## What is random intercept model?

A random intercepts model is a model in which intercepts are allowed to vary, and therefore, the scores on the dependent variable for each individual observation are predicted by the intercept that varies across groups. This model assumes that slopes are fixed (the same across different contexts).

**What is a LME model?**

2.0. The Mathematical Model Defined. As mentioned in Section 1, the LME model is an extention of a basic linear model. Recall the model for a simple linear regression: Yi=β0+β1xi+ϵi.

### What is the linear mixed effects LME model?

Linear mixed models are an extension of simple linear models to allow both fixed and random effects, and are particularly used when there is non independence in the data, such as arises from a hierarchical structure. For example, students could be sampled from within classrooms, or patients from within doctors.

**What is a random effect in a model?**

In statistics, a random effects model, also called a variance components model, is a statistical model where the model parameters are random variables. In econometrics, random effects models are used in panel analysis of hierarchical or panel data when one assumes no fixed effects (it allows for individual effects).

#### What is a two level model?

Multilevel models recognise the existence of such data hierarchies by allowing for residual components at each level in the hierarchy. For example, a two-level model which allows for grouping of child outcomes within schools would include residuals at the child and school level.

**What does Ranef mean in R?**

ranef: Extract the modes of the random effects A generic function to extract the conditional modes of the random effects from a fitted model object. For linear mixed models the conditional modes of the random effects are also the conditional means.

## How do you read mixed model results?

Interpret the key results for Fit Mixed Effects Model

- Step 1: Determine whether the random terms significantly affect the response.
- Step 2: Determine whether the fixed effect terms significantly affect the response.
- Step 3: Determine how well the model fits your data.

**What is a random effect in a mixed model?**

Random effects factors are fields whose values in the data file can be considered a random sample from a larger population of values. They are useful for explaining excess variability in the target.

### Why do we use random effects?

Random effects are especially useful when we have (1) lots of levels (e.g., many species or blocks), (2) relatively little data on each level (although we need multiple samples from most of the levels), and (3) uneven sampling across levels (box 13.1).

**Why is random effects more efficient?**

The random effects estimator allows us to look at variables that vary over time as well as those that do not. As a result, the random effects model is more efficient. While random effects is more efficient than fixed effects, problems often arise that make it not applicable as a model.

#### How to make a mixed model in R using lme4?

install.packages(“lme4”) Select a server close to you. After installation, load the lme4 package into R with the following command: library(lme4) Now, you have the function lmer() available to you, which is the mixed model equivalent of the function lm() in tutorial 1. This function is going to construct mixed models for us.

**How do I include random intercepts in a model with therapists?**

I am specifying a model with data that includes observations within subjects within therapists. We include a random intercept for subjects and one for therapists. The syntax for the random effects looks like this: /REPEATED=time | SUBJECT (ther*subject) COVTYPE (AR1).

## Can I model heteroscedastic residual variance at Level 1 in LME?

Subjects in the wait-list will not be nested, but subjects in treatment group will be nested within therapists. Only lme allows modeling heteroscedastic residual variance at level 1.

**What makes the mixed model a mixed model?**

The mixture of fixed and random effects is what makes the mixed model a mixed model. Our updated formula looks like this: pitch ~ politeness + sex + (1|subject) + ε