Linear Mixed Effects Models are Extensions of Linear Regression models for data that are collected and summarized in groups. The key advantages is the coefficients can vary with respect to one or more group variables.

However, I am struggling with when to use mixed effect model? I will elaborate my questions by using a toy example with extreme cases.

Let's assume we want to model height and weight for animals and we use species as grouping variable.

• If different group / species are really different. Say a dog and elephant. I think there is no point of using mixed effect model, we should build a model for each group.

• If different group / species are really similar. Say a female dog and a male dog. I think we may want use gender as a categorical variable in the model.

So, I assume we should use mixed effect model in the middle cases? Say, the group are cat, dog, rabbit, they are similar sized animals but different.

Is there any formal argument to suggest when to use mixed effect model, i.e., how to draw lines among

• Building models for each group
• Mixed effect model
• Use group as a categorical variable in regression

Linear Mixed Effects Models are Extensions of Linear Regression models for data that are collected and summarized in groups. The key advantages is the coefficients can vary with respect to one or more group variables.

However, I am struggling with when to use mixed effect model? I will elaborate my questions by using a toy example with extreme cases.

Let's assume we want to model height and weight for animals and we use species as grouping variable.

• If different group / species are really different. Say a dog and elephant. I think there is no point of using mixed effect model, we should build a model for each group.

• If different group / species are really similar. Say a female dog and a male dog. I think we may want use gender as a categorical variable in the model.

So, I assume we should use mixed effect model in the middle cases? Say, the group are cat, dog, rabbit, they are similar sized animals but different.

Is there any formal argument to suggest when to use mixed effect model, i.e., how to draw lines among

1. Building models for each group
2. Mixed effect model
3. Use group as a categorical variable in regression

My attempt: Method 1 is the most "complex model" / less degree of freedom and method 3 is the most "simple model" / more degree of freedom. And Mixed effect model is in the middle. We may consider how much data and how complicated data we have to select the right model according to Bais Variance Trade Off.