Explained: What is Multilevel Modeling [+3 Learning Resources]

This comprehensive guide includes everything you, as a beginner, need to know about Multilevel modeling, a technique used to deal with clustered or grouped data.

Multilevel modeling, also known as hierarchical linear modeling, mixed models, and random-effects modeling, finds its use in different domains like medical research, economics, sociology, marketing, educational psychology, and other fields.

Multilevel modeling is also used in the marketing sector for advanced survey analytics, market response modeling, and customer relationship management.

Multilevel Modeling

Multilevel modeling is a technique to manage data in a clustered or group form. This procedure can also be used to analyze the data with repeated measures. The term multilevel indicates hierarchical or nested data, and multilevel analysis means studying the relations between variables measured at different levels of the multilevel data structure.

Let’s consider a scenario. Suppose a nurse has been designated a task to record the blood pressure of a bunch of patients every week. They can consider the succeeding measurements as a group inside each subject.

All in all, multilevel modeling can handle data with different measurement periods from one subject to the next. In machine learning, the multilevel model can be employed in scenarios containing parameters that vary at multiple levels.

Let’s take a deeper dive into the multilevel modeling concepts.

Benefits of Multilevel Modeling

The Multilevel Modeling approach to model the variation between groups offers several advantages.

Make Better Inferences

The regular regression model does not regard the wider population causing underestimation of coefficients and overstatement of coefficient significance. In contrast, Multilevel modeling enables you to make better inferences about the growth curve for the grouped data from which the sample was picked.

Fewer parameters are required

A regular regression model requires several dummy variables to represent a complex data group. In contrast, multilevel modeling needs lesser perimeters for the same.

Group Effects

Multilevel models allow information sharing between groups by assuming that random effects are derived from a common distribution. This, unlike regular regression, greatly improves the prediction accuracy for the groups with fewer data.

Types of Multilevel Modeling

Moving on, let’s discuss the different types of multilevel models.

#1. Random intercepts model

In the Random Intercepts Model, the intercept term can vary across the cluster. One random variable needs to be added to represent the intercept term which helps predict the scores on the dependent variable for each observation.

This model assumes that the slopes remain constant across different contexts and gives information about the intraclass correlations, which plays a pivotal role in determining whether the multilevel model actually needs to be implemented or not.

#2. Random Slopes Model

In the random slopes model, slopes fluctuate with respect to the correlation matrix, and therefore, the slopes tend to differ across grouping variables such as time or individuals.

Here too, the intercepts remain fixed across different contexts. The random slope model or coefficient model helps understand the variability across the groups, which is not possible to determine by the random intercept model alone.

#3. Random intercepts and slopes model

In this model, as the name suggests, both the intercepts and slopes can vary across the groups. It means their value keeps changing in different contexts. The random intercepts and slopes model is considered to be the most realistic type of model.

How does Multilevel Modelling work?

Multilevel models are a type of statistical model that considers multiple levels of variation. These models are also known as hierarchical linear models, linear mixed-effect models, mixed models, nested data models, random coefficients, random-effects models, random parameter models, or split-plot designs.

Different types of data collected from observations made during human research and biological sciences depict a hierarchical or clustered structure.

For instance, children having the same biological parents possess similar physical and mental characteristics more than randomly chosen individuals from a broader population.

Similarly, employees or students can be segregated based on Individual factors like location. The individual actions linked progressively also result in multilevel data structures.

Multilevel models consider residual elements at each level within the hierarchical structure to result in the formation of a hierarchical data structure.

The layered models also assist the school authorities in arranging the outcomes of students, which commonly includes the residuals for both the school and student levels.

For the uninitiated, school residuals, or school-related effects, are a collection of unobserved school characteristics that can influence the students’ outcomes. These effects can trigger the relationship between the outcomes of students. Hence it becomes safe to split the variance of residuals into two parts: a between-school component and a within-school component.

When should you use Multilevel Modeling?

Here are some reasons why you should prefer using multilevel models:

Make Correct inferences

In standard methods of multiple regression, the unit of analysis is considered an independent observation.

The incompetence of multiple regression to recognize hierarchical structures causes an underestimation of the normal errors, leading to an overestimation of statistical significance. The omission of grouping largely affects the accuracy of predictions for high-level predictor variables.

Inference to a population of groups

The multilevel model treats the groups in the sample as a random sample picked from a group, which serves as an important area of research in several instances. This cannot be accomplished by the fixed effects model, where it is impossible to make inferences beyond the groups in the sample.

Evaluating group effects

Multilevel modeling is the best method to determine the separate effects on observations and unobserved characteristics of the group.

Substantive interest in group effects

In several research areas, a key question concerns the extent of grouping in individual outcomes and the determination of its existence in ‘outlying’ groups.

For instance, in school performance reviews, the key focus is identifying the ‘value-added’ school-related effects on student performance. This can be determined by a multilevel model after adjusting the prior accomplishments.

Learning Resources

Here are the best learning materials you can refer to for understanding the concepts of multilevel modeling.

#1. Multilevel Modeling in Plain Language

Multilevel Modeling in Plain Language by Karen Robson and David Pavalin is one of the best books about multilevel modeling as it presents the complete phases of a multilevel analysis for both students and instructors.

The “plain approach” of the book helps the reader to grasp the idea behind the subject rather than explaining the formula found in other learning materials. Likewise, educators will be able to catch up on the advanced path of multilevel analysis very quickly.

#2. Multilevel Analysis: An Introduction To Multilevel Modeling

Authored by T. A. B. Snijders, Multilevel Analysis: An Introduction To Basic And Advanced Multilevel Modeling delivers accessible content on multilevel analysis tailored to meet the requirements of advanced researchers and teachers wanting to conduct research in the same field.

Apart from that, readers looking to expand their knowledge in the field of multilevel analysis will find the book an ideal resource.

The book comprises the different methods, techniques, and issues revolving around multilevel modeling and analysis and provides the readers with a clear, conceptual, and practical understanding of multilevel studies.

#3. Multilevel Modeling Using R

Multilevel Modeling Using R by W. Holmes Finch, Jocelyn E. Bolin, and Ken Kelley is a valuable guide about multilevel data modeling using the R software environment. The book reviews and presents the basics of multilevel models and explains how to implement these models using R.

It also demonstrates the process of employing multilevel modeling with longitudinal data. Apart from this, you will also find the models for categorical dependent variables in both single-level and multilevel data.

Wrapping Up

Here we have covered the basic concepts of multilevel modeling, from its benefits, to how the technique works. If you are a student or an educator, the learning materials mentioned above will offer valuable help in understanding the advanced concepts of multilevel modeling.

You may also explore some top machine learning models.