PCA vs. Factor Analysis in Life Sciences
By Dr. Zubair Khalid, DVM, MS, PhD ·
Key Takeaways
- Choose Principal Component Analysis (PCA) for dimensionality reduction and visualization of biological variation, such as stratifying patient cohorts based on gene expression profiles or identifying batch effects in proteomics data.
- Select Factor Analysis (FA) when aiming to model latent biological constructs that explain correlations among measured variables, such as identifying underlying disease subtypes from a panel of clinical markers or behavioral phenotypes.
- PCA preserves total variance, including unique variance (e.g., technical noise in RNA-Seq data or individual measurement error in ELISA assays), whereas FA models only common variance, partitioning it into shared and unique components.
- FA requires sufficient correlation structure among variables to identify meaningful latent factors, making it suitable for datasets where variables are expected to be influenced by common biological mechanisms, unlike PCA which can be applied even to uncorrelated variables.
- Rotation is standard in FA to enhance interpretability of latent factors (e.g., varimax for orthogonal factors representing independent biological processes or promax for correlated factors reflecting interconnected pathways), whereas PCA components are typically not rotated.
- Both methods assume linear relationships; neither establishes causal biological mechanisms, necessitating integration with domain knowledge and confirmatory analyses, such as using factor scores in regression models or validating PCA-derived clusters with RT-PCR.
Quick Answer
- Choose PCA when your goal is dimensionality reduction or visualization of biological variation, and choose factor analysis when you need to model latent biological constructs that explain correlations among measured variables.
- PCA preserves total variance in the data, while factor analysis partitions variance into common and unique components, a distinction that changes how you interpret biological loadings.
- Both methods assume linear relationships, and neither method alone establishes causal biological mechanisms, so pair either approach with domain knowledge and confirmatory analysis.
At a Glance
| Decision Point | PCA | Factor Analysis |
|---|---|---|
| Primary goal | Dimensionality reduction and data visualization | Identify latent constructs or underlying factors |
| Variance treatment | Accounts for total variance in all variables | Models only common variance, separates unique variance |
| Mathematical basis | Orthogonal linear transformations of the original variables | Common factor model with shared and unique components |
| Rotation | Not typically rotated, components are fixed | Rotation is standard to improve factor interpretability |
| Interpretation | Components are linear combinations of observed variables | Factors are latent variables inferred from observed correlations |
| Data requirements | Works with covariance or correlation matrices | Requires sufficient correlation structure among variables |
| Typical biological use | Gene expression clustering, sample stratification, quality control | Psychometric traits, behavioral phenotypes, composite biomarker scores |
| Software implementation | Base R prcomp, Python scikit-learn PCA | R factanal, Python factor_analyzer |
Understanding the Core Distinction
Principal component analysis and factor analysis are both dimension reduction techniques, but they answer different research questions. PCA seeks to explain as much variance as possible with a smaller number of linear combinations of the original variables. Factor analysis seeks to explain the covariance structure among variables using a smaller number of unobserved latent variables. This distinction matters for biological researchers because the choice determines how you interpret the resulting components or factors in the context of your experimental design.
PCA is a mathematical transformation of the data. It finds the directions of maximum variance in the feature space and projects the data onto those directions. The resulting principal components are exact linear combinations of the original variables. No underlying model is assumed about how the variables relate to each other. This makes PCA a descriptive tool that is useful for exploring data structure, detecting outliers, and reducing dimensionality before downstream analysis.
Factor analysis is a statistical model. It assumes that the observed variables are influenced by a smaller number of latent factors plus unique error terms. The goal is to estimate the factor loadings that describe how strongly each observed variable relates to each latent factor. This model-based approach allows you to test hypotheses about the underlying structure of your data, which is often more aligned with biological questions about unobserved regulatory mechanisms or disease subtypes.
The distinction between explaining variance and explaining covariance is central. PCA explains the total variance in the data, including both shared and unique variance. Factor analysis explains only the shared variance among variables, treating unique variance as error. This difference has direct consequences for how you interpret the results. A principal component may be influenced by variables with high unique variance, while a factor is designed to capture only the common variance that variables share.
Mathematical Assumptions and Their Biological Meaning
Variance Decomposition
PCA decomposes the total variance of the dataset into principal components. Each component captures a decreasing amount of variance, and the sum of all components equals the total variance. This decomposition is purely mathematical and does not require any assumptions about the underlying data-generating process. For biological data, this means PCA will always produce components, regardless of whether the data actually has meaningful structure.
Factor analysis decomposes the variance of each observed variable into two parts: common variance that is shared with other variables through latent factors, and unique variance that is specific to the variable. The model is expressed as X = ΛF + ε, where X is the observed data, Λ is the factor loading matrix, F is the latent factor matrix, and ε is the unique error. This model assumes that the latent factors are independent of the unique errors and that the unique errors are independent of each other.
The biological meaning of this distinction is substantial. When you use PCA on gene expression data, the first principal component may capture technical variation such as batch effects or library size differences. These technical artifacts contribute to the total variance and will be included in the principal components. Factor analysis, by modeling only common variance, may be less sensitive to technical noise that is unique to individual samples, but it also requires that the shared variance structure is meaningful.
Assumptions About Error
PCA does not explicitly model error. The components are deterministic functions of the data. Factor analysis explicitly models unique error for each variable. This error term is important for biological data because measurement error is a real concern in many life science applications. Microarray and sequencing data have known technical noise, and protein assays have measurement variability. Factor analysis provides a framework for separating this measurement error from the shared biological signal.
The error assumption also affects how many factors you can estimate. In factor analysis, the number of factors must be small enough that the model is identified. If you have p variables and k factors, the number of parameters in the factor loading matrix must be less than the number of unique elements in the covariance matrix. This constraint means that factor analysis requires a sufficient number of observed variables to estimate a given number of factors. PCA has no such constraint because it does not estimate a model.
Rotation and Interpretability
PCA produces components that are orthogonal to each other. This orthogonality is a mathematical property of the variance decomposition, but it does not necessarily correspond to biological independence. Factor analysis allows rotation of the factor solution. Rotation changes the factor loadings to make the factors more interpretable, either by making loadings closer to zero or one, or by making factors more orthogonal or more correlated.
Varimax rotation is an orthogonal rotation that maximizes the variance of the squared loadings for each factor. This rotation tends to produce factors with a few high loadings and many low loadings, which can be easier to interpret biologically. Promax rotation is an oblique rotation that allows factors to be correlated. Correlated factors may be more realistic for biological data because biological processes are often interconnected.
The choice of rotation is a modeling decision that you must justify. Different rotations can produce different factor solutions, and the interpretation of the factors depends on the rotation. PCA does not offer this flexibility because the components are uniquely determined by the variance decomposition.
Data Inputs and Preparation
Data Types and Scaling
Both PCA and factor analysis require numerical data. Biological data often includes measurements on different scales, such as gene expression counts, protein concentrations, and metabolite levels. Scaling is essential before applying either method. If you do not scale the data, variables with larger variances will dominate the analysis. Standardization, which subtracts the mean and divides by the standard deviation, is a common approach that gives each variable equal weight.
For PCA, the choice of scaling affects the results. If you use the covariance matrix, variables with larger variances will have larger loadings. If you use the correlation matrix, all variables are standardized and have equal influence. The choice depends on whether the variance of each variable is biologically meaningful. For gene expression data, the variance may be biologically meaningful, and you may choose to use the covariance matrix. For data with mixed measurement units, the correlation matrix is often more appropriate.
Factor analysis is typically performed on the correlation matrix. The model assumes that the variables are standardized, and the factor loadings are interpreted as correlations between the observed variables and the latent factors. This standardization is important because factor analysis is scale-invariant only when the correlation matrix is used.
Missing Data
Missing data is a common issue in biological datasets. PCA cannot handle missing values directly. You must either remove samples with missing data, impute the missing values, or use a method that can handle missing data. Removing samples can reduce your sample size and introduce bias if the missingness is not random. Imputation methods, such as k-nearest neighbors or singular value decomposition, can fill in missing values, but they introduce uncertainty that is not captured by the PCA.
Factor analysis also requires a complete data matrix. The model is estimated from the covariance or correlation matrix, which requires complete data. If you have missing data, you must use a method that can handle it, such as full information maximum likelihood or multiple imputation. These methods are more complex and require additional assumptions about the missingness mechanism.
Sample Size Considerations
Sample size is a critical consideration for both methods, but the requirements differ. PCA is a descriptive method that can be applied to a small number of samples, but the results may be unstable. The principal components are estimated from the sample covariance matrix, and with few samples, the covariance matrix is not well estimated. A common rule of thumb is that you need at least 10 samples per variable, but this is not a strict requirement.
Factor analysis has more stringent sample size requirements because it is a model-based method. The factor loadings and unique variances are estimated from the covariance matrix, and the estimation requires a sufficient number of samples to be stable. A common recommendation is at least 5 to 10 samples per variable, but the number of factors and the strength of the loadings also affect the required sample size.
Workflow for Choosing Between PCA and Factor Analysis
Step 1: Define the Research Question
The first step is to clarify what you want to achieve with the analysis. If your goal is to reduce the dimensionality of the data for downstream analysis, such as clustering or regression, PCA is a suitable choice. If your goal is to identify latent variables that explain the correlations among your measured variables, factor analysis is the appropriate method.
For example, if you are working with gene expression data and you want to identify groups of samples that share similar expression profiles, PCA can help you visualize the data in a lower-dimensional space. If you are working with a set of behavioral measurements and you want to test whether a single latent trait, such as anxiety, explains the correlations among the measurements, factor analysis is the appropriate method.
Step 2: Examine the Correlation Structure
The correlation structure of your data is a key indicator of which method is appropriate. Factor analysis requires that the variables are correlated. If the variables are not correlated, there is no common variance to model, and factor analysis will not produce meaningful factors. You can examine the correlation matrix or compute the Kaiser-Meyer-Olkin measure of sampling adequacy to assess whether the data is suitable for factor analysis.
PCA does not require correlated variables. It will find components that capture variance, even if the variables are uncorrelated. However, if the variables are uncorrelated, the principal components will be the original variables, and the analysis will not provide any dimension reduction.
Step 3: Consider the Variance Structure
The variance structure of your data is another important consideration. PCA captures all variance, including unique variance. If your data has a large amount of unique variance, the principal components may be dominated by this unique variance, and the components may not reflect the shared structure. Factor analysis isolates the common variance and can provide a clearer picture of the shared structure.
For biological data, the unique variance may represent measurement error or biological variation that is specific to individual variables. If you are interested in the shared biological signal, factor analysis may be more appropriate. If you are interested in the total variation, including the unique variation, PCA is the better choice.
Step 4: Decide on the Number of Components or Factors
The number of components or factors to retain is a critical decision. For PCA, you can use the scree plot, the proportion of variance explained, or parallel analysis to determine the number of components. The scree plot shows the eigenvalues in descending order, and you look for an elbow where the eigenvalues level off. The proportion of variance explained is a more direct measure, and you can choose the number of components that explains a certain percentage of the total variance, such as 80 percent.
For factor analysis, you can use the same criteria, but you also need to consider the interpretability of the factors. The number of factors should be small enough that the factors are interpretable and large enough that the model fits the data. You can use the chi-square test of model fit to assess whether the number of factors is sufficient.
Step 5: Run the Analysis and Validate
Once you have chosen the method and the number of components or factors, you can run the analysis. After the analysis, you should validate the results. For PCA, you can check the loadings to see which variables contribute most to each component. For factor analysis, you can check the factor loadings and the communalities to see how well each variable is explained by the factors.
Validation is important because the results of both methods are sensitive to the data. You can use cross-validation to assess the stability of the results. For PCA, you can split the data into training and test sets and compare the components. For factor analysis, you can use a confirmatory factor analysis to test whether the factor structure is consistent with a hypothesized model.
Practical Implementation in Life Sciences
Gene Expression Analysis
PCA is widely used in gene expression analysis for quality control and exploratory analysis. You can use PCA to identify batch effects, outliers, and sample groups. The first few principal components often capture the largest sources of variation, which may be technical or biological. You can plot the samples in the space of the first two principal components to visualize the sample structure.
Factor analysis is less commonly used in gene expression analysis because the number of genes is large and the model is computationally intensive. However, factor analysis can be used to identify latent factors that represent biological processes, such as cell types or pathways. The factor loadings can be used to identify genes that are associated with each factor.
Proteomics and Metabolomics
In proteomics and metabolomics, PCA is used to identify patterns in the data and to reduce the dimensionality before downstream analysis. The principal components can be used to visualize the separation between groups, such as disease and control samples. Factor analysis can be used to identify latent factors that represent biological processes, such as metabolic pathways.
The choice between PCA and factor analysis in these fields depends on the research question. If you want to identify the variables that contribute most to the variation, PCA is appropriate. If you want to identify the latent factors that explain the correlations among the variables, factor analysis is appropriate.
Behavioral and Phenotypic Data
Factor analysis is commonly used in behavioral and phenotypic data to identify latent traits. For example, you might have a set of behavioral measurements and want to identify a latent trait, such as anxiety or aggression. Factor analysis can estimate the factor loadings and the factor scores for each sample.
PCA is also used in behavioral data, but it is less common because the goal is often to identify latent variables, not to reduce the dimensionality. PCA can be used to reduce the number of variables before factor analysis, but this is not always necessary.
Interpretation and Reporting
Loadings and Communalities
The loadings in PCA and factor analysis are the correlations between the variables and the components or factors. In PCA, the loadings are the coefficients of the linear combination of the variables. In factor analysis, the loadings are the correlations between the variables and the factors. The loadings can be used to interpret the components or factors.
In factor analysis, the communality of a variable is the proportion of its variance that is explained by the factors. The communality is the sum of the squared loadings for the variable. A high communality indicates that the variable is well explained by the factors. A low communality indicates that the variable has a large amount of unique variance.
Factor Scores
Factor scores are the values of the latent factors for each sample. In PCA, the principal component scores are the projections of the samples onto the principal components. In factor analysis, the factor scores are the estimated values of the latent factors. The factor scores can be used for downstream analysis, such as regression or clustering.
The factor scores are not uniquely determined in factor analysis. There are several methods for estimating factor scores, including the regression method and the Bartlett method. The choice of method can affect the factor scores, and you should be aware of this when interpreting the results.
Rotation and Interpretation
Rotation is a key step in factor analysis. The rotation is used to make the factors more interpretable. The varimax rotation produces factors that are orthogonal and have a few high loadings and a few low loadings. The promax rotation produces factors that are correlated and may be more interpretable for biological data.
The choice of rotation should be based on the research question. If you expect the factors to be independent, use an orthogonal rotation. If you expect the factors to be correlated, use an oblique rotation. The rotation does not change the fit of the model, but it changes the interpretation of the factors.
Reporting and Reproducibility
Reporting Guidelines
When you report the results of PCA or factor analysis, you should follow the reporting guidelines for your field. The EQUATOR Network provides a list of reporting guidelines for different study types. You should report the method, the number of components or factors, the rotation method, the loadings, and the communalities. You should also report the software and the version you used.
Data Management
The NIH Data Management and Sharing Policy requires that you plan for data management and sharing. You should describe how you will manage and share the data, including the data files, the analysis code, and the results. The policy applies to research that is funded by the NIH.
Reproducibility
To ensure reproducibility, you should document your analysis steps and make your code available. You should also document the version of the software and the parameters you used. This documentation is important for other researchers to reproduce your results.
Common Failure Patterns
Overfitting
Overfitting is a common problem in both PCA and factor analysis. In PCA, overfitting can occur when you retain too many components. The components may capture noise in the data, and the results may not generalize to new data. In factor analysis, overfitting can occur when you estimate too many factors. The model may fit the data well, but the factors may not be interpretable.
Underfitting
Underfitting is the opposite problem. If you retain too few components or factors, you may miss important structure in the data. The model may not capture the variance or the correlations in the data.
Misinterpretation
Misinterpretation is a common problem. The components or factors are not necessarily biologically meaningful. The interpretation of the components or factors requires domain knowledge. You should not assume that the components or factors correspond to biological processes without additional evidence.
Data Scaling
Data scaling is a common source of error. If you do not scale the data, the variables with larger variances will dominate the analysis. This can lead to misleading results. You should always scale the data before running PCA or factor analysis.
Safety and Regulatory Context
Data Sharing
The NIH Data Management and Sharing Policy requires that you share the data and the analysis code. This policy applies to research that is funded by the NIH. You should plan for data sharing and management before you start the analysis.
Publication Ethics
The Committee on Publication Ethics provides core practices for research publication. You should follow these practices when you report the results of your analysis. This includes reporting the methods accurately and avoiding plagiarism.
Researcher Identity
The ORCID for Researchers provides a unique identifier for researchers. You should use your ORCID identifier to link your research outputs. This helps to ensure that your work is attributed to you.
A Practical Decision Framework for Biological Data
The conceptual differences between PCA and factor analysis become concrete only when you apply them to a specific dataset with a specific research question. This section provides a structured decision framework that you can implement in your own analysis workflow, along with a record system for documenting your choices and a troubleshooting method for common problems.
The Decision Framework in Five Questions
The framework below translates the statistical distinctions between PCA and factor analysis into five questions that you can answer with your data and your research goal in hand. Each question has a clear branch that leads to one method or the other.
Question 1: What is your primary analytical goal?
If your goal is to reduce the number of variables for downstream analysis, such as clustering, regression, or classification, choose PCA. PCA produces a smaller set of uncorrelated variables that capture the maximum variance in your data. These components can then be used as inputs to other methods without the risk of multicollinearity.
If your goal is to identify latent constructs that explain the correlations among your measured variables, choose factor analysis. Factor analysis estimates the latent factors that are presumed to generate the observed correlations. This is the appropriate choice when you have a hypothesis about an unobserved biological process, such as a regulatory pathway or a behavioral trait, that influences multiple measured variables.
Question 2: Does your hypothesis specify a measurement model?
A measurement model is a statement about how observed variables relate to latent constructs. If you have a specific hypothesis that certain measured variables are indicators of a common latent factor, factor analysis is the appropriate method. For example, if you hypothesize that a set of inflammatory cytokine measurements are all indicators of a single systemic inflammation factor, factor analysis can test this hypothesis.
If you have no such hypothesis and you are exploring the data to see what structure emerges, PCA is the appropriate choice. PCA does not require a measurement model. It simply finds the directions of maximum variance in the data.
Question 3: How do you treat unique variance in your data?
Unique variance is the variance in each variable that is not shared with other variables. This includes measurement error and biological variation that is specific to a single variable. If you want to separate this unique variance from the shared variance, factor analysis is the appropriate method. Factor analysis explicitly models unique variance as error terms.
If you want to preserve all variance, including unique variance, PCA is the appropriate method. PCA does not distinguish between shared and unique variance. It captures the total variance in the data.
Question 4: Do you expect the underlying factors to be correlated?
If you expect the latent biological processes to be correlated, you should use factor analysis with an oblique rotation, such as promax. Oblique rotation allows the factors to be correlated, which is often more realistic for biological data. Biological processes are frequently interconnected, and forcing them to be independent may obscure the true structure.
If you expect the factors to be independent, you can use PCA or factor analysis with an orthogonal rotation, such as varimax. PCA always produces orthogonal components. Factor analysis with an orthogonal rotation also produces independent factors.
Question 5: What is your sample size relative to the number of variables?
Sample size is a practical constraint that can determine which method is feasible. PCA can be applied to datasets with a small number of samples, but the results may be unstable. Factor analysis requires a larger sample size because it is a model-based method that estimates parameters from the covariance matrix.
A common rule of thumb is that you need at least 5 to 10 samples per variable for factor analysis. For PCA, the sample size requirement is less stringent, but you still need enough samples to estimate the covariance matrix reliably. If your sample size is small, PCA is the more practical choice.
A Worked Example
Consider a study of metabolic syndrome in a cohort of 200 patients. You have measured 15 clinical variables, including fasting glucose, triglycerides, HDL cholesterol, blood pressure, and waist circumference. Your research question is whether a single latent factor, such as insulin resistance, explains the correlations among these variables.
This question specifies a measurement model. You hypothesize that the 15 variables are indicators of a smaller number of latent factors. This is a factor analysis question. You would use factor analysis with an oblique rotation because you expect the metabolic factors to be correlated.
In contrast, if your research question is simply to visualize the metabolic profiles of the patients and identify groups of patients with similar profiles, you would use PCA. PCA would reduce the 15 variables to a smaller number of components that you could plot to see the patient structure.
A Record System for Your Analysis
A record system is essential for reproducibility and for defending your methodological choices in a manuscript or grant application. The record should document each decision you make and the rationale for that decision. The following record fields are recommended for both PCA and factor analysis.
Data preparation record
- Data file name and version
- Variables included and their measurement units
- Scaling method used, such as standardization or log transformation
- Missing data handling method, such as listwise deletion or imputation
- Software and version used for data preparation
Analysis record
- Method chosen, PCA or factor analysis
- Correlation or covariance matrix used
- Number of components or factors retained
- Criterion used to determine the number of components or factors, such as eigenvalue greater than one, scree plot, or parallel analysis
- Rotation method, if factor analysis was used
- Software and version used for the analysis
Validation record
- Cross-validation method used, if any
- Stability of the components or factors across validation runs
- Sensitivity of the results to the number of components or factors
- Sensitivity of the results to the scaling method
Interpretation record
- Loadings for each variable on each component or factor
- Communalities for each variable in factor analysis
- Factor scores or component scores for each sample
- Biological interpretation of each component or factor
- Any limitations or caveats in the interpretation
This record system serves two purposes. First, it documents your analysis for reproducibility. Second, it provides a basis for troubleshooting if the results are unexpected or if a reviewer questions your choices.
Troubleshooting Common Problems
The following troubleshooting method addresses the most common problems that arise when applying PCA or factor analysis to biological data. Each problem is described with its likely cause and a practical solution.
Problem 1: The first principal component captures a large proportion of variance but does not separate the biological groups of interest.
This pattern often indicates that the first component captures technical variation, such as batch effects or library size differences, instead of biological variation. The solution is to examine the loadings of the first component. If the loadings are dominated by technical variables, such as total read count or batch indicator, you should remove the technical variation before running PCA. Methods such as ComBat or limma remove known batch effects. You can also regress out the technical variables and run PCA on the residuals.
Problem 2: The factor analysis produces a factor with only one high loading.
A factor with only one high loading is not a meaningful latent factor. It indicates that the variable has a large amount of unique variance that is not shared with other variables. The solution is to examine the communality of the variable. If the communality is low, the variable is not well explained by the factors. You may need to remove the variable or add more variables that are expected to share the same latent factor.
Problem 3: The factor analysis fails to converge or produces a Heywood case.
A Heywood case occurs when the estimated unique variance for a variable is negative, which is impossible. This problem often indicates that the model is not identified or that the data does not support the specified number of factors. The solution is to reduce the number of factors, increase the sample size, or remove variables that are highly correlated with each other.
Problem 4: The results are unstable across different samples of the data.
Instability indicates that the covariance matrix is not well estimated. This problem is common when the sample size is small relative to the number of variables. The solution is to increase the sample size, reduce the number of variables, or use a more stable estimation method. For factor analysis, you can use a regularized estimation method that shrinks the loadings toward zero.
Problem 5: The loadings are difficult to interpret biologically.
Difficulty in interpretation often arises when the loadings are spread across many variables. This pattern is common in PCA because the components are designed to capture maximum variance, not to be interpretable. The solution is to use factor analysis with rotation, which produces loadings that are closer to zero or one. You can also use a threshold to identify the variables that load most strongly on each component or factor.
Validation and Sensitivity Analysis
Validation is a critical step in any dimension reduction analysis. The results of PCA and factor analysis are sensitive to the data and the choices you make. The following validation methods can help you assess the stability and the robustness of your results.
Cross-validation for PCA
Split the data into training and test sets. Run PCA on the training set and project the test set onto the components. Compare the component scores between the training and test sets. If the scores are similar, the components are stable. If the scores are different, the components are not stable and may be capturing noise.
Parallel analysis for the number of components or factors
Parallel analysis compares the eigenvalues from your data to the eigenvalues from random data with the same number of variables and samples. Retain the components or factors with eigenvalues that are larger than the eigenvalues from the random data. This method is more objective than the scree plot or the eigenvalue greater than one criterion.
Sensitivity analysis for scaling
Run the analysis with different scaling methods, such as standardization, log transformation, or no scaling. Compare the loadings and the number of components or factors. If the results are similar across scaling methods, the results are robust. If the results are different, the results are sensitive to the scaling method, and you should report this sensitivity.
Sensitivity analysis for the number of components or factors
Run the analysis with different numbers of components or factors. Examine the loadings and the interpretation for each solution. If the interpretation is stable across different numbers, the results are robust. If the interpretation changes, you should report the range of solutions and justify your choice.
Reporting Your Analysis
The reporting of your analysis should follow the reporting guidelines for your field. The EQUATOR Network provides a list of reporting guidelines for different study types. You should report the method, the number of components or factors, the rotation method, the loadings, and the communalities. You should also report the software and the version you used.
The NIH Data Management and Sharing Policy requires that you plan for data management and sharing. You should describe how you will manage and share the data, including the data files, the analysis code, and the results. The policy applies to research that is funded by the NIH.
The Committee on Publication Ethics provides core practices for research publication. You should follow these practices when you report the results of your analysis. This includes reporting the methods accurately and avoiding plagiarism.
The ORCID for Researchers provides a unique identifier for researchers. You should use your ORCID identifier to link your research outputs. This helps to ensure that your work is attributed to you.
When to Seek Professional Help
The methods described in this section are within the reach of most researchers with a basic background in statistics. However, there are situations where you should seek help from a statistician or a bioinformatician.
- If your data has a complex structure, such as repeated measures, longitudinal data, or hierarchical sampling, the standard PCA or factor analysis may not be appropriate. You may need a mixed-effects model or a multilevel factor analysis.
- If your data has a large number of variables relative to the sample size, the standard estimation methods may be unstable. You may need a regularized method or a Bayesian approach.
- If your data is non-linear, the standard linear methods may not capture the structure. You may need a non-linear method, such as kernel PCA or a non-linear factor analysis.
- If you are not sure which method is appropriate for your data, you should consult a statistician before you run the analysis. A statistician can help you clarify your research question and choose the appropriate method.
The decision framework and the record system described in this section are designed to help you make an informed choice between PCA and factor analysis. The framework is not a substitute for statistical expertise, but it provides a structured approach that you can use to make a defensible decision.
Frequently Asked Questions
What is the main difference between PCA and factor analysis?
PCA is a data transformation that captures the total variance in the data, while factor analysis is a model that explains the shared variance among variables using latent factors. PCA is used for dimensionality reduction, and factor analysis is used for identifying latent variables.
Can I use PCA for factor analysis?
PCA and factor analysis are different methods. PCA is a data transformation, and factor analysis is a model. You cannot use PCA for factor analysis. You can use PCA to reduce the dimensionality of the data before factor analysis, but this is not the same as factor analysis.
How do I choose the number of components in PCA?
You can use the scree plot, the eigenvalue, or the proportion of variance explained to choose the number of components. The scree plot shows the eigenvalues in descending order, and you look for an elbow. The eigenvalue criterion is to retain components with eigenvalues greater than one. The proportion of variance explained is a direct measure.
How do I choose the number of factors in factor analysis?
You can use the eigenvalue criterion, the scree plot, or the likelihood ratio test to choose the number of factors. The eigenvalue criterion is to retain factors with eigenvalues greater than one. The scree plot shows the eigenvalues in descending order. The likelihood ratio test compares the fit of the model with different numbers of factors.
What is the difference between orthogonal and oblique rotation?
Orthogonal rotation produces factors that are independent, and oblique rotation produces factors that are correlated. The choice of rotation depends on the research question. If you expect the factors to be independent, use an orthogonal rotation. If you expect the factors to be correlated, use an oblique rotation.
Can I use PCA on non-linear data?
PCA is a linear method. It assumes that the relationships between the variables are linear. If the relationships are non-linear, PCA may not be appropriate. You can use non-linear methods, such as kernel PCA, but these are not the same as PCA.
What is the role of the correlation matrix in factor analysis?
The correlation matrix is the basis for factor analysis. The model is estimated on the correlation matrix, and the loadings are the correlations between the variables and the factors. The correlation matrix is used to identify the common variance among the variables.
How do I report the results of PCA or factor analysis?
You should report the method, the number of components or factors, the rotation method, the loadings, and the communalities. You should also report the software and the version you used. The EQUATOR Network provides reporting guidelines for different types of research.
Using the Evidence
| Source | Best use in this topic | Important limitation |
|---|---|---|
| Research Methods Resources | official guidance | Check the linked page for current local requirements |
| EQUATOR Network | official guidance | Check the linked page for current local requirements |
| Core Practices | official guidance | Check the linked page for current local requirements |
Related Bioinformatics Guides
- Genomic Data Analysis Tools: A Comparative Guide for Researchers
- Metabolomics Data Analysis Workflow: From Raw Data to Biological Insight
- Metagenomics Data Analysis: From Raw Reads to Biological Insights
- Proteomics Data Analysis Workflow: From Raw Spectra to Biological Insights
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Related Clinical & Scientific Guides
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References and Further Reading
- Research Methods Resources. National Library of Medicine.
- EQUATOR Network. EQUATOR Network.
- Core Practices. Committee on Publication Ethics.
- NIH Grants and Funding. National Institutes of Health.
- ORCID for Researchers. ORCID.
- Data Management and Sharing Policy. National Institutes of Health.
- NCBI Data Resources. National Center for Biotechnology Information.
- EMBL-EBI Training. European Bioinformatics Institute.
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This article is educational and does not replace validated analysis plans, institutional policy, clinical interpretation, or specialist review.