Not all variables in a data set or questions in a survey are equal when it comes to data analysis and analytics. Some variables (questions if it’s a survey) will be inherently better at classifying outcomes than others. For example, if you are using a data set to build a narrative around a particular binary behavior (i.e. people who do X vs people who don’t do X) then there are some considerations about which variables will give you a short cut to the story.
The first rule of thumb is to start with binary predictors, i.e. variables with only two different responses / values. Variables with a greater number of possible responses/values will be more likely to have spurious relationships with the variable that you are trying to predict. Predictors with two levels are less likely to suffer this phenomena.
Thesecond rule of thumb is to select those binary variables that have a similar distribution to the variable that you are trying to predict. For example if you are trying to predict a behavior that has 20% incidence among a certain population then the best predictors to use should also have a 20% / 80% spread across two values.
The reason for this condition being optimal is easily explained. The best predictor is one that identifies all cases correctly. Imagine that the best predictor has two possible values with 40% of cases at a value of 1 and 60% of the cases have a value of 2 in this variable. With this distribution, if 1s are predictive of the behavior we are modelling then only half the 1s can be correctly predictive if the behavior has a 20% incidence. The other half of the 1s are incorrectly predictive. However, if the best predictor had 15% of cases that were 1s and 85% cases had a value of 2 then all the 1s could be correctly predictive. This would be a much better predictor to use – in part because the incidence of 1s (or 2s for that matter) is close to the incidence of behavior we are predicting – meaning that 1s have a better chance of being better predictors.
I have a nice graph to show this too. Watch this space!
I used the accuracy calculation equation to make this simple form that works out how well a prediction must perform to be better than a weighted guess. For example if the incidence of what we are trying to predict is 40% (gender=female, for example) then the model prediction must have an accuracy greater than 52% for it to be better than randomly assigning 40% of cases to gender is female and assigning the other 60% to gender isn’t female. As this weighted-guess will have an accuracy of 52% over a large sample.
When it comes to designing and implementing algorithms for Knowledge Leaps I have spent a lot of time thinking about accuracy in relation to making predictions. I soon realized that there is a mathematical relationship between the accuracy of a guess and the incidence of what you are trying to predict.
For instance, if you have built a model for predicting whether or not a roulette ball will fall into the zero slot on a roulette wheel with 37 numbers (0-36) then your model has to be correct (at predicting success or failure) at least 94.67% of the time. However, if you want to predict red or black then your model needs to be correct 50.04% of the time to be better than a pure guess.
The graph below shows the relationship as a function of incidence (the rate of what we are trying to predict).
Broad conclusions we can draw from this relationship:
When we are trying to predict outcomes which have an incidence of between 20% and 80%, there is a lot of potential for producing a worthwhile model that can improve on a guess.
When the incidence of outcomes is less than 5% and greater than 95%, models need to be delivering 91%+ accuracy to be of any help. This is the realm of medical diagnosis, an area where guesswork isn’t welcome.
Since 66% of the chart is territory where a guess is better than a model, if we produced random models to make a prediction, 66% of the time a guess would be better. Obviously, if we aggregate up the results of lots of random guesses we can produce more accurate predictions (e.g. Random Forests). However we then run into the issue of not creating human readable models.