lme_alpha.Rmd

---
title: "Modeling Changes in Alpha Diversity over Time"
output:
  workflowr::wflow_html:
    toc: true
editor_options:
  chunk_output_type: console
---

This page contains the investigation of the changes in alpha diversity metrics (Observed and Shannon) over time.

```{r data, include=FALSE, echo=FALSE}
# load packages
source("code/load_packages.R")

# get data
source("code/get_cleaned_data.R")

theme_set(theme_bw())
pal = "Set1"
scale_colour_discrete <-  function(palname=pal, ...){
  scale_colour_brewer(palette=palname, ...)
}
scale_fill_discrete <-  function(palname=pal, ...){
  scale_fill_brewer(palette=palname, ...)
}



```


Here, we investigated how the metrics of alpha diversity changed over time.


## Alpha: Observed OTUs

### Unconditional Model

```{r}
ICC <- function(x){
  icc <- VarCorr(x)[[1]]/(VarCorr(x)[[1]] + sigma(x)**2)
  icc <- lapply(icc, function(x) { attributes(x) <- NULL; x })
  icc <- icc[[1]]
  return(icc)
}

mydata <- microbiome_data$meta.dat %>%
  mutate(intB = ifelse(Intervention=="B", 1,0),
         time = as.numeric(Week) - 1,
         female = ifelse(Gender == "F", 1, 0),
         hispanic = ifelse(Ethnicity %in% c("White", "Asian", "Native America"), 1, 0))

# lmer - for alpha metrics
# unconditional model
fit <- lmer(Observed ~ 1 + (1 | SubjectID),
            data = mydata)
summary(fit)
plot(fit)
ICC(fit)

```

### Fixed Effect of Time

```{r}


fit <- lmer(Observed ~ 1 + time + (1 | SubjectID),
            data = mydata)
summary(fit)
plot(fit)
# plot
dat <- cbind(mydata, fit=predict(fit))
ggplot(dat, aes(time, Observed, group=SubjectID))+
  geom_line(aes(y=fit))+
  geom_point(alpha=0.5)

```

### Fixed and Random effect of Time

```{r}


fit <- lmer(Observed ~ 1 + time + (1 + time || SubjectID),
            data = mydata)
summary(fit)
ranova(fit) # can take out random effect time
plot(fit)

dat <- cbind(mydata, fit=predict(fit))

ggplot(dat, aes(time, Observed, group=SubjectID))+
  geom_line(aes(y=fit))+
  geom_point(alpha=0.5)#+
  #geom_abline(intercept = fixef(fit)[1], slope=fixef(fit)[2],
              #linetype="dashed", size=1.5)

```


### Adding demographics

Time is only a fixed effect.

```{r}


fit <- lmer(Observed ~ 1 + time + female + hispanic + (1 | SubjectID),
            data = mydata)
summary(fit)
ranova(fit)
plot(fit)
ICC(fit)

dat <- cbind(mydata, fit=predict(fit))

ggplot(dat, aes(time, Observed, group=SubjectID, color=Gender))+
  geom_line(aes(y=fit))+
  geom_point(alpha=0.5)

```


### Intervention effect


```{r}


fit <- lmer(Observed ~ 1 + intB + female + hispanic + (1 | SubjectID),
            data = mydata)
summary(fit)
ranova(fit)
plot(fit)
ICC(fit)

dat <- cbind(mydata, fit=predict(fit))

ggplot(dat, aes(time, Observed, group=SubjectID, color=Intervention))+
  geom_line(aes(y=fit))+
  geom_point(alpha=0.5)

```


## Alpha: Shannon Diversity

### Unconditional Model

```{r}

# lmer - for alpha metrics
# unconditional model
fit <- lmer(Shannon ~ 1 + (1 | SubjectID),
            data = mydata)
summary(fit)
plot(fit)
ICC(fit)

```

### Fixed Effect of Time

```{r}


fit <- lmer(Shannon ~ 1 + time + (1 | SubjectID),
            data = mydata)
summary(fit)
plot(fit)
# plot
dat <- cbind(mydata, fit=predict(fit))
ggplot(dat, aes(time, Shannon, group=SubjectID))+
  geom_line(aes(y=fit))+
  geom_point(alpha=0.5)

```

### Fixed and Random effect of Time

```{r}


fit <- lmer(Shannon ~ 1 + time + (1 + time || SubjectID),
            data = mydata)
summary(fit)
ranova(fit) # can take out random effect time
plot(fit)

dat <- cbind(mydata, fit=predict(fit))

ggplot(dat, aes(time, Shannon, group=SubjectID))+
  geom_line(aes(y=fit))+
  geom_point(alpha=0.5)#+
  #geom_abline(intercept = fixef(fit)[1], slope=fixef(fit)[2],
              #linetype="dashed", size=1.5)

```


### Adding demographics

Time is only a fixed effect.

```{r}


fit <- lmer(Shannon ~ 1 + time + female + hispanic + (1 | SubjectID),
            data = mydata)
summary(fit)
ranova(fit)
plot(fit)
ICC(fit)

dat <- cbind(mydata, fit=predict(fit))

ggplot(dat, aes(time, Shannon, group=SubjectID, color=Gender))+
  geom_line(aes(y=fit))+
  geom_point(alpha=0.5)

```


### Intervention effect


```{r}


fit <- lmer(Shannon ~ 1 + intB + time + female +  (1 | SubjectID),
            data = mydata)
summary(fit)
ranova(fit)
plot(fit)
ICC(fit)

dat <- cbind(mydata, fit=predict(fit))

ggplot(dat, aes(time, Shannon, group=SubjectID, color=Intervention))+
  geom_line(aes(y=fit))+
  geom_point(alpha=0.5)

```