5123_Linear_Models

This repository contains shared R code for Group 1 lab assignments, HUDM 5123 Linear Models & Experimental Design, Fall 2021.

Table of Contents

• Course Overview
• Labs
• Sample Data Visualizations
• Useful Code

Course Overview

This course provides an overview of experimental design and analysis from the perspective of the general linear modeling framework. Topics include theory of experimental design, single and multiple factor experiments, between-subject and within-subject designs, factorial and nested designs, random effects, analysis of covariance, and blocking.

Labs

Below are the list topics covered. See lab_code folder for corresponding R code:

• Lab 1: Analysis of Variance (ANOVA) using GLM Framework
• Lab 2: Measures of Effect, Association, and Assumptions for ANOVA
• Lab 3: Pairwise and Complex Contrasts in One-Way ANOVA
• Lab 4: Planned Pairwise Comparisons and Corrections for Type I Error Rate
• Lab 13: One-way Mixed Effects Repeated Measures

Sample Data Visualizations

Lab 1 & 2 - ANOVA and Assumptions

Normal Q-Q Plot

Interaction Plot with Effect Heterogeneity - The interaction plot below shows that different treatments have differential effects on a given outcome variable based on individual's working status. In particular, this plot shows that treatment has a differential effect on the outcome for individuals that are not working, whereas the effect of treatment is not differential for individuals that are working.

Split Plot Design Boxplot with within (angles) and between (age group) factors

Useful Code

Common Functions and Tasks

Create Factors:

dat2$treatmentF <- factor(x = dat2$treatmentstatus, 
                          levels = c(0, 1, 2),
                          labels = c("Control", "Spillover", "Treatment"))

Checking Assumptions

Homoscedasticity of Variance:

# examine variance by group
(vars_p <- by(data = dat2$r2_know_sexual_violence, 
            INDICES = dat2$treatmentF,
            FUN = var, na.rm = TRUE))

# Levene's Test
library(car)
leveneTest(r2_know_sexual_violence ~ treatmentF, data = dat2)

Normality:

# generate full model and use model in Q-Q Plot
lmF <- lm(r2_know_sexual_violence ~ treatmentF,
          data = dat2)
qqPlot(lmF)

Omnibus Test & Pairwise Comparisons

# Omnibus test of the null with one-way ANOVA 
lmF <- lm(r2_know_sexual_violence ~ treatmentF,
          data = dat2)

# Follow up ombnibus with pairwise comparisons
library(emmeans)
emm1 <- emmeans(object = lmF,
                specs = ~ treatmentF)

# for multiple comparisons, control for Type I error rate
# using relevant correction
pairs(x = emm1, 
      adjust = "Tukey")              
                

Mixed Effects Models & Repeated Measures

Within-subjects, repeated measures designs often use wide data formats, especially for calculating variance-covariance and correlations.

dat
library(tidyverse)
# Add an id number
(dat_long <- dat %>% mutate(id = row_number()) %>% relocate(id))
# Transform to long format
dat_long <- 
  dat_long %>% pivot_longer(cols = Day1:Day4, # ?tidyr_tidy_select
                            names_to = "Day", # name of the new factor
                            names_prefix = "Day", # characters to drop from levels
                            values_to = "Weight") # name of the stacked variable
dat_long
print(dat_long, n = Inf)

# Now transform back to wide format.
dat_wide <- dat_long %>% pivot_wider(id_cols = id,
                                     names_from = "Day",
                                     names_prefix = "Day",
                                     values_from = "Weight")
dat_wide              

The packages and code below can be run for a mixed effects framework.

library(lme4)
library(lmerTest)
#random intercept model; we fit a random intercept model based on subject id 
lmer1 <- lmer(Weight ~ Day + (1|id), data = dat_long) 
anova(lmer1)