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Making the Most of Multivariate Analysis

• Scatterplot Matrix
  • Can visualize the relationship among pairs of variables
  • Look for outliers, linear and curvilinear relationships
  • Identify "striping" that could indicate missing variables
• Correlation Heatmap
  • Understand the strength of linear relationships among many variables at once
• Parallel Coordinates
  • Visualize the relationship among many variables at once
  • Order does have an impact on the analysis: place the variables with the highest correlation early in the "list"
• Principal Component Analysis
  • Reduce variables to a smaller list that keeps most of the information present in the data
  • Build linear combinations of variables the well represent the full set of variables
• Discriminant Analysis
  • Use covariates to build a model to classify observations into a group
• Model Driven Multivariate Control Charts
  • What are multivariate control charts?
    • Multivariate control charts are used to monitor two or more interrelated process variables
    • While univariate control charts are used to monitor a single independent process characteristic, multivariate control charts are necessary when process variables are correlated
  • Why use multivariate control charts?
    • Since multiple process characteristics are often correlated, the use of Principle Components can reduce the space from N (number of process characteristics) to P (number of principle components used on the chart)
    • Univariate analysis alone will results in missed signals if process characteristics are correlated (given that i.i.d. normal with a fixed mean and variance is a useful but never real situation)
    • A multivariate control chart can be used to view one plot of the data, see signals and then identify what process (or set of) variables contributed to the signal
  • Why are multivariate control charts not widely used?
    • Summarizing N variables into one chart will make it hard to know what caused a signal
    • Signals on the chart could be due to shift in the multivariate mean OR changes in the covariances
    • The data being plotted are not in engineering units and are not readily interpretable
  • Industries with the "pain"
    • Process Industries (chemical, steel, etc.)
    • Semiconductor
    • Any industry that has many process characteristics