What the SATs Taught Us about Finding the Perfect Fit

The Rasch Model is a specifically simplified case of item response theory, but I'd argue that it may not be the best one for stitch fix. That's not to say that it can't be useful, but rather that the simplifications and assumptions of the Rasch model may lead to information that does not reflect the customer's measurements as well as a more sophisticated model could. Of course it very well may be good enough, but it serves as a somewhat useful exploration of the

The Rasch model is an attempt to differentiate two associated sets of information, the latent trait of the test taker/question answerer (in this case, their measurements) and the difficulty of the question (in this case, whether the item is too big, too small or just right). Basically the Rasch model treats the level of a latent trait of an individual as a function of the difficulty of a test question and what they answered.

But the model purposely ignores the question of the discrimination of the question, that is, how good is the question at differentiating between those who's latent trait differs, and just assumes that the discrimination (the slope of the line reflecting the model of the question's difficulty) is not relevant. Other models see this as relevant.

For example, if StitchFix offers a belt with a number of different holes, some people may feel the belt is too small if they are forced to use the last hole, some the second last hole. A question about such a belt that just asked if it was too large, too small, or just right might have low discrimination in terms of identifying an individuals underlying size. Likewise someone who has bigger thighs but a relatively slim torso might have different answers about a pair of slim fit pants of size x which are too small for their thighs, and a belt of size x. Thus questions about pants may have a higher discrimination then questions about a belt.

Item Response Theory outside of the Rasch also has a third factor to consider on a per question and per individual basis, which is basically the propensity to guess. Basically, how likely is someone to think carefully about the question as opposed to just putting down a random answer , and likewise are some questions more likely to have people answer blithely instead of earnestly.

The other thing to consider is that in most IRT tests, the latent trait is assessed at a single time for multiple questions. But weight/fit/measurements are here being assessed item by item, as they are tried, and the underlying fit may be changing if a person is gaining weight or bulk, retaining water, or recovering from thanksgiving dinner. While it's unlikely that someone's weight or size would change radically in a brief period, a model that weighed items that were tested more recently might better reflect the individual's measurements.

Of course it's been years and years since I took the class, so any screwup in this comment should reflect on me, and not my professor.

1 I was writing a function in R to speed up an IRT model fitting a curve in a way that let me do it in seconds instead of hours (It's been a while but I think it was identifying the point of the curve where the slope is maximized), in any case it was a time consuming computation if you check every possibility linearly to 6 decimals for hundreds of test takers, but I figured that there weren't local maximums and optimized with something like a binary search (but by decimal place), before I had ever heard of binary searches, and getting that sort of efficiency jump was deeply satisfying.

1) Body types that aren't average (all of our bodies are irregular, but some of us are more irregular than others). Clothes sizing are based on a average model of the human body.

2) Fabric interaction with body. Softer fabrics drape in different ways from more rigid fabrics. Also how loose or muscular your flesh is can affect fit if you're in the market for really slim fits (European style).

3) Non-representative snapshots: your measurements in the morning will differ from other times of day, and it will differ over the course of weeks and months, even if your diet is stable.

4) Shrinkage/expansion: depending on material, there is some shrinkage or expansion after the first wash/wear. Although this is mostly a known quantity and good clothiers account for this.

Really good bespoke tailors understand these principles, and make allowances for them as they build your clothing. Also they know to put elastic fabrics in the right places so the suit will still fit even after a large meal.

I think the one way we can get closer to a good fit while being remote is to have pop-up stations/kiosks where we can get multiple 3D scans of our body on separate occasions (kinda like how most bespoke tailors require at least 3 fittings). That still doesn't account for fabric-body interactions, but it gets us a lot closer than recommendation systems.

p.s. the other problem is cultural. Most Americans don't know or care quite as much about fit (because it's not as prized in the culture) as their European counterparts, so their data is going to be skewed slightly towards the left end of the competence curve.

I understand why they do this, because this style is likely to fit more people. But if the technique they describe in this post actually works, perhaps they could be more adventurous?

The variance in label sizes is bad enough - and worse for women's clothing than mens - but when you get into "large/medium/small" it's just a lottery. Especially if you're a westerner ordering direct from China.

I wish they had some sort of follow up experience that would let me "complete" the outfit.

They talk a bit about why they don't have any sort of online shopping here:

http://multithreaded.stitchfix.com/blog/2015/07/07/personali...

Gelman and the rest of the crew at Columbia are doing great work. Check out https://www.generable.com/ too.

One factor that is difficult to account for is users not telling you the truth. Users may feel embarrassed to say something is too small, as that may have negative connotations for some. It’s difficult of course to control for that, but I wonder how honest people might be in their feedback.