# PCA & Cluster analysis for Typology with missing data - Choosing right approach

I am an ecology graduate with a decent practical familiarity with statistics in R, but limited experience of approaches such as PCA, and Cluster Analysis. I am currently faced with the challenge of trying to apply my skills to an entirely unfamiliar problem: my dad is writing a book on archaeological finds of blades, has collected data on 176 finds and has tasked me with analysing it.

The data selected for analysis is structured thus:

 Blade.length     Max.width     Max.thickness     Shape     Broken.back        Type

Min.   :165.0   Min.   :20.00   Min.   : 3.500   A   :70   Min.   :0.0000   Cs   :39
1st Qu.:220.0   1st Qu.:28.75   1st Qu.: 5.000   B   : 8   1st Qu.:0.0000   Hbs  :15
Median :270.0   Median :34.00   Median : 6.000   C   :14   Median :0.0000   Lbs  :17
Mean   :311.5   Mean   :35.20   Mean   : 6.464   D   :14   Mean   :0.2686   Ls   :23
3rd Qu.:353.0   3rd Qu.:39.00   3rd Qu.: 7.875   E   :30   3rd Qu.:0.5000   Ns   :43
Max.   :760.0   Max.   :62.00   Max.   :11.000   F   :12   Max.   :1.0000   Small:35
NA's   :9       NA's   :4       NA's   :86       NA's:28   NA's   :1        NA's : 4


Shape is a variable of categories pertaining to the shape of the tip of the blades - these categories are in no particular order. Broken.back is a different way of looking at "shape", effectively binary, although some cases are "in between" and have been entered as 0.5. "Type" is a supplementary variable referring to what each blade has been identified as, using a pre-existing typology. Part of the exercise is to examine if this pre-existing typology is fit for purpose.

The dataset is, necessarily, incomplete, with NAs in all variables, although blades with lots of missing data have been excluded from the analysis. Within the sample remaining, the most incomplete column is blade thickness, with 48% NAs.

So far I have attempted to visualise the data by means of factorial analysis of mixed data, with imputation, using packages MissMDA and FactoMineR. However I've found myself bewildered by the number of options and what approach is appropriate for the sort of data I have.

More importantly, I am looking to conduct hierarchical cluster analysis of the data to examine the relatedness of different finds and try and statistically define types (http://www.r-bloggers.com/hierarchical-clustering-in-r-2/), so far using HCLUST, Dist, and vegdist (package: Vegan). However, I am not clear as to;

• How to manage, prepare or transform the types of data I have for this type of analysis.
• What dissimilarity index method would be most appropriate in this context.
• What type of clustering / linkage method would be most appropriate in this context.

Sorry for the long question. As you can see I am quite bewildered and out of my depth. Thanks in advance.

• Questions solely about how software works are off-topic here, but you may have a real statistical question buried here. You may want to edit your question to clarify the underlying statistical issue. You may find that when you understand the statistical concepts involved, the software-specific elements are self-evident or at least easy to get from the documentation. – gung Jul 10 '16 at 14:28