don’t have a great understanding of how item placement or characteristics really work so I am just making up some possible connections with these arrows here. Think of them as question marks.
- purse, shoes, dress. Do you lead the (potential) customer up the path to a particular combination that looks so perfect? (As in a fashion ad—showing several pieces in combination, in context, rather than a “wide array” of the shirts she could be wearing in this scene.)
- colours. Is it better to put matching colours next to each other? Or does that push customers in one direction when we’d prefer them to spread out over the products?
- variety versus contrastability. Is it better to show “We have a marmalade orange and a Kelly green and a sky blue party dress—so much variety!” or to put three versions of the “little black dress” so the consumer can tightly specify her preferences on it?
And if you are going to put a purse or shoes along with it (now in 3-ary relations) again the same question arises. Is it better to put gold shoes and black shoes next to the “cocktail dress” to show its versatility? Or to keep it simple—just a standard shoe so you can think “Yes” or “No” and insert your own creativity independently, for example “In contrast to the black shoes they are showing me, I can visualise how my gold sparkly shoes would look in their place”? More and more issues of independence, contrast, context, and interdependence the more I think about the design challenge here.
- "random" or "space" or "comparison". You put the flowers next to the shelves to make the shelves look less industrial, more rather part of a “beautiful home”. Strew “interesting books” that display some kind of character and give the shopper the good feelings of intellect or sophistication or depth.
Or, what if you just leave a blank space in the e-store array? Does it waste more time by making the shopper scroll down more? or does it create “breathing room” the way an expensive clothing store stocks few items?
- price comparisons. You stock the really really expensive pantsuit next to the expensive pantsuit not to sell the really-really-expensive one, but to justify the price or lend even more glamour to the expensive one.
- more obvious, direct complements like put carrots and pitas next to hummous so both the hummous looks better and you will enjoy it more. Nothing sneaky in that case.
Did you ever have the experience that you buy something in the store and it read so differently in the store and when you were caught up in the magic of the lifestyle they were trying to present to you, but now it’s hanging up with your stuff it reads so different and doesn’t actually say what you thought it said at the time?
For me if I’m clothes shopping I’m thinking back on what else I own, what outfits I could make with this, how this is going to look on me, how its message fits in with my own personal style. And at the same time, the store is fighting me to define the context.
In the Modcloth example I’m talking mostly about 2- or 3-way interactions between objects. In analogy to simplicial complexes these would be the 1-faces or 2-faces of a skeleton.
But in general in a branded store, the overall effect is closer to let’s say the N-cells or N−1-cells. Maybe it’s not as precise as the painting in http://isomorphismes.tumblr.com/post/16039994007/thoroughly-enmeshed-composition-perturbation or a perfectly crafted poem or TV advertisement, where one change would spoil the perfection.
But clothing stores are definitely holistic to a degree. By which I mean that the whole is more than the sum of the parts. It’s about how everything works together rather than any one thing. And a good brand develops its own je ne sais quoi which, more than the elements individually, evokes some ideal lifestyle.
More on this topic after I finish my reading on Markov basis.
A lot of people think of “geometric” art as being math-y, in the same sense that the band Maps & Atlases is math-y.
But I don’t think lines, circles, squares, tessellations, grids, and polygons are more mathematical than globs, leaves, aleatorics, colours, nets, or scribbles. In fact, I can link to a math post about each: lines, circles, hypersquares, polytopes, aleatorics, tessellations, blobs, grids, leaves, nets, scribbles, colours.
The mathematical thought that occurs to me when looking at this painting is how, in composition, every spot on the canvas influences every other spot. Holger Lippmann couldn’t have swapped a few of these circles because it would have ruined the effect.
Similarly in painting like this, if you added a splotch of yellow in the bottom right, that would affect the look of several other parts of the canvas.
Algebraically, the pieces of the composition are like a highly connected graph (in “how good it looks” space).
If you regressed compositional outcome against the content of each point in the painting (or just against the style of each circle), the relevant explanatory variables would be highly interactive terms. All the monomial, binomial, trinomial, … terms would be irrelevant.