Table 2.

Average of the Silhouette of a k-means clustering when k = 3 and k = 4

Average silhouette measures
HTC			PMTCT			CRT
Year	K = 3	K = 4	Year	K = 3	K = 4	Year	K = 3	K = 4
2011	0.800	0.775	2011	0.674	0.706	2011	0.368	0.582
2012	0.526	0.563	2012	0.585	0.588	2012	0.556	0.599
2013	0.659	0.648	2013	0.654	0.632	2013	0.637	0.618
2014	0.669	0.669	2014	0.676	0.666	2014	0.692	0.663
2015	0.737	0.709	2015	0.649	0.711	2015	0.710	0.705
2016	0.749	0.754	2016	0.791	0.774	2016	0.708	0.710
2017	0.685	0.673	2017	0.699	0.677	2017	0.696	0.700
2018	0.593	0.714	2018	0.689	0.707	2018	0.654	0.701

VMMC			PEP			BS
Year	K = 3	K = 4	Year	K = 3	K = 4	Year	K = 3	K = 4
2011	a	a	2011	0.704	0.679	2011	a	a
2012	1.00	b	2012	0.593	0.605	2012	0.734	0.730
2013	0.64	0.669	2013	0.639	0.629	2013	0.732	0.687
2014	0.634	0.661	2014	0.675	0.667	2014	0.712	0.650
2015	0.733	0.681	2015	0.682	0.673	2015	0.617	0.641
2016	0.708	0.699	2016	0.696	0.665	2016	0.719	0.680
2017	0.765	0.733	2017	0.621	0.611	2017	0.577	0.637
2018	0.657	0.636	2018	0.650	0.673	2018	0.610	0.607

^aThere are not enough valid cases to conduct the specified cluster analysis

^bIn the data, there is insufficient variation to honor the four clusters specified. The number of clusters is reduced to 3