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I have a sample size of 50 items with 50 variables (continuous level), and want to minimise the dimension of my data in order to extract the "character" of each item through a small amount of p.

Can I use PCA? If yes, do I need to use a specific technique for small sample size?

user05
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  • When you say 'extract the "character" of each item through a small amount of p' do you want to maintain just a few of the original predictors, or reduce the effective dimension of the predictor space down from the p value of 50? Selecting a few components from PCA might still include contributions from all of the original predictors, just reweighted. Also, please say more about how you will then use the reduced-dimension data. – EdM Jun 30 '20 at 20:43
  • The raw dataset is 50 rows by 50 columns (all variables measure area). My intention is to reduce the dimension of the predictor space by creating a smaller number of new variables through PCA ( around 1 to 3 components), while capturing the majority of the variance. The objective is to analyse how each component varies through all rows - calculation of variance of components. – user05 Jun 30 '20 at 21:09

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I wouldn't think of this as a "small sample size" for PCA. The PCA example in Section 10.2.1 of An Introduction to Statistical Learning is for a data set with 50 items and only 3 continuous variables. The standard ways of performing PCA will have no inherent difficulty.

The problem you face, as is typical of small data sets, is how well your results will generalize to new data samples. If you are only maintaining 1 to 3 components it seems unlikely that you will risk overfitting the data that you have from 50 cases, but there is always the risk that your particular data sample is itself unrepresentative.

EdM
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