Publication date: 10/01/2019

Launch the Principal Components platform by selecting Analyze > Multivariate Methods > Principal Components. Principal Component analysis is also available using the Multivariate and the Scatterplot 3D platforms.

The example described in Example of Principal Component Analysis uses all of the continuous variables from the Solubility.jmp sample data table.

Figure 4.3 Principal Components Launch Window

For more information about the options in the Select Columns red triangle menu, see Column Filter Menu in Using JMP.

Y, Columns

The variables to analyze for components.

Z, Supplementary Variable

The supplementary variables to be displayed. Supplementary variables are not included in the calculation of principal components and including them does not affect the results. Supplementary variables that are continuous can be projected on to the loading plot and used to enhance interpretation.

Weight

Identifies one column whose numeric values assign a weight to each row in the analysis.

Note: The Weight role is ignored for the Wide and Sparse estimation methods.

Freq

Identifies one column whose numeric values assign a frequency to each row in the analysis.

Note: The Freq role is ignored for the Wide and Sparse estimation methods.

By

Creates a Principal Component report for each value specified by the By column so that you can perform separate analyses for each group.

Estimation Method

Specifies the method for calculating the correlations. Several of these methods address the treatment of missing data.

Default

The Default option uses either the Row-wise, Pairwise, or REML methods. A JMP Alert also recommends switching to the Wide method when appropriate.

– Row-wise estimation is used for data tables with no missing values.

– Pairwise estimation is used for data tables with missing values and either more than 10 columns, more than 5,000 rows, or more columns than rows.

– REML estimation is used otherwise.

– Wide estimation is recommended by a JMP Alert window for data tables with more than 500 columns. This is because computation time can be considerable when you use the other methods with a large number of columns. Click Wide to switch to the Wide method or click Continue to use the method you originally selected.

REML

Restricted maximum likelihood (REML) estimation uses all of the data, even if missing values are present. Due to a bias-correction factor, this method is slow if the dataset is large and there are many missing values. Therefore, REML is most useful for smaller datasets. If there are no missing cells in the data, then the REML and ML estimates are equivalent and equal to the sample covariance matrix. If there are missing cells, REML’s variance and covariance estimates are less biased than the estimates from ML estimation. For statistical details, see REML.

ML

Maximum likelihood (ML) estimation uses all of the data, even if missing values are present. Because the estimates from ML are generated quickly, this method is most useful for large data tables with missing data.

Robust

Robust estimation uses all of the data, even if missing values are present. This method down-weights extreme values and is therefore useful for data tables that might have outliers. For statistical details, see Robust in the Correlations and Multivariate Techniques section.

Row-wise

Row-wise estimation calculates the Pearson correlation for each pair of columns. For statistical details, see Pearson Product-Moment Correlation in the Correlations and Multivariate Techniques section. Row-wise estimation does not use observations with missing values. This method is useful for excluding any observations that have missing data.

Pair-wise

Pair-wise estimation uses all of the data, even if missing values are present. This estimation method calculates Pearson correlations for each pair of columns using all observations with nonmissing values for those two columns. For statistical details, see Pearson Product-Moment Correlation in the Correlations and Multivariate Techniques section. Pair-wise estimation is most useful when a data table has missing values and either more columns than rows, more than 10 columns, or more than 5,000 rows.

Wide

Wide estimation does not use observations with missing values, so rows that contain missing cells are deleted before the method is applied. This estimation method uses an algorithm based on the full singular value decomposition. The algorithm avoids calculating the covariance matrix and is therefore computationally efficient. It is useful when you have a very large number of columns in your data. For statistical details, see Wide.

Sparse

Sparse estimation uses all of the data, even if missing values are present. This estimation method uses an algorithm based on the partial singular value decomposition, which computes only the first specified number of singular values and singular value vectors. The algorithm avoids calculating the covariance matrix, as well as unnecessary principal components and is therefore computationally efficient. It is useful when your data are sparse, meaning they contain many zeros, or when there are a large number of columns in the data. For statistical details, see Sparse.

Note: If you select REML, ML, or Robust and your data table contains more columns than rows and has missing values, JMP switches the Estimation Method to Pairwise.

Number of Components

(Available only when Sparse is specified as the Estimation Method.) Specifies the number of components to be estimated. Typically, the Number of Components is much smaller than the dimension of your data.

The different estimation methods are equipped to handle missing data in a variety of ways. You can also estimate missing values in the following ways:

• Use the Impute Missing Data option found under Multivariate Methods > Multivariate. See Impute Missing Data in the Correlations and Multivariate Techniques section.

• Use the Multivariate Normal Imputation or Multivariate SVD Imputation utilities found in Analyze > Screening > Explore Missing Values. See Explore Missing Values Utility in Predictive and Specialized Modeling.

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