What Is Multicollinearity? How to Detect and Handle It in SPSS

What Is Multicollinearity

Multicollinearity occurs when two or more independent variables in the same regression model are highly correlated. The model then has difficulty separating the individual effect of each variable on the dependent variable. You may still see a fairly high R², while the regression coefficient of each variable changes considerably, the p-value behaves unexpectedly, or the coefficient sign contradicts your hypothesis. The overall model can therefore look acceptable while the interpretation of individual predictors becomes unstable.

For example, in a model explaining purchase intention, you may include “perceived value,” “benefits received,” and “positive evaluation of the product” at the same time. If these three concepts are measured by very similar items, they may provide almost the same information to the model. This is a common setting in which multicollinearity develops, especially when the questionnaire uses overlapping wording across several scales.

Multicollinearity does not mean that your data are wrong or that you must discard the entire model. It is a problem in the relationship between the independent variables. In SPSS, you usually check it with the Tolerance and VIF indicators, which appear in the Coefficients table when you run the regression. The check belongs to the particular equation you are reporting, so the result must be read together with that model's variables.

You can review the background in linear regression before reading the multicollinearity results. Technically, a variable's VIF is calculated from how much that variable is explained by the remaining independent variables:

VIF = 1 / Tolerance = 1 / (1 - R²j)

Here, R²j is the R² obtained when the jth independent variable is treated as the dependent variable and regressed on the other independent variables. Therefore, the larger the VIF, the more strongly that variable is explained by the remaining variables, indicating greater duplication of information. Tolerance is the reciprocal view of the same relationship, so a low Tolerance normally appears alongside a high VIF.

When VIF equals 1, the variable has almost no linear relationship with the other independent variables. As VIF increases, the Standard Error of the coefficient usually increases as well, making the test of the variable's unique effect less stable. Read VIF within the actual research equation, rather than taking a number from another model and applying it to your current model. A value should always be tied to the model, sample, and variables that produced it.

Why Multicollinearity Matters in Quantitative Research

When multicollinearity is present, the partial B and Beta coefficients become less stable. Changing one variable, removing a few observations, or adding a new variable can cause the coefficients of related variables to change substantially. This makes it difficult to conclude which variable actually has a unique effect on the dependent variable, even when the model as a whole remains statistically useful.

Multicollinearity also increases the Standard Error of the coefficient. As the Standard Error increases, the t value usually decreases and the p-value may increase. As a result, a variable may have a bivariate correlation with the dependent variable but become nonsignificant when it enters the regression model with the other variables. Explain this situation through the structure of the model instead of automatically concluding that the hypothesis is certainly wrong. The variable may share explanatory information with another predictor.

You need to separate two questions. First, does the overall model explain the dependent variable? Second, does each independent variable have a distinct effect after the other variables have been controlled? Multicollinearity has a clearer effect on the second question. A high R² alone does not show that every individual coefficient can be interpreted with confidence.

In a thesis, check VIF and Tolerance before interpreting the Coefficients table. If the indicators fall within the accepted range, you can continue reading B, Beta, t, and Sig.. If VIF is high, review the items, the theoretical concepts, and the way the variables enter the model before writing your conclusion. Keep the diagnostic output with the other regression tables so you can explain the decision later.

When completing an assignment, track each step rather than copying only the p-value. This linear regression exercise with solution can help you compare how the columns in the output are read. For a binary dependent variable, the procedure and output differ from linear regression, so consult logistic regression to avoid using the wrong criteria. The type of dependent variable determines which model and which diagnostics are appropriate.

Multicollinearity does not cause the model's R² to fall in an obvious way. On the contrary, R² may remain high because the independent variables explain some of the same information. The problem lies in how the effect is allocated among the individual variables. This is why you cannot look only at Model Summary and conclude that the model has no multicollinearity. You must inspect the predictor-level diagnostics as well.

What Level of Multicollinearity Is Acceptable

There is no single number that fits every field and every model. In regression reporting, the usual checks are Tolerance and VIF. The lower Tolerance becomes and the higher VIF becomes, the clearer the sign of multicollinearity. The threshold should be stated as a reference used in your analysis, not presented as a universal mechanical rule.

The table below summarises thresholds commonly cited in quantitative research. Each row identifies its source so that you do not put an unsupported number into Chapter 4.

A common statement in theses can be written as follows: the model shows no serious sign of multicollinearity when the VIF of the independent variables is below the selected threshold and Tolerance reaches an acceptable level. Agree on one threshold with your supervisor, because some sources use VIF below 5, while older reports use a wider threshold. State the selected rule in the methods or results section instead of leaving the reader to infer it.

Do not write “VIF equal to 5 is always acceptable.” A threshold is a decision tool, not an automatic verdict. Combine VIF, Tolerance, the correlation matrix, theoretical meaning, and the stability of the regression coefficients. If only one variable has a high VIF, examine which group of variables is duplicating its information. If several variables have high VIF values, the more likely explanation is that the model contains overlapping concepts. The pattern across the predictors matters more than one isolated number.

How to Read Multicollinearity in the Output

In SPSS, open Analyze > Regression > Linear. Put the dependent variable in Dependent and the independent variables in Independent(s). Click Statistics, select Estimates, Model fit, and Collinearity diagnostics, then select Continue and OK. Follow the same path for the model that you intend to report, rather than checking a preliminary model and applying its values to the final equation.

The table to inspect is Coefficients. The Tolerance and VIF columns appear to the right of the t and Sig. columns. If the Output window is narrow, drag the horizontal scroll bar to see all the columns. Do not take a VIF from another table and assign it to the regression before checking the exact model being reported. Confirm the dependent variable and the full list of independent variables first.

The following is illustrative output, not the result of a real study. The variable names, coefficients, and p-values were created to reproduce the shape of an SPSS Coefficients table.

Read the illustration as follows. The VIF values of the three variables are 1.558, 1.712, and 1.406, all below 5 under the threshold from (Hair et al., 2019). All Tolerance values are above 0.20, so this table does not indicate serious multicollinearity. The conclusion applies only to the illustrative model shown in this table.

Only then should you read the meaning of the coefficients. For example, the Sig. value for “Perceived quality” is <0.001, while Beta is 0.341. In this illustrative output, the variable has a positive and statistically significant effect after the other variables have been controlled. This is an illustration, not a finding to copy as if it came from your data. Your own interpretation must use the values printed in your output.

If you run the regression in several steps, such as entering control variables first and adding the main variables in a later step, read VIF in each model. VIF may change after a variable is added. Save each output table so you can explain why the coefficients or p-values changed between steps. This record is useful when a committee asks how the final specification was selected.

If you run the model in SmartPLS, inspect VIF in the measurement model or structural model assessment, depending on the version and the type of relationship being tested. PLS-SEM may report Inner VIF Values and Outer VIF Values. Attach VIF to the correct location of the indicator, and do not mix it with CFI, TLI, or RMSEA, which belong to CB-SEM. The software name does not remove the need to identify which relationship the diagnostic describes.

How to Handle Multicollinearity When It Fails the Threshold

Work from data checking toward model review instead of immediately deleting the variable with the high VIF. EFA rarely looks clean on the first run, and regression diagnostics also require you to inspect the sequence of decisions. Keep a record of each adjustment and rerun the model only after you can explain why the adjustment was made.

Check Data-Entry and Variable-Coding Errors

Open Variable View and Data View and check whether variables were entered in duplicate columns, reverse-coded incorrectly, or assigned the same column for two concepts. For a reversed Likert item, make sure you recoded it correctly before calculating the mean score for the latent variable. A coding error can distort the correlations between variables and produce a VIF that reflects the data-entry problem rather than the research model.

You should also check missing values and unusual data rows. If a group of variables has the same value for almost every respondent, the correlations may be inflated or distorted. Save a copy of the original data before making corrections so you can explain the changes if necessary. Do not overwrite the source file before the checking process is documented.

Check Composite and Interaction Variables

If you enter the original variable, its mean score, and an interaction term in the same model, VIF may increase because of how the variables were constructed. For an interaction variable, mean-centering may support interpretation and reduce unnecessary correlation between components, but it cannot remove multicollinearity caused by overlapping conceptual content. The transformation changes the representation of the variables, not the underlying theoretical overlap.

Check the formula used to calculate composite variables. A mean score made from several items should not appear in the same equation as all of its component items unless the research design provides a clear reason. This model-construction error often causes VIF to rise quickly. Check the syntax or calculation steps before changing the theoretical model.

Review Items and Scales

If two concepts have several items that are almost identical, return to the theoretical basis and the EFA or CFA results. Removing an item simply because it lowers VIF is difficult to defend. Remove it only when you have evidence from factor loadings, measurement content, reliability, and fit with the model. The statistical improvement must still make sense for what the scale is intended to measure.

Combine or Remove an Independent Variable with Theoretical Support

When two variables genuinely measure the same content, consider combining them or retaining the variable with the clearer theoretical basis. Record the decision, including the VIF before adjustment, the reason for the change, and the result after rerunning the model. Do not run many versions and select only the most attractive table. A defensible analysis includes the reasoning behind the final specification.

Reconsider the Research Model

Multicollinearity may reflect overlapping concepts in the model rather than a software error. Compare the linear regression model and the research equation to check which variables really need to appear in the same equation. If the theoretical model requires related variables to remain, report the problem and explain the limitation instead of hiding it. A limitation that is clearly documented is easier to defend than an unexplained deletion.

Do not handle multicollinearity by randomly deleting data rows, standardising every variable, or renaming variables. These actions do not address the cause when the independent variables already contain duplicate information. Be careful when hiring an SPSS service simply to obtain a low VIF table, because the committee may ask why a variable was removed and you may not be able to explain the decision. The person presenting the thesis must understand the model and the path from the original data to the final output.

Multicollinearity Versus High Correlation

High correlation is a relationship between two variables, usually examined in the Correlations table. Multicollinearity is a problem involving an independent variable when it is considered together with the other independent variables in a model. The concepts are related but not identical. A pairwise correlation table and a regression diagnostic answer different questions.

A variable may have a moderate correlation with each other variable, while the combined explanatory level remains high and VIF increases. Conversely, a pair of variables with fairly high correlation may not make the entire model unstable if the data structure and research objective remain appropriate. Interpret the correlation matrix as an early warning, not as a replacement for the regression diagnostics.

Multicollinearity also differs from autocorrelation of the residuals. Autocorrelation is commonly checked with Durbin-Watson in a regression context, with a reference range from 1 to 3 according to (Field, 2013). VIF cannot be used to conclude that the residuals are autocorrelated. These diagnostics concern different parts of the regression assumptions.

You should also distinguish multicollinearity from heteroscedasticity. Heteroscedasticity concerns changing residual variance across predicted values, while multicollinearity concerns duplicated information among independent variables. Each problem requires its own check. Reporting one diagnostic does not establish that the other assumptions have been met.

To review the full process from the equation to the coefficient table, compare the linear regression equation. Once you understand which variable is on the left side and which variables are on the right side, you will avoid checking VIF on the wrong model. This simple identification step prevents many reporting errors.

Common Mistakes

The first mistake is looking only at Sig. and ignoring VIF and Tolerance. A variable with a large p-value is not necessarily affected by multicollinearity, and a variable with a small p-value does not prove that the model has no multicollinearity. Significance and collinearity describe different aspects of the output.

The second mistake is using a threshold without citing its source. The statement “VIF below 10 is acceptable” appears frequently, but if your supervisor asks for the basis, you need to know which source supports that choice. The threshold table above uses sources from the permitted reference list, but you should still align your choice with your department's requirements. Write the source next to the threshold in your methods or results discussion.

The third mistake is removing a variable just to make the table look better. If the variable is a central part of the model and has a theoretical basis, removing it needs to be explained through both statistics and content. Save each output version so you know which change caused VIF to move. This also lets you report the before-and-after decision accurately.

The fourth mistake is assessing multicollinearity in one model and applying the conclusion to another. When you change the dependent variable, add control variables, or change how a composite variable is calculated, VIF may change. Check each regression equation separately. The same predictor can have a different VIF in a different equation.

The fifth mistake is mixing criteria across software. CFI, TLI, and RMSEA are used to assess CB-SEM fit, not as substitutes for VIF in regression or SmartPLS. State clearly whether you are using SPSS, SmartPLS, or AMOS and report the indicator group that belongs to that method. This distinction keeps the results section technically consistent.

Frequently asked questions

What is multicollinearity, and is it serious?

Multicollinearity is a high level of duplicated information among independent variables in the same model. It can make regression coefficients and p-values unstable, but its seriousness must be assessed through VIF, Tolerance, the theoretical structure, and the stability of the model. The same VIF value may require a different discussion depending on the variables and the purpose of the analysis.

What VIF value is acceptable?

Many reports use VIF below 5 as a reference threshold and cite (Hair et al., 2019). Do not treat it as an absolute boundary. Report Tolerance as well and explain the selected threshold in the research methods section. The committee should be able to see both the numerical rule and the reasoning for applying it.

Is VIF below 10 acceptable?

Some older sources or guidelines use VIF below 10, but you should not select this threshold simply because it makes the model pass. If you use a threshold different from 5, discuss it with your supervisor, state the source, and report the results consistently. Do not switch thresholds between models without explaining the reason.

Where do you check multicollinearity in SPSS?

Go to Analyze > Regression > Linear, click Statistics, select Collinearity diagnostics, and then inspect the Coefficients table. The two key columns are Tolerance and VIF. If they do not appear, you may not have selected the correct option or may be looking at the wrong output table. Check the dialog settings and rerun the exact equation.

Does a high VIF mean that you should delete the variable immediately?

A high VIF calls for checks first. Review the coding, reversed items, composite-score calculation, correlations between variables, and theoretical basis. Remove or combine a variable only when you have a clear methodological reason, then rerun the model and record the change in the thesis. Keep the original output so the decision can be traced.

Can multicollinearity occur in SmartPLS and AMOS?

Yes. In SmartPLS, you may see Inner VIF Values or Outer VIF Values. In AMOS, multicollinearity also needs to be considered in the structural model and input data, but CB-SEM fit indicators should not be mixed with the VIF criteria used in PLS-SEM. Report the diagnostic that matches the software and the part of the model being assessed.

Open your .sav file, run the exact regression equation used in Chapter 4, and save the Coefficients table containing Tolerance and VIF. If you need the procedure run on your SPSS or CSV data, M4 analysis by DoThesis handles this step and turns the results into thesis-ready interpretation.