2.3.2. Hierarchical Clustering on Principal Components

The hierarchical clustering on principal components (HCPC) method was applied to partition SDFs into clusters where SDFs in the same cluster had more similarity to each other in housing management than to those SDFs in other clusters [46]. Briefly, factorial analysis of mixed data method (FAMD) was applied first to transform the housing management dataset into non-correlated principal components (PCs). Then, some first PCs, which accounted for more than 70% of the total variance in the management dataset, was retained for hierarchical cluster analysis to identify an initial number of clusters [47,48]. Finally, the k-means clustering method was applied to identify an optimum number of clusters and assign SDFs into each cluster [46]. The HCPC analysis results were visualised as the dendrograms. All the multivariate statistical analyses were performed using R package ‘FactoMineR’ [49] and the results of multivariate analyses were visualised using R package ‘factoextra’ [50].

The characteristics of each management cluster were further explored by V-tests statistics [51], which compared then mean of each variable in each cluster with the mean of that variable in all clusters for quantitative variables and comparing the percentage of each category of each qualitative in each cluster to the percentage of that category in the whole the data set [48,51]. Through those comparisons, V-tests statistics could identify the advantages and disadvantages of each management cluster, thereby suggesting the management clusters with most advantages.

Although V-tests statistics could point out the management clusters with the most advanced housing management characteristics, they could not prove if the most advanced clusters were more effective than the other clusters in improving shed microclimate. Therefore, two-way ANOVA analysis was also performed to compare AT, RH, AS, THI and HLI between management clusters while accounting for the effects of altitude and latitude to assess if any management clusters were more effective than the others in improving the microclimate inside the cowsheds.