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  3. Hierarchical and Mixed Effects Models in R
  • 1

    Overview and Introduction to Hierarchical and Mixed Models

    Free

    The first chapter provides an example of when to use a mixed-effect and also describes the parts of a regression. The chapter also examines a student test-score dataset with a nested structure to demonstrate mixed-effects.

  • 2

    Linear Mixed Effect Models

    This chapter providers an introduction to linear mixed-effects models. It covers different types of random-effects, describes how to understand the results for linear mixed-effects models, and goes over different methods for statistical inference with mixed-effects models using crime data from Maryland.

  • 3

    Generalized Linear Mixed Effect Models

    This chapter extends linear mixed-effects models to include non-normal error terms using generalized linear mixed-effects models. By altering the model to include a non-normal error term, you are able to model more kinds of data with non-linear responses. After reviewing generalized linear models, the chapter examines binomial data and count data in the context of mixed-effects models.

  • 4

    Repeated Measures

    This chapter shows how repeated-measures analysis is a special case of mixed-effect modeling. The chapter begins by reviewing paired t-tests and repeated measures ANOVA. Next, the chapter uses a linear mixed-effect model to examine sleep study data. Lastly, the chapter uses a generalized linear mixed-effect model to examine hate crime data from New York state through time.

Initializing

Exercise

Rescaling slopes

The last plot showed changes in crime rate varied by county. This shows you that you should include Year as both a random- and fixed-effect in your model. Including Year this way will estimate a global slope across all counties as well as slope for each county. The fixed-effect slope estimates the change in major crimes across all Maryland counties. The random-effect slope estimates model for that counties have different changes in crime.

But, fitting this model produces a warning message! To address this warning, change Year from starting at 2006 to starting at 0. We provide you with this new variable, Year2 (e.g., 2006 in Year is 0 in Year2). Sometimes when fitting regression, you need to scale or center the intercept to start at 0. This improves numerical stability of the model.

Instructions

100 XP
  • Build a lmer() to predict Crime with Year as both a fixed-effect and random-effect slope and County as the random-effect intercept.
  • Build a second lmer() to predict Crime with Year2 as both a fixed-effect and random-effect slope and County as the random-effect intercept.