What is lmer

Term » Abbr. Filter by: Select category from list Rate it:. Couldn't find the full form or full meaning of LMER? Notify me of new comments via email. Cancel Report. Create a new account. Log In. The unobserved variable is modelled in both the fixed and random parts of a mixed model.

This model can be written as. For generalized mixed models the random effects are assumed to have a normal distribution on the link scale, which results in non normal distributions on the response scale when the link function is non linear, such as with the logit function.

There are text and papers which assume the unobserved random variable is non normally distributed. The lme4 documentation specifies an assumption of normality in the unobserved variable. This may be in addition to an intercept being interpreted as a reference level for other categorical variables in the fixed portion of the model.

Consider the following example which has a single unobserved variable and a single continuous variable. The unobserved variable in this example is sampled twenty times. This means that the variable takes on 20 different values in the data set. This variable could take on many more values, possible infinitely many if the unobserved variable is continuous.

But, we only have information on the twenty sampled levels of the unobserved variable. It is the variance of the single unobserved variable. There is a row and column for each of the twenty sampled values. All non diagonal elements are 0 since the sampled values are assumed to be independent.

A random intercept is an intercept which has a variance from the random component of the model associated with it. A random slope similarly is a slope which has a variance associated with it. Both of these are an estimate which is expected to vary over some population which is represented by a sample in the model.

When a random slope and random intercept are associated with a single population grouping variable one needs to consider if the variance of the intercept and the variance of the slope are correlated. This will be demonstrated in the random slope example. Mixed models formulas are an extension of R formulas.

An unobserved variable is specified in two parts. The first part identifies the intercepts and slopes which are to be modelled as random.

This is done using an R formula expression. A random intercept or slope will be modelled for each term provided in the R formula expression. The second part of the specification identifies the sampled levels. The sampled levels are given by a categorical variable, or a formula expression which evaluates to a categorical variable. The categorical variable given in the random effect specification is the groups identifier for the random effects.

These two parts are placed inside parenthesis, , and the two parts are separated by the bar, " ". The syntax for including a random effect in a formula is shown below. The following are a few examples of specifying random effects.

Each example provides the R formula, a description of the model parameters, and the mean and variance of the true model which is estimated by the regression and observed values. The model variable B identifies a set of groups. The groups of B can be modeled as fixed effects or as a sample from a population. There are two unobserved variables associated with with the population sampled by A.

However, because we use the lmerTest package we do get P-values. The intercept is now 2. In the last column of the Fixed effects table of the output we see the P-values, which indicate all regression coefficients are significantly different from 0.

The results of this output are not given in the book. First and Second Level Predictors We now also in addition to the level 1 variables that were both significant add a predictor variable on the second level teacher experience.

The results show that both the level 1 and level 2 variables are significant. However, we have not added random slopes yet for any variables as is done in table 2. We can now also calculate the explained variance at level 1 and at level 2 compared to the base model. Now we also want to include random slopes. In the third column of Table 2.

To accomplish this in LMER just add the variables for which we want to add random slopes to the random part of the input. We can see that all the fixed regression slopes are still significant. However, no significance test for the Random effects are given, but we do see that the error term Variance for the slope of the variable sex is estimated to be very small 0.

This likely means that there is no slope variation of the SEX variable between classes and therefore the random slope estimation can be dropped from the next analyses. Since there is no direct significance test for this Variance we can use the ranova function of the lmerTest package, which will give us an ANOVA-like table for random effects. It checks whether the model becomes significantly worse if a certain random effect is dropped formally known as likelihood ratio tests , if this is not the case, the random effect is not significant.

As a final step, we can add a cross-level interaction between teacher experience and extraversion since this had a significant random effect, that we might be able to explain. In other words, we want to investigate whether the differences in the relation between extraversion and popularity in the classes can be explained by the teacher experience of the teacher of that class. In this next step to reproduce Model M2 from Table 2. The interaction term is denoted by extrav:texp under Fixed effects and is estimated at From these results we can now also calculate the explained slope variance of extraversion by using teacher experience as second level variable: 0.

So As explained in the book and shown in the results, both the intercept and the slope of the coefficient of extraversion on popularity is influenced by teacher experience. A similar male student will improve its popularity with 0. When teacher experience increases, the intercept also increases with 0. This can be a logical vector, or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included.

All observations are included by default. Should be NULL or a numeric vector. Prior weights are not normalized or standardized in any way. In particular, the diagonal of the residual covariance matrix is the squared residual standard deviation parameter sigma times the vector of inverse weights. Therefore, if the weights have relatively large magnitudes, then in order to compensate, the sigma parameter will also need to have a relatively large magnitude.