LME to estimate Mixed Effect Models in R

In common marketing discussion, a hierarchical model estimates both group level effects and individual differences in effects. Such models are popular in marketing because they provide insight into differences among customers (heterogeneity) and distribution of preference. HLM are exemplified when we estimate the importance of effects for individuals as well as for an overall population. 

Effects that are associated with all observations are known as fixed effects, and those that differ across various grouping levels are known as random effects. 

These models are also known as mixed effect models, because the total effect for each person is composed of the effect for the overall population ( the fixed effect) plus the per-individual (random) effect. 

The difference between estimating hierarchical effects, as opposed to including the grouping variable as a factor in a standard linear model, is that a hierarchical model estimates every specified effect for each individual or group, not only a single adjustment term. 

The formula for a mixed effect model includes a grouping term + (... |group). Common models have a different intercept by group using (1|group) or different intercepts and slopes for predictors within each group using (predictor|group). To estimate an individual level model, the grouping term is typically the respondent identifier. 

Hierarchical model can be used to group observations at other levels than the individual level. For example, we might wish to group by store, advertising campaign, salesperson, or some other factor, if we went o estimate effects that are specific to such a grouping. 

Hierarchical models in marketing are often estimated with Bayesian methods that are able to pool information and produce best estimates of both group and individual effects using potentially sparse data. 

Model coefficients from a hierarchical model are inspected using summaries of the many estimates that are collected in an mcmc object.

library(nlme)
model1<-lme(mathach ~ 1, random = ~ 1 | id, data=hsb)
summary(model1)