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What are some alternatives to logistic regression for binary outcomes?

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Logistic regression is a popular method for modeling binary outcomes, such as whether a customer will buy a product or not, based on predictor variables, such as age, gender, or income. However, logistic regression has some limitations and assumptions that may not always hold in real-world data. For example, logistic regression assumes that the relationship between the outcome and the predictors is linear on the logit scale, that the predictors are independent of each other, and that there is no multicollinearity or outliers. In this article, you will learn about some alternatives to logistic regression for binary outcomes that can address some of these issues and provide different perspectives on the data.

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Decision trees:

This intuitive model splits data into subgroups based on rules from predictors, offering visual insights for non-linear relationships. It's like having a roadmap for decision-making.
Random forests:

An ensemble of decision trees, random forests average multiple predictions to reduce overfitting. Think of it as a team of experts rather than one, enhancing accuracy and stability.

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1 Probit regression

Probit regression is similar to logistic regression, but it uses a different link function to connect the outcome and the predictors. The link function is the cumulative distribution function of the standard normal distribution, which has a steeper slope near the mean and flatter tails than the logistic function. Probit regression can be useful when the outcome is influenced by extreme values or when the logistic function does not fit well. However, probit regression also has some drawbacks, such as being less interpretable than logistic regression and requiring more computational power.

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Gerard Kinneen

CoFounder and CXO of iSort AB | Blending Innovation in Robotics with Practical Solutions for Heavy Load Management | Passionate about Autonomous Vehicles for Construction Sites.
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In addition to logistic regression, I consider alternatives like probit regression, complementary log-log regression, Poisson regression, generalized linear mixed models, decision trees, random forests, support vector machines, and neural networks for modeling binary outcomes based on the data and modeling goals. The choice depends on data characteristics and modeling assumptions.

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2 Decision trees

Decision trees are a type of machine learning algorithm that can handle binary outcomes as well as categorical or continuous predictors. Decision trees split the data into smaller and more homogeneous groups based on rules derived from the predictors. The final groups are called leaves, and each leaf is assigned a probability of the outcome. Decision trees are easy to visualize and understand, and they can capture non-linear and interactive effects among the predictors. However, decision trees can also suffer from overfitting, instability, and bias.

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Yianni Mercer

Associate Data Scientist | AI & ML Consultant
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Decision trees excel as an alternative to logistic regression due to their ability to model complex, non-linear relationships and provide intuitive visualizations. They adapt to data structure, enhancing flexibility and accuracy for binary outcomes. Their visual representation facilitates interpretation, helping stakeholders gain insights into influential factors and make data-driven decisions. Decision trees offer a versatile and interpretable solution for predicting binary outcomes in various scenarios.

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3 Random forests

Random forests are an extension of decision trees that can improve their performance and accuracy. Random forests are a collection of decision trees that are trained on different subsets of the data and predictors, and then averaged to produce a final prediction. Random forests can reduce the variance and overfitting of decision trees, and they can handle large and complex data sets. However, random forests are also more difficult to interpret and explain than decision trees, and they require more computational resources.

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4 Support vector machines

Support vector machines are another type of machine learning algorithm that can handle binary outcomes as well as linear or non-linear predictors. Support vector machines try to find the best hyperplane that separates the data into two classes, while maximizing the margin between the classes. The margin is the distance between the hyperplane and the closest points from each class, called support vectors. Support vector machines can be very effective and robust, and they can use different kernels to capture non-linear relationships. However, support vector machines are also hard to interpret and tune, and they can be sensitive to outliers and noise.

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Adolfo S.

Analytics Manager | Forecasting, Model Building, Machine Learning, Leadership
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SVMs can be more flexible than logistic regression in handling non-linear relationships between the predictor variables and the outcome, but they can be computationally intensive and require careful tuning of hyperparameters to avoid overfitting. Additionally, SVMs can be sensitive to the choice of kernel function and can require a larger amount of data to train effectively compared to simpler models such as logistic regression. Overall, SVMs are a powerful method for binary classification and can be useful in situations where the data is not linearly separable, but their implementation requires careful consideration of the data and the choice of hyperparameters.

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5 Bayesian methods

Bayesian methods are a general approach to statistical inference that can be applied to binary outcomes as well as any type of predictors. Bayesian methods use prior knowledge and beliefs about the parameters of the model, and update them with the data to produce posterior distributions. Bayesian methods can incorporate uncertainty and variability into the analysis, and they can handle complex and hierarchical models. However, Bayesian methods also require more assumptions and choices, such as the prior distributions and the sampling methods, and they can be computationally intensive and challenging to validate.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Anna Bulina

Data Analyst | Economics Researcher | Educator ? ex-Yandex
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When choosing a model, I usually stick to the 'keep it simple' rule. It may be cool to have Bayesian methods or SVM in your toolkit but starting with good old logistic or probit regression can save you time and make your life easier, especially when it comes to explaining things to your boss. Moreover, logistic regression is a solid baseline for comparing more complex methods.

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What are some alternatives to logistic regression for binary outcomes?

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1 Probit regression

2 Decision trees

3 Random forests

4 Support vector machines

5 Bayesian methods

6 Here’s what else to consider

Regression Analysis

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