What Is Collinearity? How to Detect and Handle Multicollinearity
What is collinearity
You open the Coefficients table in SPSS and see the Tolerance and VIF columns. These are the indicators used to check whether the independent variables contain too much overlapping information in the regression model. When one independent variable has a strong linear relationship with one or more other independent variables, the model has collinearity. When several variables are involved, the more common term is multicollinearity.
Collinearity does not tell you whether an independent variable has a strong or weak relationship with the dependent variable. It concerns the relationships among the independent variables themselves. For example, you may use Service quality, Service satisfaction, and Customer experience to predict Repurchase intention. If the three constructs are measured by items with almost identical content, the model may struggle to separate the individual effect of each variable.
In its calculations, SPSS usually reports Tolerance and VIF for each independent variable. Tolerance represents the proportion of an independent variable's variance that is not explained by the remaining independent variables. VIF is the inverse of Tolerance:
VIF = 1 / Tolerance
Therefore, the lower the Tolerance, the higher the VIF. You need to examine these indicators in the specific regression model. Do not draw a conclusion only from a correlation matrix containing pairs of variables.
If you are reviewing the full data-processing workflow, you can also see the Statistics topic group to place the collinearity check correctly in your analysis chapter.
Why collinearity matters in quantitative research
Collinearity makes regression coefficient estimates less stable. When two independent variables contain nearly identical information, the model has difficulty identifying each variable's unique contribution. As a result, the B or Beta coefficient can change substantially when you add or remove a variable, even though the data have not changed much.
The most visible consequence is an increase in the coefficient's standard error. A variable that has a statistically significant correlation with the dependent variable may still have Sig. greater than 0.05 in the Coefficients table. The coefficient's sign may also become opposite to what your theoretical expectation suggests. This is why you should not rely on the p-value alone when deciding whether a hypothesis is problematic.
In regression, collinearity affects your conclusions in several ways:
- Partial regression coefficients become difficult to interpret because each variable is competing with another variable to explain the same part of the variance.
- Standard errors increase, which makes confidence intervals wider and p-values larger.
- Beta coefficients may be unstable across different runs.
- The model may have a fairly high
R Square, while several individual variables are not statistically significant. - Keeping several variables with highly similar content can make the discussion of your hypotheses unconvincing.
Collinearity also occurs in PLS-SEM, but you need to examine it in both the measurement model and the structural model, depending on where you are checking it. In SmartPLS, the indicator usually reported is VIF, while SPSS linear regression reports Tolerance and VIF in Coefficients. Do not bring CFI, TLI, or RMSEA into the collinearity assessment of SmartPLS. These belong to the fit-index group used in CB-SEM.
You should also distinguish collinearity from outliers. An outlier is an unusual observation, whereas collinearity is an excessively strong linear relationship among variables. Deleting one unusual data row does not automatically resolve multicollinearity among the independent variables.
What level of collinearity is acceptable
The two indicators commonly used are Tolerance and VIF. Under guidance frequently cited in PLS-SEM research, VIF below 5 is the level used to avoid a significant collinearity problem (Hair et al., 2019). In many theses using SPSS, authors also report Tolerance greater than 0.2 and VIF below 5 as practical criteria. When you use these thresholds, state clearly that they are reference criteria for the study and apply them consistently across the model.
| Indicator in the output | Practical interpretation | Reference |
|---|---|---|
VIF < 5 | No sign of serious collinearity under the commonly used threshold | (Hair et al., 2019) |
Tolerance > 0,2 | The variable still retains a relatively clear amount of unique information | (Hair et al., 2019) |
VIF ≥ 5 | Recheck variables with similar content and the model structure | (Hair et al., 2019) |
VIF = 1 | The variable has no linear relationship with the remaining independent variables under the VIF calculation | (Hair et al., 2019) |
Do not turn the threshold table into a mechanical rule. A VIF of 4,8 does not prove that the model is definitely sound, just as a VIF of 5,1 does not mean that you can delete the variable immediately. You need to consider the theory, the measurement approach, the correlations among variables, and the purpose of the model.
In linear regression, the collinearity check usually goes together with other diagnostics, such as residual distribution, homoscedasticity, and error independence. Durbin-Watson between 1 and 3 is a commonly used reference threshold for error independence (Field, 2013). This indicator does not replace VIF and Tolerance.
If you are using a new scale or a scale containing items with similar wording, check reliability and factor structure first. Cronbach's Alpha of 0.7 or above is commonly considered acceptable (Nunnally, 1978), while Corrected Item-Total Correlation of 0.3 or above is a reference threshold (Nunnally and Bernstein, 1994). This is a scale check, not a collinearity criterion for regression.
How to read collinearity in the output
In SPSS, open Analyze > Regression > Linear. Move the dependent variable into Dependent and the independent variables into Independent(s). Click Statistics, select Estimates, Model fit, and Collinearity diagnostics, then run the model. The first table to examine is Coefficients.
Find the two columns under Collinearity Statistics, usually on the right side of the table. The Tolerance column shows how much unique information remains, while the VIF column shows the variance inflation level. Read each independent-variable row. Do not use the Constant row to draw a collinearity conclusion.
The table below is illustrative output, not the result of a real study:
| Coefficientsa | B | Std. Error | Beta | t | Sig. | Tolerance | VIF |
|---|---|---|---|---|---|---|---|
| (Constant) | 0,842 | 0,291 | 2,893 | 0,005 | |||
| Service quality | 0,318 | 0,074 | 0,336 | 4,297 | 0,000 | 0,612 | 1,634 |
| Perceived value | 0,241 | 0,081 | 0,228 | 2,975 | 0,003 | 0,548 | 1,825 |
| Convenience | 0,156 | 0,069 | 0,171 | 2,261 | 0,025 | 0,421 | 2,375 |
| Trust | 0,097 | 0,078 | 0,089 | 1,244 | 0,215 | 0,236 | 4,237 |
In this example, Trust has the highest VIF at 4,237 and a Tolerance of 0,236. Under the reference thresholds of VIF below 5 and Tolerance above 0,2, this variable has not exceeded the warning threshold being used. However, its VIF is higher than those of the other variables, so you should check the scale content and the correlations among variables before writing your conclusion.
The Sig. column answers a different question: whether the variable's coefficient is statistically different from 0. You must not write that a VIF of 4,237 means that Trust has an effect 4,237 times as large. VIF is a collinearity diagnostic indicator.
In SmartPLS 4, run Calculate > PLS-SEM Algorithm, then view Collinearity Statistics (VIF). In the structural model, examine the VIF of predictors pointing to the same endogenous variable. In the measurement model, examine the location where SmartPLS reports VIF according to the indicator type and structure you are using. When reporting PLS-SEM, separate the assessment into the measurement model and the structural model (Anderson and Gerbing, 1988), then present VIF in the part that is actually being checked.
What to do when collinearity is unacceptable
Work from an explainable cause toward changes to the model. Deleting a variable only to reduce VIF often leads to questions at the defence, especially when the variable has a clear theoretical basis.
Check data entry and coding
Open Variable View and check variable names, data types, missing values, reverse-coded variables, and the way composite variables were calculated. If a reverse-coded variable has not been recoded, the scale may produce unusual results. If you accidentally entered the same column for two variables, a very high VIF is an expected possibility.
Check correlations and construct content
Run Analyze > Correlate > Bivariate to see whether pairs of independent variables are too closely correlated. The correlation matrix helps you identify pairs that deserve examination, but it does not replace VIF because collinearity can involve a combination of several variables.
Then reread the items. If Information quality and Information value use almost identical wording, the problem may lie in the scale design. Compare the theoretical model with the scale source instead of deleting a variable based on one statistical result. You can also see what a scale is if you are returning to the step of defining constructs and items.
Combine or remove a variable with theoretical justification
If two variables measure the same construct in your context, you may consider combining them, but you must revise the model, hypotheses, and interpretation. If the two variables represent different constructs, combining them only to obtain a lower VIF may remove the meaning of the study.
You may remove a variable when the theory, measurement content, and test results provide justification together. Save each version of the data and record which variable was removed, at which stage, and for what reason. Do not delete a variable directly from the original file and leave yourself with no audit trail.
Reconsider the analytical model
Collinearity sometimes appears because you have placed variables with different roles in the same model. For example, a mediator and a causal variable may be highly correlated, but that does not automatically mean that the mediator should be removed. For a moderating variable, clearly distinguish a moderator from an ordinary independent variable before creating the interaction term.
If the model contains an interaction term, center the relevant variables before creating the product term according to the appropriate procedure. Then check VIF again in the new model. Describe this step clearly in the methods section because readers need to know how the interaction variable was created.
Collect data again only when the cause is a design problem
Adding more observations does not always cure collinearity. If two scales ask about the same content, more respondents may still produce a high VIF. Recollection is reasonable only when you identify a questionnaire error, a coding error, an incorrect target sample, or wording that prevents respondents from distinguishing the constructs.
Distinguishing collinearity from correlation and related problems
Correlation is the degree of association between two variables, often examined through Pearson Correlation. Collinearity is a problem involving independent variables in the same regression model. A pair of variables with a correlation that is not especially high may still contribute to collinearity when combined with several other variables.
R Square is also not VIF. R Square shows the proportion of the dependent variable's variance explained by the full model. VIF shows the overlap between one independent variable and the remaining independent variables. A model with a high R Square can still have collinearity.
Beta is not Tolerance. Beta helps compare the relative contribution of a variable in the model, while Tolerance is a diagnostic indicator. The p-value also does not directly show collinearity. You must examine the VIF and Tolerance columns.
Collinearity differs from common method bias. Common method bias concerns bias caused by the measurement method or data source, while collinearity focuses on linear relationships among predictors. When your study requires a common method bias check, report it using an appropriate procedure, such as the Harman single-factor test with the reference threshold below 50% of the variance (Podsakoff et al., 2003). Do not label every questionnaire problem as collinearity.
Collinearity also differs from a moderator. A moderator changes the direction or strength of the relationship between an independent variable and a dependent variable. Collinearity is a condition in which explanatory variables contain overlapping information. A model with a moderator may develop a high VIF after you create an interaction variable, but the two concepts remain different.
Common mistakes
The first mistake is looking only at the Correlations table and concluding that the model has no multicollinearity. You need to run the regression and enable Collinearity diagnostics to see VIF and Tolerance. The second mistake is using the VIF of the dependent variable. In linear regression, VIF is examined for the independent variables.
Another mistake is writing, “The higher the VIF, the stronger the effect.” This interpretation is statistically incorrect. A high VIF shows that a predictor's information overlaps with that of other predictors. The effect is interpreted through the regression coefficient, confidence interval, and appropriate test.
Many students immediately delete a variable with a large p-value without checking VIF. A large p-value may result from collinearity, but it may also reflect sample size, measurement error, or a genuinely weak effect. Examine the theory, Coefficients, Model Summary, and model diagnostics together.
You should also avoid renaming VIF as an “effect coefficient.” In Chapter 4, place it in the assumption-checking or regression-diagnostics section, before the conclusion about the hypotheses. If you use SmartPLS, state clearly whether the VIF belongs to the measurement model or the structural model.
Finally, do not mix thresholds from different methods. CFI, TLI, RMSEA, and SRMR are CB-SEM fit indices, with the reference criteria reported by (Hu and Bentler, 1999). They are not criteria for assessing VIF in SPSS or SmartPLS.
Frequently asked questions
What is collinearity in SPSS?
Collinearity in SPSS is a condition in which the independent variables in a regression model have strong linear relationships with one another. You mainly detect it through the Tolerance and VIF columns in the Coefficients table after selecting Collinearity diagnostics.
What VIF value is acceptable?
VIF below 5 is a commonly used reference threshold in PLS-SEM reporting (Hair et al., 2019). When using it in SPSS, report it together with Tolerance, examine the scale content, and explain how the threshold was applied in your study.
What Tolerance value is acceptable?
In practice, Tolerance greater than 0,2 is often used together with VIF below 5 to assess whether there is no serious sign of collinearity. A Tolerance of 0,25 corresponds to a VIF of 4, so the two columns reflect the same relationship through the inverse formula.
Does unacceptable collinearity mean that I must delete a variable?
You should not delete the variable immediately. Check the coding, scale content, correlations, theoretical role, and any interaction variable. Remove or combine a variable only when you have a methodological and theoretical reason that you can explain, and keep a record of each analysis round.
Are collinearity and multicollinearity different?
In common usage, the two terms are almost interchangeable when referring to linear overlap among explanatory variables. Collinearity can describe the relationship between two variables, while multicollinearity usually emphasizes a situation in which several independent variables are related to one another.
Open the Coefficients table for your main model again, record VIF and Tolerance separately for each independent variable, and then check the variable with the highest VIF before changing the data. If you need to run the analysis on your own .sav or .csv file, DoThesis M4 analysis performs this step using your actual output.