---
title: Principal Component Analysis (PCA)
description: Run PCA using the PCA tab. View scree plots, variance explained, component loadings, and principal component scores.
priority: 0.7
---

# Principal Component Analysis (PCA) {#pca}

The PCA tab performs principal component analysis. PCA summarizes many variables into fewer composite variables (principal components) ordered by how much variance they capture. Use it to explore correlation structures among variables or to reduce dimensionality.

MIDAS computes principal components via eigenvalue decomposition of the covariance matrix.

## Basic Usage {#basic-usage}

### Opening PCA {#opening-pca}

Select **Analysis > Principal Component Analysis...** from the menu bar to open a new PCA tab.

### Setting Up Variables {#setting-up-variables}

![Variable setup](../shared/images/pca-form.webp)

**Dataset** selects the dataset to analyze.

**Variables for PCA** selects the variables for the analysis. Only numeric columns are selectable. Columns with nominal/ordinal scale or date/datetime type are grayed out with a tooltip indicating that conversion is required. To use categorical variables, convert them to dummy variables using [Dummy Coding](dummy-coding) first. At least 2 variables are required.

**Preprocessing** selects the preprocessing method.

| Option | Description |
|--------|-------------|
| Standardize (z-score) | Subtract the mean and divide by the standard deviation for each variable (default) |
| Center only | Subtract the mean for each variable |
| None | No variable transformation |

Select Standardize when variables have different scales (different units or value ranges). Without standardization, variables with larger ranges dominate the principal components. Center only or None is appropriate when all variables share the same unit and similar scales.

Regardless of the preprocessing choice, the mean is subtracted internally when computing the covariance matrix and principal component scores. With None, variable scales are unchanged but the covariance matrix is computed from mean-centered data. Standardize uses the covariance matrix of standardized data, producing results similar to correlation-matrix-based PCA. Center only and None use the covariance matrix on the original scale.

Click the **Run PCA** button to run the analysis.

## Understanding Results {#understanding-results}

![PCA results](../shared/images/pca-results.webp)

### Summary {#summary}

Displays an overview of the analysis.

| Field | Description |
|-------|-------------|
| Samples | Number of rows used |
| Features | Number of selected variables |
| Components | Number of extracted principal components (equals the number of variables) |
| Skipped Rows | Rows excluded due to missing or invalid values |

### Scree Plot {#scree-plot}

Shows the variance ratio (%) of each principal component as a line chart. The x-axis is the component number and the y-axis is the variance ratio.

The "elbow" — the point where the decline in variance ratio levels off — is one guide for choosing how many components to retain. Use it together with the cumulative variance ratio in the Variance Table. The elbow is a visual judgment and may not always be clear-cut.

Click **Add to Report** to add the chart to a report.

### Variance Table {#variance-table}

Displays the eigenvalue and variance ratio for each principal component.

| Column | Description |
|--------|-------------|
| Component | Component number (PC1, PC2, ...) |
| Eigenvalue | Eigenvalue (amount of variance explained by the component) |
| Variance Ratio | Proportion of total variance explained (eigenvalue divided by the sum of all eigenvalues) |
| Cumulative | Cumulative variance ratio |

Click **Save as Dataset** to save as a dataset. The saved dataset opens in a Data Table tab.

### Principal Component Scores {#pc-scores}

Displayed when there are 2 or more components. Plots each observation's principal component scores as a 2D scatter plot.

The X-axis and Y-axis dropdowns switch which components to display. Each option shows the variance ratio (e.g., "PC1 (45.2%)"). The default is X = PC1, Y = PC2.

Click **Save as Dataset** to save all component scores as a dataset. The saved scores can be used as input data in other analysis tabs (scatter plots, regression, etc.). Click **Add to Report** to add the chart to a report.

### Component Loadings {#component-loadings}

Displayed when there are 2 or more components. Shows how each variable contributes to each principal component.

| Column | Description |
|--------|-------------|
| Variable | Original variable name |
| PC1, PC2, ... | Loading on each component |

The loadings displayed by MIDAS are eigenvector elements (the weight of each variable in composing the component), not correlations between variables and components. Each eigenvector is normalized to unit length, so individual elements fall between -1 and 1. Variables with larger absolute loadings characterize the component more strongly. The sign indicates a positive or negative relationship with the component.

Click **Save as Dataset** to save as a dataset.

## Notes {#notes}

### Automatic Exclusion of Missing and Invalid Values {#automatic-exclusion}

Rows containing missing values (null), non-numeric values, or infinities are excluded automatically. The number of excluded rows is shown in the Summary. This exclusion is listwise deletion. With many variables, even a single missing value in any variable causes the entire row to be excluded, potentially reducing the usable sample size substantially. See [Missing Data Mechanisms](concepts-missing-data#listwise-deletion-and-mcar) for when listwise deletion is appropriate.

### Eigenvector Sign Convention {#sign-convention}

Eigenvectors have inherent sign ambiguity (if $v$ is an eigenvector, so is $-v$). MIDAS resolves this by making the element with the largest absolute value positive for each component.

### Number of Components {#number-of-components}

MIDAS extracts as many components as there are variables. It does not automatically select the number of components. Use the Scree Plot and Variance Table to decide how many components are meaningful for your analysis.

## See also {#see-also}

- **[Basic Statistics](basic-statistics)** - Examine distributions of individual variables
- **[Linear Regression](linear-regression)** - Analyze the effect of predictor variables on a specific response
- **[Dummy Coding](dummy-coding)** - Convert categorical variables to numeric
- **[Missing Data Mechanisms](concepts-missing-data)** - When listwise deletion is appropriate
- **[Reports](report)** - Collect graphs and statistical results