15-exercise_diet.Rmd

# MLM, Longitudinal: RCT - Exercise and Diet

```{r, message=FALSE, error=FALSE}
library(tidyverse)    # all things tidy
library(pander)       # nice looking genderal tabulations
library(furniture)    # nice table1() descriptives
library(texreg)       # Convert Regression Output to LaTeX or HTML Tables
library(psych)        # contains some useful functions, like headTail
library(performance) # ICC calculations
library(interactions)
library(sjPlot)       # Visualization for Models
library(effects)      # Effec displays for Models

library(lme4)         # non-linear mixed-effects models
```

## The dataset

This comes from a **Randomized Controled Trial**.

```{r}
data_raw <- read.table("https://raw.githubusercontent.com/CEHS-research/data/master/MLM/exercise_diet.txt",
                  header = TRUE, 
                  sep = ",")
```

```{r}
tibble::glimpse(data_raw)
```



```{r}
data_long <- data_raw %>% 
  dplyr::mutate(id = id %>% factor) %>% 
  dplyr::mutate(exertype = exertype %>% 
                  factor(levels = 1:3,
                         labels = c("At Rest",
                                    "Leisurely Walking",
                                    "Moderate Running"))) %>% 
  dplyr::mutate(diet = diet %>% 
                  factor(levels = 1:2,
                         labels = c("low-fat",
                                    "non-fat"))) %>% 
  dplyr::mutate(time_min = time / 60)
```




```{r}
data_long %>% 
  psych::headTail(top = 10, bottom = 10) %>% 
  pander::pander(caption = "Raw Data")
```

## Exploratory Data Analysis

### Participant Summary

In this experiment, both exercise (`exertype`) and diet (`diet`) were randomized at the subject level to create a 2x3 = 6 combinations each with exactly 5 participants.

```{r, results='asis'}
data_long %>% 
  dplyr::filter(time == 0) %>% 
  dplyr::group_by(exertype) %>% 
  furniture::table1("Diet, randomized" = diet, 
                    caption = "Participants",
                    output = "markdown")
```

### Baseline Summary



```{r}
data_long %>% 
  dplyr::filter(time == 0) %>% 
  dplyr::group_by(exertype, diet) %>% 
  dplyr::summarise(mean = mean(pulse)) %>% 
  dplyr::ungroup() %>% 
  tidyr::pivot_wider(names_from = diet,
                     values_from = mean) %>% 
  pander::pander(caption = "Baseline Pulse, Means")
  
```

### Raw Trajectories - Person Profile Plot

#### Connect the dots

```{r}
data_long %>% 
  ggplot(aes(x = time_min,
             y = pulse)) +
  geom_point() +
  geom_line(aes(group = id)) +
  facet_grid(diet ~ exertype) +
  theme_bw()
```

#### Loess - Moving Average Smoothers

```{r}
data_long %>% 
  ggplot(aes(x = time_min,
             y = pulse,
             color = diet)) +
  geom_line(aes(group = id)) +
  facet_grid(~ exertype) +
  theme_bw() +
  geom_smooth(method = "loess",
              se = FALSE,
              size = 2,
              span = 5) +
  theme(legend.position = c(0.08, 0.85),
        legend.background = element_rect(color = "black")) +
  labs(title = "Raw Pulse Trajectories",
       subtitle = "By Exercise and Diet Groupings",
       x = "Time (Minutes Post-Baseline)",
       y = "Pulse (Beats per Minute)",
       color = "Diet Plan")
```




## Multilevel Modeling

### Null Model

```{r}
fit_lmer_0re <- lmerTest::lmer(pulse ~ 1 + (1 | id),
                               data = data_long)
```


```{r, results='asis'}
texreg::knitreg(fit_lmer_0re, single.row = TRUE)
```

### ICC & R-squared

```{r}
performance::icc(fit_lmer_0re)
```


```{r}
performance::r2(fit_lmer_0re)
```


### Add fixed effects: level specific

#### Fit nested models

```{r}
# Null Model (random intercept only)
fit_lmer_0ml <- lmerTest::lmer(pulse ~ 1 + (1 | id),
                               data = data_long,
                               REML = FALSE)

# Add quadratic time
fit_lmer_1ml <- lmerTest::lmer(pulse ~ time_min + I(time_min^2) + (1 | id),
                               data = data_long,
                               REML = FALSE)

# Add main effects for 2 interventions (person-specific, i.e. level-2 factors)
fit_lmer_2ml <- lmerTest::lmer(pulse ~ diet + exertype + time_min + I(time_min^2) + (1 | id),
                               data = data_long,
                               REML = FALSE)

# Add interaction between level-2 factors
fit_lmer_3ml <- lmerTest::lmer(pulse ~ diet*exertype + time_min + I(time_min^2) + (1 | id),
                               data = data_long,
                               REML = FALSE)

# Add exercise interacting with [time & time-squared]
fit_lmer_4ml <- lmerTest::lmer(pulse ~ diet*exertype + exertype*time_min + exertype*I(time_min^2) + (1 | id),
                               data = data_long,
                               REML = FALSE)

# Add diet interacting with [time & time-squared]
fit_lmer_5ml <- lmerTest::lmer(pulse ~ diet*exertype*time_min + diet*exertype*I(time_min^2) + (1 | id),
                               data = data_long,
                               REML = FALSE)
```


```{r, results='asis'}
texreg::knitreg(list(fit_lmer_1ml, 
                     fit_lmer_2ml, 
                     fit_lmer_3ml, 
                     fit_lmer_4ml, 
                     fit_lmer_5ml))
```

#### Evaluate Model Fit, i.e. variable significance

```{r}
anova(fit_lmer_1ml, 
      fit_lmer_2ml, 
      fit_lmer_3ml, 
      fit_lmer_4ml, 
      fit_lmer_5ml)
```

```{r}
performance::compare_performance(fit_lmer_1ml, 
                                 fit_lmer_2ml, 
                                 fit_lmer_3ml, 
                                 fit_lmer_4ml, 
                                 fit_lmer_5ml,
                                 rank = TRUE)
```



### Final Model

Refit via REML

```{r}
fit_lmer_5re <- lmerTest::lmer(pulse ~ diet*exertype*time_min + 
                                 diet*exertype*I(time_min^2) + (1 | id),
                               data = data_long,
                               REML = TRUE)
```


#### Visualize

```{r}
sjPlot::plot_model(fit_lmer_5re,
                   type = "pred",
                   terms = c("time_min", "diet", "exertype"))
```

```{r}
interactions::interact_plot(fit_lmer_5re,
                            pred = time_min,
                            modx = diet,
                            mod2 = exertype,
                            interval = TRUE)
```




```{r}
effects::Effect(focal.predictors = c("diet", "exertype", "time_min"),
                mod = fit_lmer_5re) %>% 
  data.frame %>% 
  ggplot(aes(x = time_min,
             y = fit,
             fill = diet,
             color = diet)) +
  geom_line(size = 1.5) +
  theme_bw() +
  facet_grid(~ exertype) +
  theme(legend.position = c(0.08, 0.85),
        legend.background = element_rect(color = "black")) +
  labs(title = "Raw Pulse Trajectories",
       subtitle = "By Exercise and Diet Groupings",
       x = "Time (Minutes Post-Baseline)",
       y = "Estimated Marginal Mean\nPulse (Beats per Minute)",
       fill = "Diet Plan",
       color = "Diet Plan")
```


```{r}
effects::Effect(focal.predictors = c("diet", "exertype", "time_min"),
                mod = fit_lmer_5re,
                xlevels = list("time_min" = seq(from = 0, 
                                                to   = 12, 
                                                by   = 0.5))) %>% 
  data.frame %>% 
  dplyr::mutate(diet = fct_rev(diet)) %>%  # reverse the order of the levels
  ggplot(aes(x = time_min,
             y = fit)) +
  geom_ribbon(aes(ymin = fit - se,
                  ymax = fit + se,
                  fill = diet),
              alpha = 0.3) +
  geom_line(aes(linetype = diet),
                size = 1) +
  theme_bw() +
  facet_grid(~ exertype) +
  theme(legend.position = c(0.12, 0.85),
        legend.background = element_rect(color = "black"),
        legend.key.width = unit(2, "cm")) +
  labs(title = "Raw Pulse Trajectories",
       subtitle = "By Randomized Exercise and Diet Intervention",
       x = "Time (Minutes Post-Baseline)",
       y = "Estimated Marginal Mean\nPulse (Beats per Minute)",
       fill = "Diet Plan",
       color = "Diet Plan",
       linetype = "Diet Plan") +
  scale_fill_manual(values = c("black", "gray50")) +
  scale_linetype_manual(values = c("solid", "longdash")) +
  scale_x_continuous(breaks = seq(from = 0, to = 14, by = 5))
```