Using a custom statistic with its error bar"

cat("this will be hidden; use for general initializations.")
library(superb)
library(ggplot2)

By default, superbPlot generates mean plots along with 95% confidence intervals of the mean. However, these choices can be changed.

The defaults are statistic = "mean", errorbar = "CI", gamma = 0.95. For error bar functions that accept a gamma parameter (e.g., CI, the gamma parameter is automatically transfer to the function). For other functions that do not accept a gamma parameter (e.g., SE), the gamma parameter is unused.

Changing the summary function to be plotted

In what follow, we use GRD() to generate a random dataset with an interaction then make plots varying the statistics displayed.

# shut down 'warnings', 'design' and 'summary' messages
options(superb.feedback = 'none') 

# Generate a random dataset from a (3 x 2) design, entirely within subject.
# The sample size is very small (n=5) and the correlation between scores is high (rho = .8)
dta <- GRD( 
    WSFactors  = "Moment(3): Dose(2)", 
    Effects    = list("Dose*Moment"=custom(0,0,0,1,1,3)), 
    SubjectsPerGroup = 50, 
    Population = list( mean=10, stddev = 5, rho = .80)
)

# a quick function to call superbPlot
makeplot <- function(statfct, errorbarfct, gam, rg, subttl) {
    superbPlot(dta, 
        WSFactors  = c("Moment(3)","Dose(2)"), 
        variables = c("DV.1.1","DV.2.1","DV.3.1","DV.1.2","DV.2.2","DV.3.2"), 
        statistic = statfct, 
        errorbar  = errorbarfct, 
        gamma     = gam, 
        plotStyle = "line",
        adjustments = list(purpose="difference", decorrelation="CM")
    ) + ylab(subttl) + coord_cartesian( ylim = rg )
} 

p1 <- makeplot("mean",      "CI", .95, c(6,14), "Mean +- 95% CI of the mean")
p2 <- makeplot("mean",      "SE", .00, c(6,14), "Mean +- SE of the mean")
p3 <- makeplot("median",    "CI", .95, c(6,14), "Median +- 95% CI of the median")
p4 <- makeplot("fisherskew","CI", .95, c(-2,+2), "Fisher skew +- 95% CI")

library(gridExtra)
p <- grid.arrange(p1,p2,p3,p4, ncol=2)

Determining that a summary function is valid to use in superbPlot

Any summary function can be accepted by superbPlot, as long as it is given within double-quote. The built-in statistics functions such as mean and median can be given. Actually, any descriptive statistics, not just central tendency, can be provided. That includes IQR, mad, etc. To be valid, the function must return a number when given a vector of numbers.

In doubt, you can test if the function is valid for superbPlot with (note the triple colon):

superb:::is.stat.function("mean")

Any error bar function can be accepted by superbPlot. These functions must be named "interval function"."descriptive statistic". For example, the following CI.mean is the confidence interval of the mean. Other functions are SE.mean, SE.median, CI.fisherskew, etc. The superb library provides some 20+ such functions. @htc14 and @htc15 reviewed some of these functions.

The error bar functions can be of three types:

The interval function can be tested to see if it exists:

superb:::is.errorbar.function("SE.mean")

To see if a gamma is accepted for a certain interval function, you can try

superb:::is.gamma.required("SE.mean")

Creating a custom-made descriptive statistic function to be used in superbPlot

As an example, we create from scratch a descriptive statistic function that will be fed to superbPlot. Following @gc18 , we implement the single-group design Cohen's d ($d_1$). This descriptive statistic is computed relative to an hypothetical population mean. Herein, we use the data from dataFigure1 and assume that the population mean is 100.

    # create a descriptive statistics
    d1 <- function(X) {
      mean(X-100)/sd(X) 
    } 

    # we can test it with the data from group 1...
    grp1 <- dataFigure1$score[dataFigure1$grp==1]
    grp2 <- dataFigure1$score[dataFigure1$grp==2]
    d1(grp1)

    # or check that it is a valid statistic function
    superb:::is.stat.function("d1")

Once we have the function, we can ask for a plot of this function with

    superbPlot(dataFigure1, 
        BSFactors = "grp", 
        statistic = "d1", errorbar = "none",
        plotStyle="line",
        adjustments = list(purpose = "difference"),
        variable = "score",
        errorbarParams = list(width=0) # so that the null-width error bar is invisible
    )+ ylab("Cohen's d_1") +
    labs(title="d_1 with no error bars") +
    coord_cartesian( ylim = c(-0.5,+1.5) ) 

Creating a custom-made interval function to be used in superbPlot

It is also possible to create custom-made confidence interval functions.

Hereafter, we add a confidence interval for the Cohen's $d_1$. We use the predictive approach documented in Lecoutre [@l99; @cg20] which requires the lambda-prime distribution provided in the sadists library [@p20].

    library(sadists)

    CI.d1 <- function(X, gamma = .95) {
        n    <- length(X)
        dlow <- qlambdap(1/2-gamma/2, df = n-1, t = d1(X) * sqrt(n) ) 
        dhig <- qlambdap(1/2+gamma/2, df = n-1, t = d1(X) * sqrt(n) ) 
        c(dlow, dhig) / sqrt(n)
    }

    # we test as an example the data from group 1
    CI.d1(grp1)  

    # or check that it is a valid interval function
    superb:::is.errorbar.function("CI.d1")

We have all we need to make a plot with error bars!

    superbPlot(dataFigure1, 
        BSFactors = "grp", 
        statistic = "d1", errorbar = "CI",
        plotStyle="line",
        adjustments = list(purpose = "single"),
        variable = "score"
    )+ ylab("Cohen's d_1") +
    labs(title="d_1 with 95% confidence interval of d_1") +
    coord_cartesian( ylim = c(-0.5,+1.5) ) 

Note that this difference-adjusted confidence interval is fully compatible with the Cohen's $d_p$ (between the two groups) as $d_p$ is 0.498 with a 95% confidence interval of [-0.068, +1.059] [all the formulas are from @gc18;@cg20].

    # compute the Cohen's dp
    dp <- (mean(grp1)-mean(grp2))/ sqrt((var(grp1)+var(grp2))/2)
    dp

    # get the confidence interval of this 
    lecoutre2007 <- function(dp, n, gamma = .95) {
        dlow <- qlambdap(1/2-gamma/2, df = 2*(n-1), t = dp * sqrt(n/2) ) 
        dhig <- qlambdap(1/2+gamma/2, df = 2*(n-1), t = dp * sqrt(n/2) ) 
        limits <- c(dlow, dhig) / sqrt(n/2)
        limits
    }
    lecoutre2007(dp, length(grp1) )

Creating bootstrap-based confidence intervals

It is also possible to create bootstrap estimates of confidence intervals and integrate these into superb.

The general idea is to subsample with replacement the sample and compute on this subsample the descriptive statistics. This process is repeated a large number of times (here, 10,000) and the quantiles containing, say, 95% of the results is a 95% confidence interval.

Here, we illustrate this process with the mean. The function must be name "interval function.mean", so we choose to call it myBootstrapCI.mean.

    # we define myBootstrapCI which subsample the whole sample, here called X
    myBootstrapCI.mean <- function(X, gamma = 0.95) {
      res = c()
      for (i in 1:10000) {
        res[i] <- mean(sample(X, length(X), replace = T))
      }
      quantile(res, c(1/2 - gamma/2, 1/2 + gamma/2))
    }

    # we check that it is a valid interval function
    superb:::is.errorbar.function("myBootstrapCI.mean")

This is all we need to make the plot which we can compare with the parametric CI

    plt1 <- superbPlot(dataFigure1, 
        BSFactors = "grp", 
        variable = c("score"), 
        plotStyle="line",
        statistic = "mean", errorbar = "myBootstrapCI",
        adjustments = list(purpose = "difference")
    ) + 
    xlab("Group") + ylab("Score") + 
    labs(title="means and difference-adjusted\n95% confidence intervals") +
    coord_cartesian( ylim = c(85,115) ) +
    theme_gray(base_size=10) +
    scale_x_discrete(labels=c("1" = "Collaborative games", "2" = "Unstructured activity"))

    plt2 <- superbPlot(dataFigure1, 
        BSFactors = "grp", 
        variable = c("score"), 
        plotStyle="line",
        statistic = "mean", errorbar = "CI",
        adjustments = list(purpose = "difference")
    ) + 
    xlab("Group") + ylab("Score") + 
    labs(title="means and difference-adjusted\n95% bootstrap confidence intervals") +
    coord_cartesian( ylim = c(85,115) ) +
    theme_gray(base_size=10) +
    scale_x_discrete(labels=c("1" = "Collaborative games", "2" = "Unstructured activity"))

    library(gridExtra)
    plt <- grid.arrange(plt1, plt2, ncol=2)

As seen, there is not much difference between the two. This was expected: when the normality assumption and the homogeneity of variances assumption are not invalid, the parametric approach (based on these assumptions) is identical on average to the bootstrap approach.

In summary

The function superbPlot() is entirely customizable: you can put any descriptive statistic function and any interval function into superbPlot(). In a sense, superbPlot() is simply a proxy that manage the dataset and produces standardized dataframes apt to be transmitted to a ggplot() specification. It is also possible to obtain the summary dataframe by issuing the argument showPlot=FALSE or by using the related function superbData().

The function superbPlot is also customizable with regards to the plot produced. Included in the package are

Vignette 5 shows how to create new layouts. Proposals are welcome!

References



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superb documentation built on April 22, 2021, 1:06 a.m.