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The terms in LME i.e. fixed and random create confusion? What is the genesis that can distinguish between the two ?

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  • $\begingroup$ A dog's response to medicine may depend on number of days it is sick and its sex or breed. $\endgroup$ – Subhash C. Davar Mar 24 at 7:21
  • $\begingroup$ LME assumes two components- fixed and random. Fixed effect (mean) is constant and consistent. THE random part shows a number of variables that influence the dependent effect-size individually. $\endgroup$ – Subhash C. Davar Mar 24 at 23:49
  • $\begingroup$ In case, we have predictor variables of continuous as well as nominal(or level-type 2 or 3) categories data, it becomes necessary to use linear as well as non-linear (probabilistic) models. Therefore, Mixed models convey use of two types of models - linear and non-linear. Nonlinear models work under probability and linear models perform under fixed effect plus random effects. The goof up is Mixed model. $\endgroup$ – Subhash C. Davar Mar 25 at 1:53
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    $\begingroup$ stats.stackexchange.com/questions/4700/… $\endgroup$ – StupidWolf Mar 25 at 15:11
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    $\begingroup$ Maybe worth reading the link and the article above.. I have no idea where this question is going without a context, and what is its relevance to bioinformatics? $\endgroup$ – StupidWolf Mar 25 at 15:11
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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.

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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.

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