Difference between Linear Mixed Models and Classic Linear Models

The Linear Mixed Models (LMMs) and Classic Linear Models (CLMs) are both statistical models used to analyze data with continuous dependent variables. However, they differ in terms of their assumptions and the types of data they can handle.

• Assumptions: the CLMs assume that the data points are independent of each other, whereas LMMs relax this assumption by allowing for correlated data points. LMMs account for the correlation structure among observations by including random effects in the model.
• Handling of correlated data: the CLMs are suitable for analyzing independent data or data where the correlation structure is not of interest. LMMs, on the other hand, are specifically designed to handle correlated data, such as longitudinal or repeated measures data, where observations within the same group or subject are likely to be correlated.
• Incorporation of random effects: the LMMs incorporate random effects in addition to the fixed effects. Random effects capture the variability between different groups or subjects in the data and allow for the estimation of group-level or subject-level effects. CLMs only include fixed effects, which represent the average effects across all groups or subjects.
• Flexibility in modeling: the LMMs provide more flexibility in modeling complex data structures and can handle nested or crossed random effects. They can account for within-group or within-subject variability, as well as between-group or between-subject variability. CLMs, on the other hand, are more straightforward and assume that the fixed effects are constant across all groups or subjects.

Linear mixed models (LMMs) are statistical models that are used to analyze data with both fixed and random effects. They are particularly useful when analyzing data with hierarchical or nested structures, such as longitudinal or clustered data. In R Programming Language, the lme4 package provides a comprehensive framework for fitting and interpreting linear mixed models.