PISA 2012 - multi dimensional Gaussian merging

Agnieszka Sitko

2017-10-04

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       42 0.32207   776.81    126 813837 < 2.2e-16 ***
#> Residuals 271279                                             
#> ---
#> 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

pisaIdxSubset <- sample(1:nrow(pisa2012), size = 500)
pisaFM <- mergeFactors(pisa2012[pisaIdxSubset, 1:3],
                       factor(pisa2012$country[pisaIdxSubset]))

plot(pisaFM, responsePanel = "profile")

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

pisaIdxSubset <- which(pisa2012$country %in% c("Belgium",
                                           "Netherlands",
                                           "Poland",
                                           "Germany",
                                           "Finland",
                                           "Estonia"))
pisaFMHClust <- mergeFactors(pisa2012[pisaIdxSubset, 1:3],
                       factor(pisa2012$country[pisaIdxSubset]),
                       method = "fast-fixed") 

plot(pisaFMHClust, responsePanel = "profile", 
     penalty = log(NROW(pisaFMHClustMath$factor)), 
     panel = "response", nodesSpacing = "effects", 
     panelGrid = F, palette = "Dark2",
     title = "PISA 2012 - students' performance")

Let’s now have a try using European countries only.


pisaEuropean <- filter(pisa2012, country %in% c("Austria", "Belgium", "Bulgaria",
                                            "Czech Republic", "Germany", "Denmark",
                                            "Spain", "Estonia", "Finland",
                                            "France", "Hungary", "Ireland",
                                            "Italy", "Netherlands", "Norway",
                                            "Poland", "Portugal",
                                            "Russian Federation", "Slovak Republic",
                                            "Slovenia"))


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

plot(pisaFMHClustEurope)