Monday, 5 March 2012

Promotional regressions

A mathematical equation for holiday happiness, or banal tautology?

Expedia hired a couple of researchers to analyze a survey about Kiwis' recent holiday experiences. It looks like they set up a regression with "how happy did your last holiday make you" on the left hand side and a bunch of stuff on the right hand side like "the weather was good", "there were plenty of activities", "it was value for money", "plenty of partying", and that "it made my neighbours envious"*. Then they put out a press release presenting the regression equation and coefficients as being the mathematical formula for holiday happiness.

And it's gotten press. Radio New Zealand called me for comment on it last night;** I told them that if I understood the method correctly, it doesn't exactly provide would-be travellers with useful advice for happier travels. Who doesn't look for good weather when on holiday? Worse, most of what's on the right hand side seems to be just alternative ways of expressing what's on the left hand side; it would be surprising to find somebody who reported having had a bad time on holiday but that it was good value for money. Value-for-money kinda has happiness as the numerator.

And there's reverse causality all over the place: are people flying more than seven hours away happier because of the more remote destination, because they're richer and can afford long-haul travel, or because people are more willing to spend more on stuff once they've travelled that distance than when they've driven out to the bach? Are couples travelling together happier because they're travelling in pairs, or because single people travelling alone tend to be unhappier people in general?

Here's the funniest part of the press release:

A group of experts including a psychologist, a mathematician and travel experts from
Expedia.co.nz set out to find just that, and have created the formula for holiday happiness.

With Kiwis taking over two million holidays a year, the formula proves there is a science that every holiday‐maker can apply to their next escape to guarantee themselves a top trip.

What are those sciency looking things? I'm pretty sure it's the following: HH is Holiday Happiness. It's a function of some constant {b}, "Good Weather" {GW}, "Plenty of Activities" {PA}, "returning home relaxed and de-stressed" {RD}, going to a Great Destination {GD}, finding Value for Money {VM}, engaging in Plenty of Partying {PP}, and inducing "Holiday Envy" {HE}. So update your vacation plans accordingly. Never mind that without units on any of the regressors, you've no clue whether the relative coefficient magnitudes signify anything, so you don't really know the tradeoffs on the happiness production frontier between "Plenty of Partying" and "Great Destination". Or that pervasive potential endogeneity problems mean you really can't use it as a guide for action.

At least Radio NZ looked for folks to comment on it - the reporter there noted having talked also with a statistician. Stuff.co.nz seems mostly to have copied the press release.
Psychologist Meredith Fuller, who worked on the equation, said people could use the factors when planning their next break.

"It's essentially taking the guesswork out of a holiday that could be an expensive disaster."

Choosing a top destination, getting value for money and lots of partying also feature highly.

The most satisfied people spent at least five nights away, took a long-haul flight to their destination, and travelled with between two and five friends. Fuller says five was the ideal number.

"There is less chance of individual conflict, more mental stimulation, and enough variety in interests to broaden our experiences."

A partner is fine, but including in-laws or family decreases the chance of holiday joy. "The worst people to go away with are your relatives," she said.

Lording it over your mates – more politely called "creating holiday envy" – also increases the prospect of a good result. About half of those surveyed used social media while away to post snaps to make friends jealous.

"It seems it's no longer a case of `wish you were here', but `I'm here and you're not'," Fuller said.
So, a lesson for the kiddies out there. Take your intro to econometrics course. You too can easily produce the mathematical formula for anything, at least as far as some of the media is concerned. All you need is r-e-g.***

And kudos to Expedia for getting press mileage on this one.

* Weird Al said it best, and without running a regression, in his ode to the world's greatest tourist destination:****
Then we went to the gift shop and stood in line
Bought a souvenir miniature ball of twine
Some window decals, and anything else they'd sell us.
And we bought a couple post cards, "Greetings from the twine ball, wish you were here!"
Won't the folks back home be jealous.
Note that I'm not at all disputing that people enjoy vacations. I just can't really see how the survey and regressions really provide any kind of useful guide to action.

** I have no clue whether anything aired. UPDATE: here. But they left out all the "these econometrics are crap" bits. Ah well.

*** Maybe they used ordered probit. I haven't the full paper.

**** I regret, but Susan does not, that we drove within an hour of the place but I didn't realize we were anywhere near it. Had I realized, we'd have gone. Missed opportunities.

1. I love this bit Some factors have a bigger bearing than others, as denoted by the numerical values and it is great to know that the experts included "a psychologist and mathematician" (is she both rolled into one)?

I have to acknowledge that I'm devastated because of all the time I have wasted not looking for value for money and wishing for crappy weather. Now the equation will guide my holiday plans.

I can also see a whiff of IP protection, keeping the {b} coefficient secret so other sites can not use the equation. Further, they made public only the first decimal place for the betas, so we can't get only an approximation for HH.

1. I'm pretty sure there were two separate experts.

Hard pressed to see any case in which the constant matters. And, if anything, it's better that they truncate to one digit: surely the survey responses were scales of 1-5 or 1-10 or some such; too many decimal places would be spurious precision.

2. Please don't take me seriously when I'm writing anything about HH models (or TSA agents, or...). Of course the intercept is pretty useless and any resemblance of precision in the model is coincidental.

3. Of course your comment wasn't serious. But the sarcasm tag that was obvious to me mightn't have been obvious to other folks.

2. They could have been a little less serious. Along the lines of:

http://www.ritholtz.com/blog/2012/03/birther-economic-index/

1. Oh, that's fun. Thanks!

3. It's nice to see somebody focussing on the big issues for a change.

4. How large is the sample size? Given just how large the sample size could be there must be a large sample problem in that any t-stat will be hugely significant.

1. And doubly so when some of the independent variables are effectively the same thing as the dependent variable.

5. What you do is get the quote from Expedia, and then go back to the Airline Emirates to book.
No formula is required Eric
Do not book with Expedia
The airlines treat bookings with themselves Emirates, Quantas etc more favourably.
Try to change a booking with Expedia afterwards and suffer.
After suffering you get incoming mail from adverts Expedia.
Go to Greece here it says
Mark as spam.
Expedia is spam