What Is Statistical Modeling? When and Where to Use It

You can interpret data in multiple ways.

It helps you understand datasets and create reports while applying multiple statistical models to make predictions.

Statistical models are a mathematical representation of observed data that helps analysts and data scientists visualize the relationships and patterns between datasets. Moreover, it provides them with a solid foundation to forecast and project data for the foreseeable future.

Simply put, models are relationships between two variables. For example, the term “model mouse weight and size” means establishing a relationship between them. With the size, the weight also increases. Applying statistical modeling in this example allows you to understand the relationship between size and weight, helping you better analyze datasets.

This is a simple example. Enterprises use statistical analysis software for performing complex statistical modeling.

Statistical modeling helps project data so that non-analysts and other stakeholders can base their decisions on it. In statistical modeling, data scientists look for patterns. They use these patterns as a sample and make predictions about the whole set.

As you implement statistical models, start identifying the best models that fit your purpose. Adopting these models would enable you to perform analysis and generate better data visualizations.

Purpose of statistical modeling

Statistical models help understand the characteristics of known data and estimate the properties of large populations based on it. It’s the central idea behind machine learning.

It allows you to find an error bar or confidence interval based on sample size and other factors. For example, an estimate X calculated from 10 samples would have a wider confidence interval than an estimate Y calculated from 10000 samples.

Statistical modeling also supports hypothesis testing. It provides statistical evidence for the occurrence of specific events.

Where are statistical models used?

Statistical models are used in data science, machine learning, engineering, or operations research. These models have various real-world applications.

• Spatial modeling works with a graphical information system (GIS) and establishes a relationship between processes and properties within a geographic space. It helps researchers understand and predict real-world phenomena and plan effectively.
• Survival analysis observes the time duration in which a series of events occurs. Depending on the study area, survival analysis is also known as reliability analysis, duration modeling, or event history analysis. These models are used to predict time-to-event (TTE). For example, survival analysis answers questions like how long it takes to fire the first bullet after purchasing a gun.
• Time series analysis involves investigating a series of data points that occur successively over time. It provides insights into factors that influence certain events from time to time.
• Recommendation systems predict a user’s choice or preference for an item and the ratings they’re likely to give. 
• Market segmentation creates different market fragments based on potential buyers’ needs, preferences, and priorities. Statistical modeling helps marketers identify relevant market segments to better position their products and focus on target groups.
• Association rule learning enables the discovery of interesting relationships between variables in large databases. It’s used in threat detection, where association rules allow cybersecurity specialists to detect fraud.
• Predictive modeling helps researchers predict the results or outcomes of an event, regardless of when it happens. These models are often used to predict the weather or stock market prices, detect crimes and identify suspects.
• Scoring models are based on logistic regression and decision trees. Investigators use them in combination with multiple algorithms to detect credit card fraud.
• Clustering, or a cluster model, groups items into a cluster so that there are more similarities within the group than other items across different groups.

Statistical modeling vs. mathematical modeling

Although statistical and mathematical modeling help professionals understand relationships between data sets, they’re not the same.

Mathematical modeling involves transforming real-world problems into mathematical models that you can analyze to gain insights. It uses static models formulated from real-world situations, making it less flexible.

On the flip side, statistical models aided by machine learning are comparatively more flexible in including new patterns and trends.

Statistical modeling vs. machine learning

Statistical modeling and machine learning are not the same. Machine learning (ML) involves developing computer algorithms to transform data into intelligent actions, and it doesn’t rely on rule-based programming.

Before trusting an outcome of statistical analysis, all assumptions need to be satisfied. It makes the uncertainty tolerance low. Unlike statistical analysis, machine learning concepts don’t rely on assumptions. ML models are more flexible.

Moreover, statistical models work with finite data sets and a reasonable number of observations. Increasing the data might lead to overfitting (when statistical models fit against its training data). On the contrary, machine learning models need vast amounts of data to learn and perform intelligent actions.

When should you use statistical modeling?

You can use statistical models when most assumptions are satisfied while building the model and the uncertainty is low. 

For example, when a content marketing agency wants to build a model to track an audience’s journey, they’ll likely prefer a statistical model with 8-10 predictors. Here, the need for interpretability is higher than the predictions’ accuracy as it would help them develop an engagement strategy based on business domain knowledge.

When should you use machine learning?

Machine learning models are used to analyze a large volume of data, and the predicted outcome doesn’t have a random component. For example, in visual pattern recognition, an object must be an ‘E,’ not an ‘E’.

For example, when e-commerce websites such as Amazon want to recommend products based on previous purchases, they need a powerful recommendation engine. Here, the need for predictive accuracy is more important than the model’s interpretability, making the machine learning model an appropriate choice.

Statistical modeling techniques

Data is at the heart of creating a statistical model. You can source this data from a spreadsheet, data warehouse, or a data lake. Knowledge of data structure and management would help you fetch data seamlessly. You can then analyze it using common station statistical data analysis methods categorized as supervised learning and unsupervised learning. 

Supervised learning techniques include:

• A regression model: Used for analyzing the relationship between a dependent and an independent variable. It’s a common predictive statistical model that analysts use in forecasting, time series modeling, and identifying causal effect relationships between variables. There can be different types of regression models, such as simple linear regression and multiple linear regression.
• A classification model: An algorithm that analyzes existing, large, and complex datasets to understand and classify them accordingly. It’s a machine learning model that includes decision trees, nearest neighbor, random forest, and neural networks used in artificial intelligence.

Companies can also use other techniques such as re-sampling methods and tree-based methods in statistical data analysis.

Unsupervised learning techniques include:

• Reinforcement learning: A deep learning concept that iterates and trains the algorithm to learn an optimal process by rewarding favorable outcomes and penalizing steps that produce adverse outcomes
• K-means clustering: Assembles a specified number of data points in clusters based on certain similarities
• Hierarchical clustering: Helps develop a multi-level hierarchy of clusters by creating a cluster tree

How to build statistical models

While building a statistical model, the first step is to choose the best statistical model based on your requirements.

You can choose the best model for your purpose once you have answered all of the above questions. After selecting the statistical model, you can start with descriptive statistics and graphs. Visualize the data as it’ll help you recognize errors, understand variables and their behavior. Observe how related variables work together by building predictors and see the outcome when datasets are combined.

You should understand the relationship between potential predictors and their correlation with the outcomes. Keep track of outcomes with or without control variables. You can eliminate non-significant variables at the beginning and keep all variables involved in the model. 

You can keep primary research questions in check while understanding existing relationships between variables, testing and categorizing every potential predictor. 

Organizations can leverage statistical modeling software to collect, organize, examine, interpret, and design data. This software comes with data visualization, modeling, and mining capabilities that help automate the entire process.

Model datasets to predict future trends

Employ statistical modeling to understand the relationships between datasets and how changes in them would affect others. After analyzing this relationship, you can understand the current state and make future predictions. 

With proper statistical modeling, you can interpret the relationship between variables and leverage the insights to predict variables you’d change or influence to get the expected outcome in the future.

Learn more about statistical analysis and find better ways to make business decisions using present data.