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I have the following prediction problem-

Train data: A person's personality traits(around 50 correlated features) and his/her GPA in a course(related to HR/Management)

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Given the test sample with the the candidates personality traits, I have to predict the person's gpa if he would take the course.

The issues I am facing with the data set are -

  1. No. of sample is small= 20-30
  2. No of features is small=50
  3. Some features have strong correlation such as extraversion and self-expression

Could someone guide me on

  1. What models will be desirable
  2. Should I go for PCA or feature selection
  3. Do I apply LOOCV for better performance?
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To me, the issue is less about the sample size, although that does impact the magnitude of the error around any estimates, and more about the fact that you have more features than observations not to mention that these features are not independent. The usual rule of thumb in any multivariate analysis is that you have more data than metrics at a rough ratio of 10 observations per measure. While not a hard and fast rule, this would apply to PCA or any exploratory factor analysis as a cautionary note. In other words, using PCA as a feature selection method could be fraught with hazard.

That said, there are known instances where the number of metrics is much, much greater than the data, e.g., chemometrics. The usual multivariate workaround to this challenge is partial least squares (PLS). It is well described in this Wiki article -- https://en.wikipedia.org/wiki/Partial_least_squares_regression -- as a kind of "factor analytic" regression. As the article notes, many packages offer it. It's worth a try with your data.

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