What Is Multicollinearity? How to Identify and Fix It in SPSS
What Is Multicollinearity
Multicollinearity occurs when one independent variable has a fairly strong linear relationship with one or more other independent variables in the same regression model. The model then has difficulty separating the individual effect of each variable on the dependent variable. You can still run the regression, but the regression coefficients, standard errors and p-values may become unstable.
In linear regression, multicollinearity is assessed among the independent variables, not between an independent variable and the dependent variable. The two indicators you usually see in the Coefficients table in SPSS are Tolerance and VIF.
The formulas commonly used are:
Tolerance_j = 1 - R²_j
VIF_j = 1 / Tolerance_j
Here, R²_j is the coefficient of determination obtained when independent variable j is regressed on the remaining independent variables. The smaller the Tolerance, the larger the VIF, which suggests that the variable may be sharing a substantial amount of information with the other variables.
You need to distinguish multicollinearity from outliers. Outliers are unusual observations, while multicollinearity concerns the relationships among variables in the model.
Why Multicollinearity Matters in Quantitative Research
Multicollinearity directly affects decisions about retaining variables, interpreting hypotheses and drawing conclusions about the effects of different factors. When two independent variables measure very similar content, the model may struggle to determine which variable actually explains the dependent variable.
A common pattern is a model with a reasonably good R Square, while several variables have large p-values in the Coefficients table. The sign of a regression coefficient may also run against the hypothesis or change substantially when you add or remove a variable. These signs are not enough to establish that multicollinearity exists, but they are good reasons to check Tolerance and VIF.
Common consequences include:
- The standard errors of regression coefficients increase, reducing the ability to detect statistically significant effects.
- Regression coefficients may fluctuate substantially across very similar models.
- The positive or negative sign of a coefficient may contradict the theoretical expectation.
- Interpreting the separate effect of each variable becomes difficult to defend before the committee.
- A variable may not be statistically significant even when its bivariate correlation with the dependent variable is fairly clear.
Multicollinearity does not automatically mean that you must immediately remove a variable from the model. If two concepts are theoretically distinct, you need to consider the statistical evidence, the scale content and the research model together. Deleting a variable only to make the VIF look better can strip the model of meaning.
If your study includes an interaction variable, distinguish multicollinearity from moderation. A moderator answers the question of how a relationship changes under another condition, while multicollinearity reflects the degree of overlap among variables entered into the same equation. You can also read what moderating means and what a moderator is to keep these concepts separate.
You can consult other articles in the Statistics topic when you need to compare multicollinearity with other regression checks.
What Level of Multicollinearity Is Acceptable
In quantitative theses, VIF and Tolerance are commonly used to assess multicollinearity. However, you should state the threshold together with its source rather than presenting it as an absolute rule for every study. The table below focuses on common thresholds used when reporting regression and PLS-SEM.
| Indicator or criterion | How to read it in practice | Source |
|---|---|---|
| Tolerance | A value closer to 1 indicates that the variable is less explained by the remaining independent variables. Very low Tolerance is a sign that multicollinearity needs to be checked. | (Field, 2013) |
| VIF in regression | VIF below 5 is commonly used as a practical checking threshold. | (Hair et al., 2019) |
| VIF in PLS-SEM | VIF below 5 is commonly reported when assessing collinearity among predictors. | (Hair et al., 2019) |
| VIF from 5 upward | Review the correlations, variable content, coding and model structure before deciding how to handle it. | (Hair et al., 2019) |
| Regression sample size | With m independent variables, a cited rule is n at or above 50 + 8m. This is a sample-size criterion, not a VIF threshold. | (Tabachnick and Fidell, 2013) |
In SPSS, you can use VIF below 5 as the main criterion when it fits your method and the literature for your study. Tolerance is usually read alongside VIF as a cross-check. Do not write that every VIF below 10 is definitely acceptable if your methods chapter uses a threshold below 5.
In SmartPLS, VIF belongs to the assessment of collinearity in the measurement model or structural model, depending on where you check it. CFI, TLI and RMSEA belong to fit assessment in CB-SEM, so they should not be included in a PLS-SEM multicollinearity report.
How to Read Multicollinearity in the Output
If you are checking linear regression in SPSS, open Analyze > Regression > Linear. Move the dependent variable into Dependent and the explanatory variables into Independent(s), then click Statistics. Select Estimates, Model fit, Collinearity diagnostics and run the model.
The table to read is Coefficients. The Tolerance and VIF columns appear under Collinearity Statistics. Read each independent-variable row separately. There is no single VIF value for the whole model.
Illustrative Output
The table below is illustrative output formatted like SPSS output. It is not the result of a specific study.
| Coefficients | B | Std. Error | Beta | t | Sig. | Tolerance | VIF |
|---|---|---|---|---|---|---|---|
| Constant | 0.842 | 0.317 | 2.657 | 0.009 | |||
| Perceived quality | 0.286 | 0.071 | 0.301 | 4.028 | 0.000 | 0.642 | 1.558 |
| Perceived value | 0.194 | 0.083 | 0.176 | 2.337 | 0.022 | 0.514 | 1.946 |
| Convenience | 0.091 | 0.078 | 0.084 | 1.167 | 0.247 | 0.238 | 4.202 |
| Continuance intention | 0.358 | 0.096 | 0.326 | 3.729 | 0.000 | 0.205 | 4.878 |
In this example, Continuance intention has VIF = 4.878. It is still below 5, but already fairly close to the threshold. You should not look only at the Sig. column and draw a conclusion. This variable has a p-value displayed as 0.000 by SPSS, but statistical significance does not rule out the possibility that the variable shares information with the other predictors.
Convenience has VIF = 4.202. If the study uses a VIF threshold below 5, this value may be accepted, but you should also check the correlations among variables and the content of the items. If VIF is 5 or higher, review the model before interpreting the coefficient.
Do not read VIF as a percentage effect. VIF = 4 does not mean that the variable has a 4% effect on the dependent variable. It reflects the inflation of the variance of the estimate caused by the variable's relationship with the other independent variables.
What to Do When Multicollinearity Is Not Acceptable
Work from data-related causes toward model-related causes. Record every change so that you can explain it in Chapter 4.
Check Coding and the Original Data
First, check whether any variables were entered on the wrong scale, reverse-coded incorrectly or duplicated in another column. A variable that should be coded from 1 to 5 but contains a value of 51 will distort the results. You should also check whether identifier variables, control variables and dummy variables were coded correctly.
If you use composite variables, make sure that the mean or total score was calculated correctly from the items that met the required criteria. You can review the scale-handling approach in what a scale is, especially when two scales contain several items with almost identical wording.
Review the Correlation Matrix and Variable Content
Run Analyze > Correlate > Bivariate to examine the correlations among the independent variables. A high correlation is a warning sign, but it does not replace VIF in the regression model. Then read the wording of the items again. Two concepts may correlate because they are genuinely close in theory, or because the questionnaire uses almost duplicate wording.
Remove the Variable With the Weaker Theoretical Basis
If two variables measure nearly the same content and one has a weaker theoretical basis, you may consider removing that variable. The decision should be based on the research model, the original scale, reliability and the research objective, not only on which variable has the larger p-value.
After removing it, rerun the model and save both the output before and after the change. Do not keep deleting variables until VIF is acceptable without recording each run.
Combine or Adjust the Model When Theory Allows It
In some studies, variables that are too close may be modelled as one broader concept. This approach is suitable only when supported by a theoretical argument and the scale. You should not combine two variables simply because they have a high correlation.
If multicollinearity appears because you created an interaction variable, you may consider mean-centering the component variables before creating the interaction product. This can reduce unnecessary correlation between the original variable and the interaction variable, but it does not solve the problem when the two original concepts already overlap in content.
Retain the Variable and Explain the Decision When VIF Is Within the Threshold
If VIF is below your chosen threshold, the variable can be retained even when VIF is not equal to 1. In your thesis, state the threshold, the highest observed value and your conclusion about collinearity. If VIF is high but still below the threshold, report it carefully and explain why the variable was retained based on theory.
If VIF clearly exceeds the threshold, changing software or rerunning the analysis repeatedly does not remove the cause. AMOS, JASP and R may provide other ways to check the issue, but the data and model structure remain the foundation. Paying for an SPSS analysis service may save time on the mechanics, but you still need to understand why a variable was retained or removed when the committee asks.
Distinguishing Multicollinearity From Correlation and a Mediator
Correlation describes how strongly two variables move together and is usually examined pair by pair. Multicollinearity is a problem involving an independent variable when it is considered together with all the other independent variables in one equation. Therefore, low pairwise correlations do not necessarily guarantee that the model has no collinearity in every configuration, and a high correlation does not automatically mean that you must delete a variable.
A mediator is a variable that explains the mechanism through which an effect travels from X to Y. For example, X affects the mediator, and the mediator then affects Y. This is a question about paths and indirect effects, not another name for multicollinearity. You can read what a mediator is when your model includes a mediation effect.
You also need to distinguish a moderator from a mediator. A moderator changes the strength or direction of a relationship, while a mediator lies in the mechanism through which the effect is transmitted. Both types of models can produce collinearity when several variables are entered into an equation, but the hypotheses and tests are different.
Common Mistakes
Looking Only at p-value to Conclude There Is No Multicollinearity
The p-value provides evidence about a coefficient in the model, while VIF and Tolerance help assess the degree of overlap among predictors. A variable with a large p-value is not necessarily the source of multicollinearity, and a variable with a small p-value does not prove that the model has no such problem.
Using a Threshold Without Citing the Source
The statement “VIF below 10 is acceptable” appears frequently in theses, but the committee may ask for the basis if your threshold differs from the methods literature. State the criterion you used, cite the source and report the largest observed VIF.
Removing Variables Only to Make the Output Look Better
Removing a variable may reduce VIF while also changing the meaning of the model. Before deleting it, check whether it is a required component of a hypothesis, whether the scale will lose important content and whether the result after deletion still answers the research question.
Confusing VIF With Scale Reliability
VIF does not replace Cronbach's Alpha, Composite Reliability or AVE. Reliability and validity address whether a scale measures its construct consistently and appropriately. VIF addresses whether the predictors overlap in the model.
Frequently asked questions
What is multicollinearity in SPSS?
In SPSS, multicollinearity is a situation in which the independent variables in a regression model have strong linear relationships with one another. You mainly check it through the Tolerance and VIF columns in the Coefficients table, while also considering the theoretical context and the original data.
What VIF value is acceptable?
VIF below 5 is commonly used as a practical threshold in PLS-SEM reporting and collinearity checks, according to (Hair et al., 2019). State the threshold you selected, and do not claim that a value close to the threshold definitely requires no further review.
What Tolerance value is acceptable?
The lower the Tolerance, the higher the risk of multicollinearity, because Tolerance indicates the amount of unique information that remains for a predictor after the other predictors are considered. When reading the output, use Tolerance together with VIF rather than separating the two indicators. If the value is unusually low, check the coding, duplicated variables and model structure.
What should I do if I have multicollinearity?
Check the data, coding, correlations among variables and scale content first. Then consider removing a variable with a weaker theoretical basis, adjusting the model or retaining the variable if VIF remains within the threshold you selected. Save and explain every change.
Do I need to rerun the regression when VIF is high?
If VIF exceeds the threshold, rerun the model after making a justified decision about how to handle the problem. Rerunning the analysis without changing the data or model only creates another output file and does not address the cause. Save the original output and the output after the change so that you can compare them.
How to write this in your thesis
[Insert the chosen VIF threshold, source, highest observed VIF and decision about retaining or removing variables here.]
Open your file, go to the Coefficients table, record the VIF and Tolerance for each variable, and then check the threshold against its source before deciding whether to remove or retain a variable. If you need to run the analysis on your .sav or .csv file and track each processing round, you can use M4 analysis by DoThesis.