Can Logistic Regression Be Performed with a Sample Size of 100?

Logistic regression is a powerful statistical method used to model the relationship between one or more independent variables and a binary outcome variable. It is often used in fields such as healthcare, social sciences, and business analytics. The question often arises whether this method can be applied when the sample size is as small as 100. This article explores the considerations and limitations associated with using logistic regression in such scenarios.

Considerations for Using Logistic Regression with a Sample Size of 100

When dealing with a sample size of 100, several factors need to be taken into account to ensure the reliability and validity of the results. These factors include the number of predictor variables, the event rate, model complexity, and the statistical power of the analysis.

Number of Predictor Variables

Logistic regression requires a sufficient number of observations relative to the number of predictor variables to ensure reliable estimates. A common rule of thumb is to have at least 10 events per predictor variable. This rule is particularly important if the outcome is rare. Therefore, with a sample size of 100, the number of predictor variables you can include is limited if the event rate is low.

Event Rate

The proportion of the outcome variable, often denoted as the event rate, can significantly impact the stability and reliability of the model. For example, if the event rate is very low, the estimates may be less reliable, leading to potential issues in identifying meaningful relationships. This is especially true with a smaller sample size, where the variability of estimates is higher.

Model Complexity

To improve the robustness of the results, it is advisable to keep the model relatively simple, with fewer predictor variables. This approach helps to reduce the risk of overfitting, where the model fits the training data too closely and performs poorly on new, unseen data. Simplifying the model can also help to ensure that the results are generalizable and reliable.

Statistical Power

A sample size of 100 may limit the statistical power of the analysis, especially if the goal is to detect small effects. Statistical power is the probability that the test will correctly reject the null hypothesis when the alternative hypothesis is true. With lower statistical power, the likelihood of identifying true relationships is reduced, leading to potential false negatives. Therefore, when working with a smaller sample size, it is important to be cautious about the ability to detect meaningful associations.

In conclusion, while logistic regression can be performed with a sample size of 100, careful consideration must be given to the number of predictor variables, the event rate, model complexity, and statistical power. By adhering to these considerations, researchers can enhance the reliability and validity of their results.

Alternatives and Solutions

In situations where the sample size is limited and the number of features is relatively large, alternative strategies can be employed. These include the use of regularization techniques, such as L1 or L2 regularization, to penalize the complexity of the model and prevent overfitting. Cross-validation can be used to tune the regularization parameters effectively.

Another approach is feature selection, which involves identifying the most relevant predictors for the model. While feature selection can improve model performance, there is a risk of overfitting if the data is small. Therefore, it is crucial to apply robust validation techniques, such as "leave-one-out" cross validation and bootstrapping methods, to assess the out-of-sample error and model robustness.

In summary, while it is possible to conduct logistic regression with a sample size of 100, researchers must carefully consider the number of predictors, the event rate, and the model complexity. Additionally, employing strategies such as regularization and feature selection can help improve the reliability and generalizability of the results. By following these guidelines, researchers can ensure that their logistic regression models are both valid and meaningful.