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meta-hyperedge. Finally, each object is assigned to the meta-cluster that it is most associated with. The association is computed by averaging all hyperedges of a meta-cluster. We run MCLA for k = 2 to 10, as the optimal k for our clustering solutions did not go beyond 5. Intuitively, it is highly unlikely that the optimal k associated with the consensus solution will go beyond 10.

We also perform two other consensus clustering algorithms described in Strehl and Ghosh (2002). Cluster-based Similarity Partitioning Algorithm (CSPA) finds the consensus solution by first creating a n x n binary similarity matrix in which two objects are denoted as 1 if they are in the same cluster, and 0 if otherwise. An induced similarity measure is then calculated. Subsequently, the algorithm utilises METIS (Karypis and Kumar, 1998) to recluster the objects based on the similarity measure, yielding a consensus clusters solution. HyperGraph Partitioning Algorithm (HGPA) re-partitions the data by viewing original clusters as indications of strong bonds. To find clusters, the algorithm partitions the hypergraph by separating the least number of hyperedges.

1.1.2.Cross - Sectional Regressions

To investigate whether our sample supports our hypotheses, consistent with Ahn et al. (forthcoming), we model the number of directorships as a function of directorial characteristics and associated firm characteristics. Accordingly, we use age, education qualifications and prior or current employment as proxies for directors' quality. We also include tenure to measure a director's commitment to a firm. For firm quality variables, we include firm size, firm age, inclusion in the Straits Times Index and governance quality. We also investigate the relation between block ownership and optimal number of directorships.

A total of eighteen independent variables are investigated; half being directorial characteristics and the other half being firm characteristics. Directorial characteristics are: age, tenure, founder of a listed company, prior or current employment as civil servant, CEO or Chairman, CFO or COO, partner of tier 1 accounting or law firms or academic, gender and education qualifications. Firm characteristics are: governance quality, firm age, block ownership structure defined as family firms, GLCs or founder-managed firms, inclusion in Straits Times Index, firm size and main country of business. We control for firms' financial and operation stability measured by its leverage and stock return volatility, industry growth opportunities and profitability measured by industry average market to book ratio and industry average Return on assets (ROA). The dependent variable comprises of the number of directorships held by a director as of Dec 31, 2008.

There are two possible ways of performing the regression, one by considering the total number of directorships and the other by considering the total number of directors. To ensure that our results are robust, we perform regressions based on both ways. Moreover, to ensure that the results are robust to board appointments, both partial and full models are performed on the full sample of all directors, a subsample comprising of outside directors and a subsample consisting of only independent directors.

The full model is given as,

Log(Number of Directorships held) =

α + β1Age + β2Tenure + β3Founder-Director +