# Correlation Matrix using rmcorr_mat

#### Jonathan Bakdash and Laura Marusich

#### 2023-08-09

#### Running Examples Requires corrplot (Wei and Simko 2021)

    #Install corrplot
     install.packages("corrplot")
     require(corrplot)

## Plotting a Correlation Matrix

The output from rmcorr_mat can be used be used to plot a correlation matrix.

    dist_rmc_mat <- rmcorr_mat(participant = Subject,
                               variables = c("Blindwalk Away",
                                             "Blindwalk Toward",
                                             "Triangulated BW",
                                             "Verbal",
                                             "Visual matching"),
                               dataset = twedt_dist_measures,
                               CI.level = 0.95)

    corrplot(dist_rmc_mat$matrix)

## Plotting Multiple Models

The output can also be used to plot multiple models side-by-side.

    #Number of models being plotted
    n.models <- length(dist_rmc_mat$models)

    #Change graphing parameters to plot side-by-side
    #with narrower margins
    par(mfrow = c(3,4),
        mar = c(2.75, 2.4, 2.4, 1.4))

    for (i in 1:n.models) {
        plot(dist_rmc_mat$models[[i]])
        }

    #Reset graphing parameters
    #dev.off()

## Adjusting for Multiple Comparisons

The third component of the output from rmcorr_mat() contains a summary of results. Using the summary component, we demonstrate adjusting for multiple comparisons using two methods: the Bonferroni correction and the False Discovery Rate (FDR).
This example also compares the unadjusted p-values to both adjustment methods. Because most of the unadjusted p-values are quite small, many of the adjusted p-values tend to be similar to the unadjusted ones and the two adjustment methods also tend to produce similar p-values.

    #Third component: Summary
    dist_rmc_mat$summary
    #>            measure1         measure2  df  rmcorr.r    lowerCI   upperCI
    #> 1    Blindwalk Away Blindwalk Toward 175 0.8065821 0.74808182 0.8526427
    #> 2    Blindwalk Away  Triangulated BW 174 0.2382857 0.09366711 0.3730565
    #> 3    Blindwalk Away           Verbal 175 0.7355813 0.65965209 0.7966468
    #> 4    Blindwalk Away  Visual matching 174 0.7758245 0.70930425 0.8286489
    #> 5  Blindwalk Toward  Triangulated BW 176 0.2254866 0.08109132 0.3606114
    #> 6  Blindwalk Toward           Verbal 177 0.7160551 0.63619996 0.7807308
    #> 7  Blindwalk Toward  Visual matching 177 0.7575109 0.68718940 0.8137687
    #> 8   Triangulated BW           Verbal 178 0.1835838 0.03835025 0.3212218
    #> 9   Triangulated BW  Visual matching 177 0.2537431 0.11120971 0.3860478
    #> 10           Verbal  Visual matching 179 0.7341831 0.65888265 0.7949162
    #>          p.vals effective.N
    #> 1  8.228992e-42         177
    #> 2  1.449081e-03         176
    #> 3  2.056415e-31         177
    #> 4  1.226384e-36         176
    #> 5  2.476132e-03         178
    #> 6  1.937983e-29         179
    #> 7  1.302874e-34         179
    #> 8  1.362964e-02         180
    #> 9  6.095365e-04         179
    #> 10 6.400493e-32         181

    #p-values only
    dist_rmc_mat$summary$p.vals
    #>  [1] 8.228992e-42 1.449081e-03 2.056415e-31 1.226384e-36 2.476132e-03
    #>  [6] 1.937983e-29 1.302874e-34 1.362964e-02 6.095365e-04 6.400493e-32

    #Vector of original, unadjusted p-values for all 10 comparisons
    p.vals <- dist_rmc_mat$summary$p.vals

    p.vals.bonferroni <- p.adjust(p.vals,
                                  method = "bonferroni",
                                  n = length(p.vals))

    p.vals.fdr <- p.adjust(p.vals,
                           method = "fdr",
                           n = length(p.vals))

    #All p-values together
    all.pvals <- cbind(p.vals, p.vals.bonferroni, p.vals.fdr)
    colnames(all.pvals) <- c("Unadjusted", "Bonferroni", "fdr")
    round(all.pvals, digits = 5)
    #>       Unadjusted Bonferroni     fdr
    #>  [1,]    0.00000    0.00000 0.00000
    #>  [2,]    0.00145    0.01449 0.00181
    #>  [3,]    0.00000    0.00000 0.00000
    #>  [4,]    0.00000    0.00000 0.00000
    #>  [5,]    0.00248    0.02476 0.00275
    #>  [6,]    0.00000    0.00000 0.00000
    #>  [7,]    0.00000    0.00000 0.00000
    #>  [8,]    0.01363    0.13630 0.01363
    #>  [9,]    0.00061    0.00610 0.00087
    #> [10,]    0.00000    0.00000 0.00000

Wei, Taiyun, and Viliam Simko. 2021. R Package ’Corrplot’: Visualization of a Correlation Matrix. https://github.com/taiyun/corrplot.