Visualizing Maryland crime data

Before fitting a model, plotting the data can be helpful to see if trends or data points jump out, outliers exist, or other attributes of the data require future consideration. Using ggplot2, you can plot lines for county and examine how crimes change through time. For this exercise, examine Maryland crime data (md_crime). This includes the Year, a count of violent Crimes in the county, and the County's name.

To explore this data, first plot the data points for each county through time. This lets you see how each county changes through time. Rather than using an aesthetic such as color, group is used here because there are too many counties to easily distinguish colors. After plotting the raw data, add trend lines for each county.

Both the connect points (geom_line) and trend lines (geom_smooth) provide insight into what, if any, kinds of random effects are required. If all of the points appear to have similar ranges and means, a random-effect intercept may not be important. Likewise, if trends look consistent across counties (i.e., the trend lines look similar or parallel across groups), a random-effect slope may not be required.

This exercise is part of the course

Hierarchical and Mixed Effects Models in R

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Plot the change in crime through time by County
plot1 <- 
	ggplot(data = md_crime, 
           aes(x = ___, y = ___, group = ___)) +
    geom_line() + 
    theme_minimal() +
    ylab("Major crimes reported per county")
print(plot1)

# Add the trend line for each county
plot1 + ___

Edit and Run Code

This exercise is part of the course

Hierarchical and Mixed Effects Models in R

AdvancedSkill Level

4.6+

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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.

Exercise 1: What is a hierarchical model?Exercise 2: Examples of hierarchical datasets Exercise 3: Multi-level student data Exercise 4: Exploring multiple-levels: Classrooms and schools Exercise 5: Parts of a regression Exercise 6: Intercepts Exercise 7: Slopes and multiple regression Exercise 8: Random-effects in regressions with school data Exercise 9: Random-effect intercepts Exercise 10: Random-effect slopes Exercise 11: Building the school model Exercise 12: Interpreting the school model

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.

Exercise 1: Linear mixed effect model- Birth rates data Exercise 2: Building a lmer model with random effects Exercise 3: Including a fixed effect Exercise 4: Random-effect slopes Exercise 5: Uncorrelated random-effect slope Exercise 6: Fixed- and random-effect predictor Exercise 7: Understanding and reporting the outputs of a lmer Exercise 8: Comparing print and summary output Exercise 9: Extracting coefficients Exercise 10: Displaying the results from a lmer model Exercise 11: Statistical inference with Maryland crime data Exercise 12: Visualizing Maryland crime data

Current Exercise

Exercise 13: Rescaling slopes Exercise 14: Null hypothesis testing Exercise 15: Controversies around P-values Exercise 16: Model comparison with ANOVA

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.

Exercise 1: Crash course on GLMs Exercise 2: Logistic regression Exercise 3: Poisson Regression Exercise 4: Plotting GLMs Exercise 5: Binomial data Exercise 6: Toxicology data Exercise 7: Marketing example Exercise 8: Calculating odds-ratios Exercise 9: Count data Exercise 10: Internet click-throughs Exercise 11: Chlamydia by age-group and county Exercise 12: Displaying chlamydia results

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.

Exercise 1: An introduction to repeated measures Exercise 2: Paired t-test Exercise 3: Repeated measures ANOVA Exercise 4: Sleep study Exercise 5: Exploring the data Exercise 6: Building models Exercise 7: Comparing regressions and ANOVAs Exercise 8: Plotting results Exercise 9: Hate in NY state?Exercise 10: Exploring NY hate data Exercise 11: Building the model Exercise 12: Interpreting model results Exercise 13: Displaying the results Exercise 14: Hierarchical models in R review Exercise 15: Conclusion