To determine if data is suitable for factor analysis, you must evaluate several statistical and structural characteristics to ensure the validity and reliability of the resulting factors.
Key Indicators for Data Suitability
Factor analysis relies on specific data properties to produce meaningful and interpretable results. Assessing these characteristics is a crucial preliminary step.
1. Sample Size
An adequate sample size is fundamental for stable factor solutions. While there are no absolute rules, general guidelines suggest:
- A minimum of 100-200 observations.
- Ideally, a ratio of 5 to 10 participants per variable (e.g., for 20 variables, at least 100-200 participants). Larger samples generally lead to more stable factor structures.
2. Measurement Level
The variables included in factor analysis should ideally be measured at the interval or ratio scale. While ordinal data can sometimes be used, especially if categories are numerous and treated as quasi-interval, it should be done with caution and a clear understanding of its implications for the underlying correlation calculations.
3. Inter-item Correlations (Linear Relations)
The presence of meaningful linear relationships between variables is essential for factor analysis.
- Sufficient Correlations: There should be a reasonable number of moderate correlations among the variables (e.g., absolute values typically above 0.3). If all variables are largely uncorrelated, there are no common factors to extract.
- No Perfect Correlations: Crucially, there must not be a perfect correlation (a correlation coefficient of +1.0 or -1.0) between any pair of variables. Perfect correlation indicates redundancy, implying the variables measure the exact same construct. If such a perfect correlation exists, one variable from that pair should be dropped to prevent computational issues (like a singular correlation matrix) and improve the stability of the factor solution.
4. Normality
While not strictly required for all factor extraction methods (e.g., Principal Components Analysis makes no distributional assumptions), features with a normal distribution significantly improve the results of statistical tests involved in factor analysis, particularly for methods like Maximum Likelihood.
- You can check for normality using visual inspections (histograms, Q-Q plots) and statistical tests (e.g., Shapiro-Wilk, Kolmogorov-Smirnov), as well as by examining skewness and kurtosis values.
- Mild deviations are often acceptable, but severe non-normality might warrant data transformation or the use of robust factor analysis methods.
5. Absence of Multicollinearity and Singularity
This point extends the idea of inter-item correlations.
- Multicollinearity occurs when variables are highly, but not perfectly, correlated. While some multicollinearity is expected and desired in factor analysis (as it indicates shared variance), extreme levels can make it difficult to ascertain the unique contribution of each variable to a factor.
- Singularity is the extreme case of perfect multicollinearity. As mentioned, if two variables are perfectly correlated, the correlation matrix becomes singular and cannot be inverted, which is necessary for many factor analysis calculations.
6. Statistical Tests for Factorability
Before proceeding with factor extraction, specific statistical tests help confirm the data's suitability.
- Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy:
- The KMO statistic assesses the proportion of variance in your variables that might be common variance, indicating how well each variable is explained by the other variables in the dataset.
- Values range from 0 to 1. Generally:
- KMO ≥ 0.6 is considered acceptable.
- KMO ≥ 0.8 is very good.
- Values below 0.5 suggest that the data may not be suitable for factor analysis.
- For a deeper understanding, explore resources on Kaiser-Meyer-Olkin (KMO) Test.
- Bartlett's Test of Sphericity:
- This test examines the null hypothesis that the correlation matrix is an identity matrix, meaning all variables are uncorrelated in the population.
- A statistically significant result (p-value < 0.05) indicates that the correlation matrix is significantly different from an identity matrix, suggesting that there are sufficient relationships among variables to proceed with factor analysis. If the test is not significant, factor analysis may not be appropriate.
- Learn more about Bartlett's Test of Sphericity.
7. Absence of Outliers
Extreme outliers can heavily influence correlation coefficients, potentially distorting the factor structure. It's important to:
- Identify outliers through methods like box plots or Mahalanobis distance.
- Decide on an appropriate handling strategy, which might include removal, transformation, or using robust estimation methods if necessary.
Practical Steps to Assess Data Suitability
Follow these steps to systematically evaluate your data:
- Descriptive Statistics: Calculate means, standard deviations, skewness, and kurtosis for all variables. Examine histograms and Q-Q plots to visually assess distributions and identify potential outliers.
- Correlation Matrix Inspection: Generate and visually inspect the correlation matrix. Look for a reasonable number of correlations (absolute values) above 0.3. Crucially, verify that there are no perfect correlations (1.0 or -1.0) between any variable pairs.
- Run KMO and Bartlett's Test: Implement these statistical tests using appropriate software (e.g., R, SPSS, Python) and interpret their results based on the guidelines provided above.
- Check Sample Size: Confirm that your sample size meets or exceeds the general recommendations.
- Theoretical Basis: Consider whether it makes theoretical sense for the variables to share common underlying constructs. Statistical suitability should always be combined with theoretical justification.
Summary of Suitability Criteria
| Criterion | Description | Ideal Indication |
|---|---|---|
| Sample Size | Number of observations relative to variables. | N > 200, or N:items > 10:1 (ideally) |
| Measurement Level | Variables are appropriate for correlation calculation. | Interval or Ratio scale (Ordinal with caution) |
| Inter-item Correlations | Sufficient, non-perfect linear relationships among variables. | Many correlations > 0.3, no perfect correlations |
| Normality | Distribution of individual variables. | Generally normal (improves results) |
| KMO | Measure of sampling adequacy. | KMO ≥ 0.6 (good: ≥ 0.8) |
| Bartlett's Test | Tests if the correlation matrix is an identity matrix. | Statistically significant (p < 0.05) |
| Outliers | Presence of extreme values. | Minimal or appropriately handled |
