英语论文网

rectors will appear to be different when one sits on a firm with large market capitalization while the other sits on a small market capitalization firm. In our study, we attempt to cluster directors by the latter method as it is reasonable to expect that individual director characteristics (e.g. previous experience) have been considered by companies themselves when they invite those directors to join their boards. In this way, our cluster analysis also takes in consideration individual director characteristics. In defining clustering variables, we follow a deductive approach in which the suitability of variables is theory-based (Ketchen et al., 1993). This is often considered a better approach to guide variable choices as irrelevant variables may affect the validity of a clusters solution (Punj and Stewart, 1983). We employ the seven firm characteristics previously discussed in Chapter Three as our clustering variables.

As cluster analysis groups objects by maximizing distance between groups along all clustering variables, variables with larger ranges tend to dominate (i.e. given more weight) the clusters solution in comparison to those variables with smaller ranges (Hair et al., 1992). Considering that the range of firm size (measured by market capitalization) is several times larger than the range of ownership structure variables, firm size variables are likely to dominate our clusters solution. Although some studies claim that standardization of variables to equally scaled data is not necessary (Dolnicar, 2002) and may distort results, we choose to standardize the variables by Z-scores to avoid clusters solutions that are dominated by market capitalization.

1.1.1.1.Cluster Analysis Algorithms, Cluster Validation and Consensus Clustering

In the following sections, we describe the three algorithms employed to perform cluster analysis. Subsequently, we discuss the cluster validations steps taken and illustrate the use of consensus clustering to find a single consensus solution. We perform the following steps on three sets of data; all directors, outside directors and independent directors as extant research have found that dissimilar behaviours between inside and outside directors can lead to contrasting results in studies (Mak et al., 2003 and Fich and Shivdasani, 2006).

1.1.1.1.1.Cluster Analysis Algorithms

Hierarchical clustering

Hierarchical clustering can be either agglomerative or divisive. Divisive methods begin with every object in one cluster and end when each object is in individual clusters. Divisive methods are not readily available and are thus rarely cited. In this thesis, we employ the more commonly used agglomerative method and discuss the basic process below.

The basic process of an agglomerative hierarchical clustering for N objects is (Johnson, 1967):

Assign each object to its own cluster, thus the method begins with N clusters.

The closest (most similar) pair of clusters are merged into a single cluster, thus there are now (N-1) clusters.

Recompute distances (similarities) between the new cluster and the old clusters individually.

Iterate through steps 2 and 3 until there is only a single cluster left.

In step 2, several methods to compute distances exist, and they are referred to as linkage function. For instance, single linkage clustering