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# Hierarchical Linear Modeling

Updated on January 6, 2024
Article byKhalid Ahmed
Edited byShreeya Jain
Reviewed byDheeraj Vaidya, CFA, FRM

## What Is Hierarchical Linear Modeling (HLM)?

Hierarchical Linear Modeling (HLM), also known as Multilevel Modeling (MLM), is a statistical method used for analyzing data that has a nested or hierarchical structure. HLM is a powerful approach for analyzing complex data structures, providing insights into individual and group-level effects simultaneously.

For eg:
Source: Hierarchical Linear Modeling (wallstreetmojo.com)

It aids in modeling the behavior of interest rates, credit risk, and stock prices in accordance with financial hierarchical structure. Moreover, it examines how the elements at different hierarchical levels impact the financial outcome of a company. Researchers use it to account for the hierarchical nature of their data and to understand the sources of variability at different levels of analysis.

### Key Takeaways

• HLM assesses relationships between variables at various hierarchical levels, analyzing their impact on a company’s financial outcomes.
• Various industries utilize it in areas such as education, healthcare, organizational research, social sciences, and financial domains to assess school-level influences, health outcomes, organizational performance, and individual investor behaviors.
• Moreover, it offers benefits in various industries, including handling nested data structures, modeling complex relationships, accounting for group differences, and versatile model definitions.
• These can analyze nested or hierarchical data, while Hierarchical Regression can only analyze data with a single level of observation.

### Hierarchical Linear Modeling Explained

Hierarchical Linear Modeling (HLM) can be defined as multilevel modeling having a statistical approach considering the nested structure of the data. It includes two levels – a higher level and a lower level. Moreover, it models the influence of various variables on the result of interest on the individual scale at a lower level. On the other hand, it models the influence of group-level factors on the desired outcome at a higher level.

Furthermore, it is mainly of great use in financial research since it enables researchers to analyze correlations between variables at many levels of examination within populations or individuals. Therefore, various phenomena of finance, like the connection between executive salaries and company value, as well as how macroeconomic conditions affect stock returns.

In addition, it expands on conventional linear regression models. Thus, it enables the analysis of both within-group plus between-group changes by including random effects at various levels. Hence, the hierarchical linear modeling approach entails estimating random effects, which reflect variability at various levels, and fixed effects, all of which indicate the average associations between variables.

HLM works by dividing the dependent variable‘s overall variance into several components related to each level of analysis. As a result, it is possible to estimate distinct intercepts in addition to slopes for every level, highlighting the distinctive qualities and connections within each group. In comparison to conventional regression models, HLM gives more accurate estimates and minimizes bias by taking into consideration these hierarchical patterns.

These assess individual and group-level factors like industry conditions and investor profiles, unveiling performance-related insights across different levels. It uncovers variations in how interest rates impact large and small financial firms, impacting industry decisions. HLM in finance clarifies outcome-influencing factors by examining individual and group effects on investments, portfolios, and risk management through hierarchical analysis.

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### Examples

Let us use a few examples to understand the topic:

#### Example #1

Researcher Getinet Seifu Walde from the Beijing Institute of Technology employed a two-level Hierarchical Linear Model to assess 361 Ethiopian pupils in a study. According to the study, the collaboration between students and instructors, as well as support from the family, had a good impact on kids’ arithmetic performance. On the other hand, feedback given to the entire class had a detrimental effect.
Gender did not significantly impact achievement.

The examples also illustrate how educators may use it to understand and improve students’ arithmetic performance in secondary schools in Ethiopia.

#### Example #2

Imagine a finance researcher, Jacob, exploring the determinants of financial performance across various investment portfolios within different asset management firms. In this context, Jacob can apply Hierarchical Linear Modeling (HLM) to analyze the nested structure of the data. At Level 1, the units of analysis are individual portfolios, and variables such as portfolio risk, diversification, and historical returns are under consideration. Furthermore, at Level 2, the higher-level units are the asset management firms, and the analysis examines factors such as firm size, investment strategies, and fund manager expertise.

Hence, the HLM approach allows the researcher to assess how individual portfolio characteristics contribute to financial outcomes. While considering the influence of firm-level factors. Random effects at Level 2 capture the variability in financial performance between asset management firms, accounting for unobserved or latent factors affecting the entire firm. Therefore, this modeling technique enables a comprehensive understanding of the factors influencing financial performance at both the portfolio and firm levels. Thus facilitating more nuanced insights for investment strategies and risk management in the finance domain.

### Applications

Various industries, including education, healthcare, organizational research, social sciences, and longitudinal studies, use hierarchical linear modeling (HLM). Therefore, let’s discuss its advantages below:

• Education Research: It is applied to assess school-level influences on student results while considering individual factors.
• Healthcare Research: It helps to assess health outcomes and treatment efficacy; data at the patient and hospital level are analyzed.
• Organizational Research: It aids in investigating the effects of both individual and group factors on organizational outcomes like work performance.
• Social Sciences: It facilitates understanding diverse social processes through the analysis of data involving individuals throughout social groups.
• Longitudinal Studies: In investigations with several time points, modeling changes over time and hierarchical data structures are necessary.
• Financial domain: It finds application in modeling individual investor behaviors and portfolio risk, analyzing investments, asset allocation strategies, plus portfolio performance, and conducting longitudinal financial studies over multiple periods.
• Psychology: Investigating the impact of individual characteristics and group-level factors on psychological well-being, motivation, or other psychological outcomes.

HLM provides a number of benefits and a range of uses in many industries. Listed below are some of them:

• Handling Nested Data Structures: It handles nested data structures, offering a precise representation of hierarchical datasets having within- and between-group effects.
• Modeling Complex Relationships: It provides a thorough knowledge of processes by simulating complicated relationships by looking at interactions between factors at many levels.
• Accounting for Group Differences: It takes into account the differences between groups, producing accurate estimates and preventing bias.
• Efficient Missing Data Management: It efficiently manages missing data through maximum likelihood estimation, which is particularly advantageous in longitudinal studies and situations with high attrition rates.
• Versatile Model Definition: It provides versatility in model definition, allowing for a range of data kinds and research topics and making it adaptable to a variety of study approaches.

Moreover, HLM software plays a crucial role in data analysis. Researchers commonly use HLM software to conduct hierarchical linear modeling in R, Stata, and SPSS. These software tools allow for the exploration of complex hierarchical data structures, making them valuable for various research fields.

### Hierarchical Linear Modeling vs Hierarchical Regression

The table below lists key differences between both statistical techniques, which are used to analyze hierarchical data structures, such as nested or clustered data.

1. When to use hierarchical linear modeling?

Analysis of data having a hierarchical structure, such as pupils nested within schools or workers nested within enterprises, benefits greatly from the usage of hierarchical learning models (HLM). It also suits the desire to examine individual- and group-level predictors concurrently.

2. What software can be used to perform HLM analysis?

For doing HLM analysis, a number of software programs are available, including HLM7, Mplus, and R with packages like lme4 or nlme. These software packages include instruments for defining and estimating HLM models as well as performing other analyses.

3. What are the key steps involved in conducting an HLM analysis?

The main phases in carrying out an HLM analysis include defining the model structure, estimating model parameters using maximum likelihood estimation, evaluating model fit, deciphering fixed and random effects, and carrying out hypothesis testing on model parameters.

4. How does HLM handle nested data structures?

HLM handles the data’s layered structure by including random effects at several levels of analysis. It permits the estimate of both random effects (individual-level departures from the group mean) and fixed effects (group-level predictors).

This article has been a guide to what is Hierarchical Linear Modeling (HLM). We explain its applications, examples, advantages, & comparison with hierarchical regression. You may also find some useful articles here –