Selecting the Best Model
After understanding the importance of using multiple representations and knowing how to compare different models, the next step is to determine which model best fits your data. This is crucial for making accurate predictions and informed decisions based on your data analysis.
Criteria for Model Selection
When choosing the best-fitting model, consider the following criteria: Goodness of Fit, Simplicity, Predictive Accuracy and Interpretability. Let’s explore each of these in detail.
Goodness of Fit
Goodness of fit is a statistical measure that tells you how well your model replicates the observed data. In other words, it quantifies the discrepancy between observed values and the values expected under the model. Common statistical tests for this include Chi-Square for categorical data and [latex]R^2[/latex] for linear regression models.
A healthcare researcher trying to model the spread of a contagious disease has various models at their disposal, from simple SIR (Susceptible-Infected-Removed) models to more complex SEIR (Susceptible-Exposed-Infected-Removed) models with additional parameters.
The researcher would use goodness-of-fit tests like Chi-Square or [latex]R^2[/latex] to see which model best fits the observed data on disease spread. This step is crucial for ensuring that the model accurately captures the dynamics of the disease.
While a higher [latex]R^2[/latex] value often suggests a better fit, it’s crucial to remember that it doesn’t indicate the quality of the model by itself. A high [latex]R^2[/latex] could also mean that the model is overfitting, especially if the model is too complex.
Simplicity (Principle of Parsimony)
The principle of parsimony, often referred to as Occam’s Razor, suggests that given two models that equally well explain the observed data, the simpler one is generally better. Simplicity here refers to the number of parameters in the model, the form of the model, and how easy it is to interpret.
An economist modeling consumer spending habits could use a simple linear model that considers income as the sole factor, or a complex model that also includes age, location, education, etc.
If both models fit the data almost equally well, the principle of parsimony would suggest using the simpler model. This is because a simpler model is easier to interpret and less likely to overfit.
Complexity isn’t always bad; sometimes complex phenomena require complex models. However, a complex model that doesn’t significantly improve the fit compared to a simpler model is usually not preferable, as it may not generalize well to new data.
Predictive Accuracy
Predictive accuracy refers to how well the model performs on new, unseen data. This is often assessed using techniques like cross-validation, where the data is split into a training set to build the model and a test set to evaluate its predictive performance.
A data scientist at a tech company trying to predict user engagement for a new feature has historical data from similar features that were launched in the past.
The scientist would split this historical data into a training set and a test set. After training a model on the training set, they’d use the test set to evaluate its predictive accuracy. Techniques like cross-validation can help ensure that the model generalizes well to new data.
Always validate the model’s predictive accuracy using a separate dataset that wasn’t used in the model training. This helps ensure that the model will perform well in real-world applications.
Interpretability
Interpretability is about how easily an individual can understand and make sense of the model’s inner workings. This is especially important in fields like healthcare, finance, and public policy, where model decisions can have significant real-world implications.
A policy analyst trying to understand factors that influence voter turnout has a complex neural network model that has high predictive accuracy but is hard to interpret.
If the goal is to provide actionable recommendations to increase voter turnout, interpretability may be crucial. In such a case, the policy analyst might opt for a simpler, more interpretable model like logistic regression, even if it sacrifices a bit of predictive accuracy.
Even if a complex model like a neural network has high predictive accuracy, it might not be the best choice if interpretability is crucial for your application. In such cases, simpler models like linear regression or decision trees might be more appropriate.