PISA 2012 - multi dimensional Gaussian merging

Agnieszka Sitko

2018-04-04

Libraries

library(factorMerger)
library(ggplot2)
library(dplyr)
library(reshape2)

Load data

data("pisa2012")

Explore

pisa2012 %>% ggplot(aes(x = country)) + geom_bar() + 
    theme(axis.text.x = element_text(angle = 90, hjust = 1))

meltedPisa <- pisa2012 %>% melt(na.rm = TRUE)
pisaResultsBySubject <-  meltedPisa %>% 
    ggplot(aes(x = reorder(country, value, FUN = median), y = value)) + geom_boxplot() + 
    facet_wrap(~variable) + 
    theme(axis.text.x = element_text(angle = 90, hjust = 1)) + 
    xlab("Country") 
pisaResultsBySubject + 
    geom_hline(data = meltedPisa %>% group_by(variable) %>% summarise(mean = mean(value)), 
               aes(yintercept = mean, group = variable), col = "red")

TODO: Find countries significantly better, worse and not significantly different from global averages. Cluster countries into three groups.

Run MANOVA

manova(cbind(math, reading, science) ~ country, pisa2012) %>% summary()
#>              Df   Pillai approx F num Df den Df    Pr(>F)    
#> country      10 0.066994   136.91     30 179817 < 2.2e-16 ***
#> Residuals 59939                                              
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

It seems that there exist some differences among countries included in PISA. Let’s find them!

Factor Merger

Let’s now have a try using factorMerger for exploration.

It’s faster to use “fast-adaptive” or “fast-fixed” methods on a big dataset. They enable comparisons between neighbours only (neighbours are pairs of groups with close means).

pisaFMHClustEurope <- mergeFactors(response = pisa2012[,1:3],
                       factor = factor(pisa2012$country),
                       method = "fast-fixed") 

plot(pisaFMHClustEurope)