What Cross-Loadings Mean and How to Handle Them (2026 Guide)?

If you have ever run an exploratory factor analysis and stared at your pattern matrix wondering why an item loads on two or three factors at once, you are dealing with cross-loadings. Cross-loadings in factor analysis occur when a single observed variable has a meaningful loading on more than one latent factor, meaning that item is measuring multiple constructs at the same time instead of cleanly representing just one.

For researchers validating a questionnaire, developing a new scale, or running a confirmatory model, cross-loadings are one of the most common and frustrating problems you will encounter. They threaten your discriminant validity, muddy your factor interpretations, and can call your entire measurement model into question.

In this guide, we break down exactly what cross-loadings mean, why they happen, and walk through five practical methods for handling them. Whether you are working in SPSS, R, or another statistical package, you will find step-by-step guidance, threshold rules of thumb, and a decision framework you can apply to your own data right away.

We also cover topics that most resources gloss over, including when it is actually acceptable to keep cross-loading items, how cross-loadings differ between EFA and CFA, and how to report your cross-loading decisions in an academic paper using APA style.

Prerequisite: Understanding Factor Loadings First

Before we can talk about cross-loadings, we need to make sure the basics of factor loadings are clear. A factor loading represents the strength and direction of the relationship between an observed variable (like a survey item) and an underlying latent factor.

Think of it this way: each item on your questionnaire is an indirect measurement of something you cannot observe directly. A factor loading tells you how strongly that item reflects the latent construct it is supposed to measure.

What Is a Factor Loading?

A factor loading is essentially a correlation coefficient (in orthogonal rotation) or a regression weight (in oblique rotation) between an observed variable and a latent factor. Values range from -1 to +1, and higher absolute values mean the item is a stronger indicator of that factor.

When you run a factor analysis, the software produces a loading matrix showing every item’s loading on every extracted factor. Your goal is to find items that load strongly on one factor and weakly on all others. That clean pattern is what statisticians call simple structure, and it is the benchmark we aim for in a well-defined factor solution.

Factor Loading Thresholds: What Counts as Significant?

One of the most common questions on statistics forums is about what factor loading value counts as meaningful. The answer depends on your sample size and field standards, but there are widely used guidelines.

According to Hair and colleagues’ widely cited guidelines, a factor loading of 0.30 is considered the minimum threshold for significance with a sample size of 350 or more. A loading of 0.40 is considered important for smaller samples around 200. Loadings of 0.50 or higher are considered practically significant regardless of sample size.

For primary loadings, many researchers use a stricter threshold of 0.60 or even 0.70. Stevens (2002) recommended that loadings above 0.40 be considered for interpretation, while Tabachnick and Fidell suggest 0.32 as a minimum cutoff because it corresponds to approximately 10 percent overlapping variance.

Here is a quick reference for the three most commonly cited thresholds:

• 0.30 – Minimum significance level, acceptable with large samples (350+). Often used for identifying cross-loadings.

• 0.40 – A more conservative cutoff recommended for smaller samples (around 200). A common threshold for considering a loading meaningful.

• 0.50 – Considered practically significant across sample sizes. Many researchers use this as the bar for a strong primary loading.

• 0.60 to 0.70 – Considered very strong. Often used as the threshold for primary loadings in scale development and questionnaire validation studies.

The key takeaway is that no single threshold is universally correct. You should choose your cutoff based on your sample size, field conventions, and the purpose of your analysis.

What Are Cross-Loadings in Factor Analysis?

Cross-loadings in factor analysis occur when an observed variable loads significantly on more than one latent factor simultaneously. Instead of loading cleanly on a single factor, the item shares meaningful variance with two or more factors, making it unclear which construct the item truly measures.

In practical terms, you spot a cross-loading when you look at your rotated factor matrix and see an item with a coefficient above your threshold (commonly 0.30 or 0.40) on two or more factors. For example, if Item 5 loads at 0.62 on Factor 1 and 0.45 on Factor 2, that item is cross-loading.

The highest coefficient is called the primary loading, and all other significant coefficients on different factors are the cross-loadings. In a perfect simple structure, every item would have one strong primary loading and all other loadings would be near zero.

Cross-loadings are especially common when your factors are correlated with each other, which is why oblique rotations like promax and oblimin tend to reveal them more readily. This is not a flaw of oblique rotation. It is actually a more realistic representation of how psychological and social science constructs actually relate to each other.

It is worth noting that small cross-loadings below your threshold are completely normal and expected. You do not need every off-factor loading to be exactly zero. The concern is when cross-loadings are large enough to create ambiguity about factor membership and interpretation.

Pattern Matrix vs Structure Matrix: Where Cross-Loadings Appear

One of the biggest sources of confusion we see on forums like Reddit’s r/statistics and Cross Validated is the difference between the pattern matrix and the structure matrix. If you are using an oblique rotation, your software will produce both, and they tell you different things.

The pattern matrix shows the unique contribution of each variable to each factor, controlling for the other factors. Think of these as regression weights. This is the matrix you should use when deciding whether an item has a cross-loading problem.

The structure matrix shows the zero-order correlations between each variable and each factor, without controlling for factor correlations. Because factors are correlated in oblique rotation, the structure matrix will almost always show larger values across more factors, making cross-loadings look more severe than they actually are.

This distinction matters enormously. Many researchers panic when they see the structure matrix filled with moderate values across multiple factors, but this is a natural consequence of correlated factors. Always evaluate cross-loadings using the pattern matrix, not the structure matrix.

As a rule of thumb: use the pattern matrix for interpreting what each factor means and for identifying cross-loading items. Use the structure matrix only for reporting correlations between items and factors when needed.

Why Cross-Loadings Are a Problem

Cross-loadings create several serious issues for your measurement model. Understanding these problems will help you explain to reviewers and advisors why addressing cross-loadings is not optional.

First and most importantly, cross-loadings threaten discriminant validity. Discriminant validity means that each factor is distinct from the others. When an item loads significantly on two factors, those factors are overlapping in what they measure, which undermines the claim that they are separate constructs.

Second, cross-loadings make factor interpretation difficult. If Item 5 loads equally on a factor labeled “anxiety” and a factor labeled “depression,” which construct does that item actually represent? This ambiguity makes it hard to name your factors confidently or to use them in subsequent analyses.

Third, cross-loadings can affect your reliability estimates. If you calculate Cronbach’s alpha for a factor that includes cross-loading items, the alpha may be inflated or deflated depending on how the shared variance is distributed across factors.

Fourth, cross-loadings complicate convergent validity. Items that cross-load dilute the strength of the relationship between the item and its primary factor, potentially lowering the average variance extracted and other convergent validity indicators.

Finally, in structural equation modeling and regression contexts, cross-loading items introduce measurement error that can bias path coefficients and weaken the overall model fit. This is why dealing with cross-loadings at the EFA stage saves significant headaches later.

How to Identify Cross-Loadings in Your Output

Identifying cross-loadings requires running a factor analysis with rotation, then carefully examining the resulting loading matrix. The process is similar across software packages, but the specific steps differ between SPSS and R.

Before running the factor analysis, always check your data adequacy. Run the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy and Bartlett’s test of sphericity. A KMO value above 0.60 and a significant Bartlett’s test indicate that your data are suitable for factor analysis.

Detecting Cross-Loadings in SPSS

SPSS makes detecting cross-loadings relatively straightforward once you know where to look. Here is the step-by-step process our team recommends.

Step 1: Go to Analyze, then Dimension Reduction, then Factor. Move your items into the analysis box.

Step 2: Click the Extraction button. Choose Principal Axis Factoring or Maximum Likelihood as your method. Select the number of factors based on your scree plot or eigenvalue-greater-than-one criterion. Click Continue.

Step 3: Click the Rotation button. Choose Direct Oblimin or Promax for an oblique rotation (recommended for most social science data). If you have a strong theoretical reason to believe factors are uncorrelated, choose Varimax. Click Continue.

Step 4: This is the critical step. Click the Options button and check the box for “Suppress small coefficients.” Set the absolute value cutoff to 0.30 or 0.40 depending on your threshold. This will hide all loadings below your cutoff, making cross-loadings immediately visible. Click Continue, then OK.

Step 5: Examine the Pattern Matrix table in your output. Items that show values above your threshold on more than one factor are cross-loading. The suppressed output makes these easy to spot because each row should ideally show only one visible coefficient.

If you see an item with two or more visible coefficients, flag it for further action using the methods described in the next section.

Detecting Cross-Loadings in R

For R users, the psych package by William Revelle provides excellent tools for factor analysis and cross-loading detection. Here is a practical workflow.

First, install and load the psych package and your data. Run the KMO and Bartlett tests using the KMO() and cortest.bartlett() functions to confirm data adequacy.

Next, determine the number of factors using a scree plot with fa.parallel(), which compares your eigenvalues to both principal components and factor analysis parallel analysis. This helps you avoid over-extracting factors, which is a common cause of cross-loadings.

Then run the factor analysis using fa() from the psych package. Specify your rotation (we recommend “oblimin” for most applications) and the number of factors identified from your parallel analysis.

After running the analysis, examine the loadings output. The psych package automatically highlights loadings and suppresses small values by default. Any item showing meaningful loadings (by default above 0.20, but you can adjust) on multiple factors is cross-loading.

For a cleaner view, use print(fa_result, sort = TRUE, cut = 0.3) to sort items by their primary loading and suppress values below 0.30. This sorted output makes cross-loading items immediately obvious because they will show multiple non-dashed values in their row.

You can also use the fa.diagram() function to visualize the factor structure. Cross-loading items will show arrows pointing to multiple factors, giving you a clear visual flag.

How to Handle Cross-Loadings: 5 Practical Methods

Once you have identified cross-loading items, you need to decide how to address them. Here are five methods, ranging from the most common to the most nuanced, with clear guidance on when to use each approach.

Method 1: Remove the Cross-Loading Item

This is the most common and straightforward approach. If an item cross-loads and you cannot make a strong theoretical argument for why it should be retained, removing it is the cleanest solution.

The key rule here is to remove cross-loading items one at a time, not all at once. Removing one item changes the factor structure, which may resolve other cross-loadings that were artifacts of the previous solution. After each removal, rerun the EFA and re-examine the pattern matrix.

This iterative process continues until all remaining items show a clear simple structure with no problematic cross-loadings. Many researchers on forums report frustration with not knowing when to stop. The answer is: stop when every remaining item has one primary loading above your threshold and no other loadings above that same threshold, and you have at least three to four items per factor.

Method 2: Re-Specify the Number of Factors

Sometimes cross-loadings are a symptom of having extracted too many or too few factors. If you extracted too many factors, the variance from a clean item gets split across two factors, creating artificial cross-loadings. If you extracted too few, distinct constructs get merged, forcing items to load on a combined factor.

Re-examine your scree plot and parallel analysis results. Try adding or removing one factor and see whether the cross-loading pattern resolves. This method is particularly effective when multiple items cross-load onto the same pair of factors, which may indicate an over-extraction problem.

Method 3: Change the Rotation Method

The rotation method you choose affects how cross-loadings appear in your output. Orthogonal rotations like varimax force factors to be uncorrelated, which can suppress cross-loadings but may distort the true factor structure. Oblique rotations like promax and oblimin allow factors to correlate, which is more realistic but may reveal more cross-loadings.

If you are seeing many cross-loadings with varimax, try switching to an oblique rotation. The factors may be correlated, and forcing orthogonality could be distorting your results. Conversely, if promax reveals cross-loadings that varimax did not, those cross-loadings were always there. Varimax was just hiding them by constraining the solution.

The general recommendation in modern psychometric practice is to default to oblique rotation unless you have a compelling theoretical reason to believe your factors are perfectly uncorrelated.

Method 4: Consider a Higher-Order Factor Model

If several items consistently cross-load between the same two or three factors, this may indicate that those factors are themselves indicators of a broader, higher-order construct. Instead of forcing items into one factor or another, you can model a second-order factor that accounts for the shared variance among the lower-order factors.

This approach is particularly useful when your factors are moderately to highly correlated (above 0.50) and the cross-loading pattern suggests a meaningful hierarchical structure. For example, if items cross-load between “emotional exhaustion” and “depersonalization,” it may be because both are sub-dimensions of a higher-order “burnout” construct.

Higher-order models can be specified in CFA using software like lavaan in R or AMOS in SPSS. This approach preserves all your items while accounting for the cross-loading variance in a theoretically meaningful way.

Method 5: Retain the Item with Theoretical Justification

This is the most nuanced approach and one that most guides do not cover. In some cases, it is theoretically defensible to keep a cross-loading item if the cross-loading makes substantive sense.

For instance, an item about “feeling nervous in social situations” might legitimately load on both an anxiety factor and a social functioning factor. If this dual loading aligns with your theoretical framework, you can retain the item and report the cross-loading transparently.

The key is that the retention must be justified, not just convenient. Document your reasoning clearly, report the cross-loading in your results, and be prepared to defend the decision to reviewers. This approach is more defensible in CFA contexts, where you can assess model fit with and without the cross-loading specified.

Rotation Methods and Their Effect on Cross-Loadings

Your choice of rotation method has a direct impact on how cross-loadings appear in your results. Understanding this relationship will help you interpret your output more accurately.

Varimax is the most popular orthogonal rotation. It maximizes the variance of squared loadings within each factor, which tends to produce a cleaner simple structure with fewer apparent cross-loadings. However, this cleanliness comes at a cost: varimax forces factors to be uncorrelated, which may not reflect reality. Cross-loadings that varimax hides do not disappear. They are simply redistributed.

Promax is an oblique rotation that starts with a varimax solution and then raises the loadings to a power (kappa) to allow factors to correlate. This means promax will generally show more cross-loadings than varimax because it allows the factor correlations to surface. Many forum users ask whether cross-loadings in promax are acceptable, and the answer is: yes, promax reveals cross-loadings that were always present. The cross-loadings are not caused by the rotation.

Oblimin (specifically Direct Oblimin) is another oblique rotation that gives you a delta parameter to control the degree of factor correlation. With delta set to 0 (the default), oblimin allows moderate factor correlations. Oblimin and promax will usually produce similar results, but oblimin offers slightly more flexibility in controlling how much factors are allowed to correlate.

Here is a practical comparison:

• Varimax (orthogonal): Fewest apparent cross-loadings. Factors are forced to be uncorrelated. Good for exploring data when you have no prior theory about factor correlations. May hide real cross-loadings.

• Promax (oblique): More realistic for correlated factors. Will reveal cross-loadings that varimax may suppress. Recommended for most social science applications where constructs are theoretically related.

• Oblimin (oblique): Similar to promax but with more control over the degree of factor correlation via the delta parameter. Useful when you want to fine-tune how much overlap between factors your solution allows.

The modern consensus in psychometric methodology is to use oblique rotations by default. Real-world constructs in psychology, education, and social science are almost always correlated, and pretending they are orthogonal can distort your results.

Cross-Loadings in EFA vs CFA: Key Differences

Cross-loadings present differently and require different responses depending on whether you are running exploratory factor analysis or confirmatory factor analysis. Most resources cover one or the other but not both.

In EFA, cross-loadings are something you discover. Every item is free to load on every factor, and the analysis reveals the loading pattern. Your job is to identify cross-loadings and decide how to handle them, typically through item removal, factor re-specification, or rotation changes.

In CFA, cross-loadings are something you specify (or fail to specify). In CFA, you tell the software exactly which items load on which factors. By default, each item is allowed to load on only one factor. Cross-loadings in CFA are actually the opposite of the EFA problem: you may have a misspecified model because you did not allow a cross-loading that actually exists.

This means that in CFA, you might need to add cross-loadings to improve model fit, not remove them. Poor fit indices (RMSEA above 0.08, CFI below 0.90, SRMR above 0.08) may indicate that an item needs to cross-load on another factor. Modification indices in CFA software can help you identify which cross-loadings to add.

The key difference: in EFA, cross-loadings are a problem to eliminate. In CFA, missing cross-loadings can be a source of model misspecification that you may need to add to improve fit. This distinction is something that trips up many researchers who move from EFA to CFA in the scale development process.

When Is It Acceptable to Keep Cross-Loading Items?

The default response to cross-loadings in most textbooks and tutorials is to remove the offending items. However, this is not always the best choice. There are legitimate situations where retaining a cross-loading item is both defensible and methodologically sound.

The first scenario is when the cross-loading has theoretical meaning. If your theoretical framework predicts that an item should relate to multiple constructs, the cross-loading is confirming your theory rather than causing a problem. For example, in health-related quality of life measures, items about pain often legitimately relate to both physical functioning and emotional well-being.

The second scenario is when the primary loading is substantially stronger than the cross-loading. If an item loads at 0.70 on its primary factor and 0.33 on a secondary factor, many methodologists would argue the item still primarily measures the intended construct. The cross-loading, while above threshold, is not strong enough to create serious interpretive problems.

The third scenario is when removing the item would harm the scale. If removing a cross-loading item would leave you with fewer than three items on a factor, or would significantly reduce your Cronbach’s alpha below acceptable levels, retaining the item may be the lesser of two evils.

The fourth scenario is in CFA with model fit considerations. If your CFA model fits poorly without the cross-loading and adding it produces acceptable fit indices, and the cross-loading makes theoretical sense, it can be retained and reported.

What you should never do is silently keep a cross-loading item without reporting it. If you retain a cross-loading item, report the cross-loading, explain your reasoning, and let readers and reviewers judge the decision on its merits.

Decision Guide: Choosing the Right Method

With five methods available, how do you choose? Here is a practical decision process you can follow.

If the cross-loading is small (close to your threshold, say 0.31 or 0.32): Check whether it persists across rotation methods. If it only appears in one rotation, it may be an artifact. Consider keeping the item and reporting it.

If the cross-loading is moderate (0.35 to 0.45): Try removing the item and rerunning the EFA. If removing it resolves other issues and you still have enough items per factor (at least three to four), removal is the cleanest option.

If the cross-loading is large (close to the primary loading): The item likely genuinely measures two constructs. Consider whether a higher-order factor model is appropriate, or whether the item needs to be removed or rewritten.

If multiple items cross-load between the same two factors: Consider whether you have over-extracted. Try reducing the number of factors by one. If that resolves the cross-loadings, your original model may have been splitting one construct into two.

If you are in CFA and model fit is poor: Examine modification indices for cross-loading suggestions. Add cross-loadings that make theoretical sense and report them transparently.

How to Report Cross-Loadings in Academic Papers

Reporting cross-loadings properly in your thesis, dissertation, or journal article is important for transparency and reproducibility. Reviewers and future researchers need to understand exactly what you found and what decisions you made.

Following APA style guidelines for factor analysis reporting, you should report the rotation method used, the threshold applied, and the specific items that cross-loaded. Include the full pattern matrix (with suppressed small coefficients) as a table so readers can see the cross-loadings for themselves.

When describing your handling of cross-loadings, state explicitly which items were removed and why. For example: “Three items (Items 3, 7, and 12) demonstrated cross-loadings above 0.32 on more than one factor. Items were removed one at a time, starting with the item showing the smallest difference between primary and secondary loadings. After each removal, the EFA was rerun.”

If you retained any cross-loading items, justify the decision: “Item 9 was retained despite a secondary loading of 0.34 on Factor 2 because the item reflects a theoretically meaningful overlap between the constructs, and its primary loading of 0.68 on Factor 1 was substantially stronger.”

Always report your final factor solution with communalities, eigenvalues, percentage of variance explained, and the factor correlation matrix (if oblique rotation was used). This gives readers the complete picture they need to evaluate your measurement model.

FAQs

Conclusion

Cross-loadings in factor analysis are a common challenge, but they are also a solvable one. By understanding what cross-loadings mean, how to identify them in your pattern matrix, and the range of methods available for addressing them, you can handle this issue with confidence rather than frustration.

The key takeaways are simple. Always evaluate cross-loadings using the pattern matrix, not the structure matrix. Use oblique rotations like promax or oblimin by default because real constructs are correlated. Remove cross-loading items one at a time and rerun the analysis after each removal. Consider alternative explanations like over-extraction or higher-order factor structures before defaulting to item deletion.

And remember that removing items is not your only option. Sometimes the best response to a cross-loading is to recognize that it tells you something meaningful about your constructs and to report it transparently rather than eliminating it.

If you are working through a factor analysis right now and feeling stuck, you are not alone. The iterative process of identifying, evaluating, and resolving cross-loadings is something every researcher goes through. Take it one item at a time, document your decisions, and trust the process. Your final factor structure will be stronger for the careful attention you give to each cross-loading decision.