Interpreting Silhouette plot for Cluster Analysis I am running a mixed type data cluster analysis in R and I am trying to interpret the Silhouette Plot. For whatever reason, it is telling me that more clusters is ideal for analysis. Why could this be? I am using a sample of 10k with 6 variables (4 of which are categorical).  
 A: Silhouette values less than 0.4 are bad.
So none of your clusterings worked well. The clusters are not reliable. You probably need to use a different algorithm, metric, or your data might not contain any clusters at all (categoricial data frequently does not contain clusters).
P.S. Silhouette plot commonly refers to a plot showing the Silhouette of each point in just one data set, not parameter k vs. average Silhouette like you used for plotting.
A: There's no way we can reasonably answer this question, especially without context into the problem you are working on. The number of clusters that naturally occur in your data doesn't have to have any correspondence to the number of variables you're modeling against. Consider the following example:
n_classes <- 10
n_feats <- 2
n_obs <- 100

y <- sample(n_classes, n_obs, replace=TRUE)
X <- sapply(1:n_feats, function(i) y + rnorm(n_obs))/n_classes

plot(X, col=y)

I chose n_feats <- 2 here just to give you something easy to plot, but as long as n_classes < n_obs, you can pick whatever values you want for those three parameters. My point here is that as soon as you introduce a single continuous variable, there is no limit to the number of classes your available features could represent because any continuous interval ([0,1] in the example above) can be divided into infinite segments of arbitrary length. 
The number of classes your available features are capable of representing has absolutely no bearing on the number of classes that it might be appropriate to use when modeling your data. Silhouette is just a heuristic: if your subject matter knowledge about the problem suggests the silhouette plot is giving you bad advice, go find a different heuristic to direct your choice of the number of clusters.
