Multiplot Layout

The multiplot function allows for multiple visualizations to be added into a single image. The multiplot function for ggplot2 was taken from the Winston Chang. (2017). Cookbook for R. http://www.cookbook-r.com/.

#Layout
multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) {
  # Make a list from the ... arguments and plotlist
  plots <- c(list(...), plotlist)
  
  numPlots = length(plots)
  
  # If layout is NULL, then use 'cols' to determine layout
  if (is.null(layout)) {
    # Make the  panel
    # ncol: Number of columns of plots
    # nrow: Number of rows needed, calculated from # of cols
    layout <- matrix(seq(1, cols * ceiling(numPlots/cols)),
                     ncol = cols, nrow = ceiling(numPlots/cols))
  }

  if (numPlots==1) {
    print(plots[[1]])
    
  } else {
    # Set up the page
    grid.newpage()
    pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))
    
    # Make each plot, in the correct location
    for (i in 1:numPlots) {
      # Get the i,j matrix positions of the regions that contain this subplot
      matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))
      
      print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row,
                                      layout.pos.col = matchidx$col))
    }
  }
}

Visualization themes and parameters

Before visualizing the results, ggplot2 package themes are set. A categorical color palettes is generate using the colorspace package. Labels used for the student groups based on certificate status.

#Theme for ggplot2
theme_set(theme_light())

##Color Scales and setting for graphs
strip <- c("#DCDCDC") #Grey

#Pink/Orange/Yellow
pal2 <- function (n, h = c(-83, 43), c. = c(100, 43), l = c(56, 86), 
                  power = c(0.166666666666667, 0.9), fixup = TRUE, gamma = NULL, 
                  alpha = 1, ...) 
                    {
                      if (!is.null(gamma)) 
                        warning("'gamma' is deprecated and has no effect")
                      if (n < 1L) 
                        return(character(0L))
                      h <- rep(h, length.out = 2L)
                      c <- rep(c., length.out = 2L)
                      l <- rep(l, length.out = 2L)
                      power <- rep(power, length.out = 2L)
                      rval <- seq(1, 0, length = n)
                      rval <- hex(polarLUV(L = l[2L] - diff(l) * rval^power[2L], 
                                           C = c[2L] - diff(c) * rval^power[1L], H = h[2L] - diff(h) * 
                                             rval), fixup = fixup, ...)
                      if (!missing(alpha)) {
                        alpha <- pmax(pmin(alpha, 1), 0)
                        alpha <- format(as.hexmode(round(alpha * 255 + 1e-04)), 
                                        width = 2L, upper.case = TRUE)
                        rval <- paste(rval, alpha, sep = "")
                      }
                      return(rval)
                    }

#Color Scales for Student Certification Cohort Assignments
stdColors <- pal2(3)

##Label groups
#Certification Groups
userGrps <- as_labeller(c('unq_stu_per' = paste0("All students (", length(students$user_id)," students)"),
                           'unq_stu_per.1'  = paste0("Certificate granted, grades between 100%-70% (",
                                                     length(students[students$grade>=.7,]$user_id)," students)"),  
                           'unq_stu_per.2'  = paste0("No certification but active, with grades less than 70% (",
                                                     length(students[students$grade<.7,]$user_id)," students)")))
userGrps2 <- as_labeller(c('unq_stu_per' = paste0("All students\n(", length(students$user_id)," students)"),
                          'unq_stu_per.1'  = paste0("Certificate granted\n(",
                                                    length(students[students$grade>=.7,]$user_id)," students)"),  
                          'unq_stu_per.2'  = paste0("No certification active\n(",
                                                    length(students[students$grade<.7,]$user_id)," students)")))

6A Student Grades and Number of Events

#6A Grades vs Events (Unq.)
m <- glm(grade ~ poly(events,3), data = students[students$grade>0,])
eq <- substitute(italic(y) == b %.%italic(x)^3* c %.%italic(x)^2* + d %.%italic(x)* + a*","~~italic(r)^2~"="~r2,
                 list( a=format(coef(m)[1], digits=3), 
                       b=format(coef(m)[2], digits=3),
                       c=format(coef(m)[3], digits=3),
                       d=format(coef(m)[4], digits=3),
                       r2=format(1-(m$deviance/m$null.deviance), digits = 3)))
p4 <- ggplot(students[students$grade>0 & abs(scale(students$events))<=5,], aes(x=grade,y=events)) +
        geom_point(aes(color=cert_status)) +
        geom_smooth(method = "glm", formula = y ~ poly(x,3),fullrange=F) +
        geom_text(x = .43, y = 2264, aes(label = eq), data=data.frame(eq=as.character(as.expression(eq))), parse=TRUE) +
        scale_colour_manual(values=stdColors[1:2]) + 
        labs(x="Final Grade",y="Events (within 5 sd. of mean)") +
        theme(legend.position="none")
p4

6B Student Grades and Number of Unique Modules Accessed

#6B Grades vs Mods Accessed (Unq.)
m <- glm(grade ~ poly(mods_unq,3), data = students[students$grade>0,])
eq <- substitute(italic(y) == b %.%italic(x)^3* c %.%italic(x)^2* + d %.%italic(x)* + a*","~~italic(r)^2~"="~r2,
                 list( a=format(coef(m)[1], digits=3), 
                       b=format(coef(m)[2], digits=3),
                       c=format(coef(m)[3], digits=3),
                       d=format(coef(m)[4], digits=3),
                       r2=format(1-(m$deviance/m$null.deviance), digits = 3)))

p3 <- ggplot(students[students$grade>0,], aes(x=grade,y=mods_unq)) +
        geom_point(aes(color=cert_status)) +
        geom_smooth(method = "glm", formula = y ~ poly(x,3),fullrange=F) +
        geom_text(x = .46, y = 258, aes(label = eq), data=data.frame(eq=as.character(as.expression(eq))), parse=TRUE) +
        scale_colour_manual(values=stdColors[1:2]) + 
        labs(x="Final Grade",y="Modules Accessed (Unq.)") +
        theme(legend.position="none")
p3

6C Student Grades and Number of Open Assessment Events

#6C Grades vs Open Assessment Events
m <- glm(grade ~ poly(oa_events,3), data = students[students$grade>0,])
eq <- substitute(italic(y) == b %.%italic(x)^3* c %.%italic(x)^2* + d %.%italic(x)* + a*","~~italic(r)^2~"="~r2,
                 list( a=format(coef(m)[1], digits=3), 
                       b=format(coef(m)[2], digits=3),
                       c=format(coef(m)[3], digits=3),
                       d=format(coef(m)[4], digits=3),
                       r2=format(1-(m$deviance/m$null.deviance), digits = 3)))
p5 <- ggplot(students[students$grade>0 & abs(scale(students$oa_events))<=2,], aes(x=grade,y=oa_events)) +
        geom_point(aes(color=cert_status)) +
        geom_smooth(method = "glm", formula = y ~ poly(x,3),fullrange=F) +
        geom_text(x = .43, y = 61.5, aes(label = eq), data=data.frame(eq=as.character(as.expression(eq))), parse=TRUE) +
        scale_colour_manual(values=stdColors[1:2]) + 
        labs(x="Final Grade",y="Open Assessment Events (within 2 sd. of mean)") +
        theme(legend.position="none")
p5

6D Student Events and Number of Sessions

#6D Events vs Sessions
m <- glm(sessions ~ poly(events,3), data = students[students$grade>0 & abs(scale(students$events))<=5,])
eq <- substitute(italic(y) == b %.%italic(x)^3* c %.%italic(x)^2* + d %.%italic(x)* + a*","~~italic(r)^2~"="~r2,
                 list( a=format(coef(m)[1], digits=3), 
                       b=format(coef(m)[2], digits=3),
                       c=format(coef(m)[3], digits=3),
                       d=format(coef(m)[4], digits=3),
                       r2=format(1-(m$deviance/m$null.deviance), digits = 3)))
p7 <- ggplot(students[students$grade>0 & abs(scale(students$events))<=5,], aes(x=events,y=sessions)) +
        geom_point(aes(color=cert_status)) +
        geom_smooth(method = "glm", formula = y ~ poly(x,3),fullrange=F) +
        geom_text(x =1150, y=145, aes(label = eq), data=data.frame(eq=as.character(as.expression(eq))), parse=TRUE) +
        scale_colour_manual(values=stdColors[1:2]) + 
        labs(x="Events",y="Sessions")+
        theme(legend.position="none")
p7

6E Number of Student Events and Number of Problem Attempts

#6E Events vs Problem Attempts
p10 <- ggplot(students[students$grade>0 & abs(scale(students$events))<=4,], aes(x=events,y=prb_attempts)) +
  geom_point(aes(color=cert_status)) +
  scale_colour_manual(values=stdColors[1:2]) + 
  labs(x="Events",y="Problem Attempts") +
  theme(legend.position="none")
p10

6F Number of Student Events and Number of Open Assessment Events

#6F Events vs OA Events
p11 <- ggplot(students[students$grade>0 & abs(scale(students$events))<=5,], aes(x=events,y=oa_events))  +
        geom_point(aes(color=cert_status)) +
        scale_colour_manual(values=stdColors[1:2]) + 
        labs(x="Events",y="Open Assessment Events") +
        theme(legend.position="none")
p11

Composite of Fig 6

multiplot(p4+ggtitle("A")+ theme(plot.title = element_text(hjust = 0)),
          p3+ggtitle("B")+ theme(plot.title = element_text(hjust = 0)),
          p5+ggtitle("C")+ theme(plot.title = element_text(hjust = 0)),
          p7+ggtitle("D")+ theme(plot.title = element_text(hjust = 0)),
          p10+ggtitle("E")+ theme(plot.title = element_text(hjust = 0)),
          p11+ggtitle("F")+ theme(plot.title = element_text(hjust = 0)),
          cols=2)