Models consisting of multiple levels are also referred to as linear mixed, hierarchical, or mixed-effect models. The data structure in real-life situations could be hierarchical or clustered.
Additionally, longitudinal studies present multilevel data, which correlate individuals’ responses over time. Hence, these models have become increasingly popular in analyzing data with repeated measurements or nested data. As their name implies, these models also aim to determine how parameters change over time.
The use of multilevel models can be attributed to several factors. As the units of analysis are treated as independent observations in traditional multiple regression techniques, it is critical to make the proper inferences. Thus, when this occurs, the regression coefficients’ standard errors will be overstated, resulting in a decrease in statistical significance. Multilevel models may improve model co-efficiency to account for clustering by changing the standard error.
Multilevel models allow for residual components at each level with such data hierarchies. One can conceptualize a two-level model for school-based interventions that groups student outcomes by schools and considers residuals at both levels.
Due to their subject-specific nature, mixed effects and multilevel models can also be described as conditional models. Based on these models, researchers can estimate the parameters of each subject or participant. Using a mixed-effects model, researchers can also create a population-level model that is the average of the subject-specific models.
A multivariate model employs multiple variables to estimate the result or outcome. With multivariate models, researchers can experiment with different situations and determine what impact each might have on the outcome. The Monte Carlo simulation is a well-known multivariate model that uses the probability distribution function to show how different things could happen.
A multivariate analysis is a statistical method that incorporates multiple independent variables and multiple dependent variables. A regression model, for instance, is classified based on how an outcome variable is modeled. The outcome variable in linear regression is continuous. In contrast, it is dichotomous in the case of logistic regression, and a time-to-event outcome is recorded in survival analysis.
A multilevel model emphasizes not the number of variables but the level and the relationship between them. In addition to measuring the performance of individual students, performance measures are also calculated for classrooms within which the students are grouped.
In nested data structures, multilevel models are particularly useful for organizing data at multiple levels. Although the analysis units typically are people nested within higher levels, the lowest level of information for multilevel models is generally an individual. Therefore, repeat measurements of people can also be considered.
An ensemble of multiple dependent variables can be considered to form a multivariate model. In essence, it combines the features of both multivariate and multilevel models. Using multivariate analysis in multilevel situations can add complexity. It’s an important technique that allows you to assess the combined impact of a few explicatory variables on various dependent variables.
Kultar Singh – Chief Executive Officer, Sambodhi