Part of project: College Rankings

Introduction

We use the latest Times Higher Education (THE) World University Rankings data for this analysis. THE ranks colleges based on five categories: (1) Teaching (30%), (2) Research (30%), (3) Citations (30%), (4) International outlook (7.5%), and (5) Income (2.5%). Each colleges have a 1-100 score for each categories and the final score is simply the sum of each categories according to the weights. The colleges are then assigned a rank based on their overall score.

While high-ranking colleges will obviously have high scores in each category, this does not necessarily mean the distribution of scores are the same. For example, School A might score very high in citations but have a low score for Teaching than School B. While they both may be in the Top 50, they maybe more different than they are alike. Let us perform cluster analysis to see if we can spot any groupings.

Heatmap
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The first thing I did was to examine the heatmap based on hierarchical clustering. While the results of hierarchical clustering is subjective, it can give some interesting insights. In this case, the rows are ordered of the Top 50 schools and the shaded tiles corresponds to how they fare for each category.

Notice that the top ~25 schools scored very well for citations which implies that the research from these institutions are very, very impactful. The quality of teaching is very high for the top 5 schools but gradually lower as the rankings go on. Same goes with the research category. The international and income categories are spotty which makes sense since they make up a small percentage of the overall score. I also plotted the country of origin for each school but it was pretty obvious that the top schools are predominantly American and European.

Partitional Clustering

From the heatmap we see that impact matters a lot. While it has the same weight as teaching and research, it is a much stronger commonality between the very best institutions. Let us apply partition clustering using k-means to be more in-depth. Before doing so, it is worth it to figure out the optimal number of clusters. Two popular ways of doing so is the Elbow Method and Average Silhouette Width. In the figures below, we see that both method points to k=3.

Optimal k
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We now perform k-means with three clusters. I plotted the pairs plot for each category in the figure below. The upper triangular contains the Pearson’s correlation between the two categories and the lower triangular are the clusters.

Optimal k
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While it is obvious that there should be a positive correlation coefficient for each categories, one thing that stood out to me is the high correlation between research and teaching. For research universities, it is common that teaching duties comes second to research for faculty. It turns out that at the top universities, these two things go hand in hand. The clustering result is very unclear as there are a lot of overlaps between universities. There are clearly 3 clusters for international reputation versus income however. There are clearly some universities with high income and and international reputation but also some with low international reputation and low income.

Now, which of the top universities are most similar to one another? We examine the two components of the data that explains the most variations. The cluster plot is given below which clearly shows 3 clusters of universities.

Optimal k
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I was not really surprised that my university, UIUC, is close to Northwestern, UW-Madison and Michigan since the Big Ten schools tends to be ranked very close to one another. The biggest insight I gather from the data is that colleges that are close to one another are ranked very similarly in terms of the five categories. Aside from the Big Ten schools, notice that the UK schools (Edinburgh, Kings College, LSE) as well as the Asian schools (Tsinghua, Peking, Tokyo) are close together. Of course, the elite universities will be in a class of their own as see the giant clutter of Harvard, Yale, Princeton, OxBridge.