The terms in LME i.e. fixed and random create confusion? What is the genesis that can distinguish between the two ?
I do not know much about statistics but I will try my best to explain.
First, random effects are defined as the factors (categories) in the population that we are not aware of (not observed), so we are randomly sampling levels of those factors when we sample the population.
Practically speaking, random effects can be found when there are hierarchical structures in the data. For example, we want to compare the relationship between students' SAT score and their college admission rates. You might just want to run a simple linear regression. But there might be some structure in the data that is hidden. For example, the students can be grouped into classes, and then schools. You can also group students by the social-economic status of their parents.
The idea is that students belonging to different categories may have different college admission rates even if they have the same SAT score. Therefore, it is important to consider some of these "random effects" when building your model.
Linear regression hypothesis is that effect of a variable is comprised as a constant component plus variability. In other words, the independent variable (s) is deemed to reflect a fixed (constant) part - determined as population effect size - and a variable part - random effect. Further, the term - Linear Mixed(regression)model is used to reflect use of continuous variables and nominal variables acting as independent variables that influence the dependent variable. THE CONTINUOUS VARIABLE is comprised of population effect size - and a variable part - random effect . The nominal or categories based variable effect is probabilistic and we use the term probabilistic variable for such variables. Sometimes academics mistakenly call its effect on dependent variable as random effect. Finally, this may be noted that principles of ANOVA and probability have been combined to formulate linear Mixed effects models.