How to Report Multicollinearity in APA 7: VIF and Tolerance

SPSS hands you the VIFs on the same output tab as the regression, and that is where the trouble starts: nobody is sure where to put them. Some authors build them a four-row table of their own, some mention them in the Discussion as though they were a finding, and most say nothing until a reviewer asks in round one. Here is where they actually belong, which cut-offs you can cite without an argument, and what to do when the number really is high. The rest of the section is covered in how to report a regression in APA 7.

Where it goes: in the text or in the table note

APA 7 has no rule for VIF, and it helps to know that before you go looking for one. The manual governs how numbers are written, not which diagnostics you run. What does exist is a well-settled convention across psychology and health journals: multicollinearity gets mentioned once, briefly, and takes up no space of its own. It is a quality check on the analysis, not a result.

The first home is the text. One sentence in the assumptions paragraph, at the end of the data analysis section of your Method or at the start of Results, before the first model: "Multicollinearity among the predictors was examined; variance inflation factors ranged from 1.12 to 2.68, below the conventional criterion of 10." The range is enough. Nobody needs six VIFs listed one by one, and if you are only going to give one number, give the maximum, since that is the only one that can get you into trouble.

The second home is the table note, and it is often the better one, because the reader wondering about collinearity is looking at the table at that exact moment: "Note. B = unstandardised coefficient; β = standardized coefficient; VIF = variance inflation factor. No VIF exceeded 2.68." Note is italicized along with its full stop; the rest of the note is not.

The third home is a VIF column inside the table itself. It is legitimate, and some health science journals ask for it, but you pay in width: the table already carries B, SE, the 95% CI, β, t and p. If you include it, it goes last, after p, to two decimals. If you are building that table by hand, the APA regression table generator lays out the columns and the note for you. Where multicollinearity never goes is the Discussion, and it gets a table of its own only if a reviewer explicitly asks — and then it goes in the supplementary materials.

VIF and tolerance are the same number, inverted

A predictor's VIF comes from an auxiliary regression in which that predictor becomes the outcome and is predicted from every other predictor in the model. Take the R² from that regression and VIF = 1 / (1 − R²). Tolerance is the other half of the same arithmetic: tolerance = 1 − R² = 1/VIF. A VIF of 5 is a tolerance of .20, a VIF of 10 is a tolerance of .10, a VIF of 9.14 is a tolerance of .11. Reporting both is repeating yourself, so pick one.

VIF has won out because its scale says something concrete: how much the variance of the coefficient is multiplied relative to a world with no collinearity. What the standard error is multiplied by is the square root of that, and this is where the damage becomes visible. At VIF = 4, your SE is twice what it would be with independent predictors. At VIF = 10, it is 3.16 times larger. A confidence interval three times wider is the difference between a coefficient you can publish and one that says nothing at all.

The same arithmetic explains why a correlation matrix cannot rule collinearity out. Two predictors correlated at .87, alone in the model, produce a VIF of 4.11 each — below 5. Reaching 10 with only two predictors would take correlations of .95. VIF rises when a predictor is predictable from the combination of the others, and that combination appears in no single cell of the matrix. You can have serious collinearity without one bivariate correlation above .60.

One writing point: VIF and tolerance are set in roman type, not italics. They are abbreviations, not single-letter statistical symbols like t or F, and abbreviations do not lean. Spell the term out the first time with the abbreviation after it — "variance inflation factor (VIF)" — and if you report tolerance, write it lower case, as a term in the sentence, not as the column heading your software printed.

The 10 and 5 cut-offs are conventions, not rules

The 10 comes out of the applied regression tradition (Marquardt, 1970, and from there into the textbooks) and it means something specific: that predictor has an R² of .90 against the rest, so 90% of its variance is already in the model. The 5 is the warning line, equivalent to an R² of .80. Some authors use 4; some drop to 2.5 in logistic models with few events. None of those figures comes from a proof. They are round numbers somebody proposed that have been copied for fifty years.

That does not make them worthless, but it changes how you write them. "No VIF exceeded the conventional criterion of 10" is fine. "There was no multicollinearity, as all VIFs were below 10" is not, because it treats a convention as a test with a null hypothesis and a verdict. The honest version names the cut-off, makes clear it is a convention, and stops short of turning it into a ruling. A methodological reviewer spots the difference on the first read.

O'Brien (2007) devoted a whole paper to this, and the argument still holds: a high VIF is only a problem if the standard error it produces is too large for your question. With a large sample, a VIF of 10 can still leave you a perfectly usable interval. With N = 62, a VIF of 3 can leave you B = 0.35, SE = 0.28, 95% CI [−0.21, 0.91] — an interval that spans zero, half a large effect and everything in between. Look at the confidence interval of the coefficient, where the damage is expressed in the units of your own variable rather than on an abstract scale.

There is a companion diagnostic almost nobody reports that can rescue a reply to a reviewer: the condition indices of the predictor matrix (Belsley et al., 1980), where the convention is to look above 30. Unlike VIF, they arrive with variance proportions, so they tell you which variables share the problem instead of only telling you that one of them has it. They come from the same SPSS checkbox that already gives you the VIFs, but in a table of their own: eigenvalues, condition index and variance proportions, printed below the coefficients table.

Three high VIFs that are not a problem

Interaction terms and polynomials. Once you put the product X·Z in the model, that product correlates with X and with Z by construction, and all three VIFs shoot up with nothing wrong in your data. Centering X and Z on their means before multiplying brings those VIFs back to ordinary values. Describe it accurately, though: centering is a reparameterisation, not a cure. The interaction coefficient and its p value are identical either way; what changes is that the lower-order terms are now interpreted at the mean and the VIFs you report stop looking alarming.

Dummy variables from one categorical predictor. The VIFs of a dummy set with three or more levels are not read one at a time, because each dummy is partly deducible from its siblings. That is what the generalized VIF is for (Fox & Monette, 1992), and it is what car::vif() returns in R as soon as a predictor has more than one degree of freedom. Read the GVIF^1/(2·df) column and compare it against the square root of your cut-off, not the cut-off itself: against 10, the comparison point is 3.16.

A misspecified model. The silliest case and the most common one: you have put a scale's total score in the same model as its subscales, or two variables where one is the other plus a remainder. That is no longer high collinearity, it is near-linear dependence, and the VIF climbs to 30, to 80, or the software drops the variable for zero tolerance. There is no diagnostic to fix there. Decide what the model is measuring and remove the structural redundancy before you look at another VIF.

What to do when the collinearity is real

Start by being clear about what breaks and what does not. Multicollinearity does not bias the coefficients, does not lower R² and does not damage prediction: if your aim is forecasting, you can live with it. All it does is inflate standard errors, and that produces the classic symptom, a significant overall model with almost nothing significant inside it: F(4, 193) = 16.43, p < .001, R² = .254, and a table full of p values above .05. The other symptom is a predictor that correlates positively with the outcome yet comes out with a negative B.

Combine them. When two predictors measure the same thing — two subscales of one construct, two indices of perceived stress — the answer is usually a single score. In a model of depressive symptoms in 198 undergraduates, two overlapping stress measures with a VIF of 9.14 (tolerance .11) left the first at B = 0.29, SE = 0.17, t(193) = 1.71, p = .090. Averaged into one standardized composite, that predictor became B = 0.44, SE = 0.10, t(194) = 4.40, p < .001. If you do this, report the reliability of the composite as you would for any scale; which coefficient applies is covered in alpha, omega or ICC.

Drop one. This works, but the justification has to be theoretical and written down before you look at the results. Dropping a predictor because it came out non-significant is not a remedy for collinearity, it is variable selection by p value, and a reviewer will call it that. When you do drop one, report the model with and without it, even in a note: what the reader wants to verify is that your conclusions do not hinge on that single decision.

Keep them and change your claim. This is the most honest route when both variables have to be there by design. You interpret the block as a set, using the increment in explained variance that hierarchical regression gives you naturally, rather than the individual coefficients — and you say so: "given the collinearity between the two measures (VIF = 9.14), individual coefficients are not interpreted separately and the joint increment in explained variance is reported instead." A larger N will not lower the VIF, but it does shrink standard errors, so it counts as an answer too, even if it arrives too late for the data you already collected. Ridge regression and PLS exist, work, and are the last resort: they stabilize the estimates by biasing them, and they change entirely what you are allowed to claim about any one coefficient.

What it looks like written out

When there is no problem, multicollinearity takes one sentence inside the paragraph where you already report the other regression assumptions: "Linearity, homoscedasticity, normality of residuals and independence were checked (Durbin-Watson = 1.94). Variance inflation factors ranged from 1.12 to 2.68 and tolerances from .37 to .89, within the conventional criteria (VIF below 10, tolerance above .10)." Note that the VIFs carry two decimals and the tolerances carry no leading zero, because they cannot exceed 1.

When there is a problem, the sentence moves and changes register, because it stops being a formality and starts shaping how the table is read: "The two stress measures had VIFs of 9.14 and 8.47 (tolerances of .11 and .12), above the 5 commonly taken as a warning. As both index the same construct, they were averaged into a single standardized composite; analyses retaining the two measures separately are reported in the supplementary materials." What a reviewer is looking for there is not a low number. It is evidence that you saw it and decided something.

One last thing that appears in no style guide and settles a surprising number of first rounds: consistency. If your Method says you used the criterion of 10, do not invoke 5 in the Results to justify dropping a variable. If you give VIFs in one table, give them in every regression table in the paper. A threshold that appears and disappears as it suits the argument is exactly what makes a reviewer start recomputing your numbers for themselves.

Already drafted it? Paste your Results section into Review one section before it goes to your supervisor or the journal. You get the first thing a reviewer would object to, with your own sentence quoted.

Frequently asked questions

What VIF value is acceptable in a regression?

The most cited convention is that above 10 there is a clear problem and that from 5 upwards it is worth a close look, though you will also see 4 and, in logistic models with few events, 2.5. These are conventions, not demonstrated thresholds: a VIF of 10 simply means that predictor has an R² of .90 against the others. What actually decides the matter is whether the coefficient's confidence interval is still narrow enough to answer your question.

Do you report VIF or tolerance?

One of them, not both. They are the same number inverted: tolerance = 1/VIF, so a VIF of 5 is a tolerance of .20 and a VIF of 10 is a tolerance of .10. VIF is the more common choice in psychology because its scale reads directly as the inflation in the variance of the coefficient. If you report tolerance, write it without a leading zero (.11), since it cannot exceed 1.

Where do you put VIF in an APA 7 paper?

In the assumptions paragraph as a range ("VIFs ranged from 1.12 to 2.68"), or in the note beneath the regression table. A VIF column inside the table itself is also acceptable, placed after the p column. It does not get a table of its own, it does not belong in the Discussion, and you do not need to list every value: the range, or the maximum, is enough.

Is reporting multicollinearity required in APA 7?

The APA 7 manual does not require it in so many words, because it does not prescribe which diagnostics to run, but it does require you to report assumptions and analytic decisions. In practice most psychology and health journals expect it for any multiple regression, and leaving it out is one of the most routine revision requests there is. One sentence covers it, and saves a round.

What should I do if my VIF is above 10?

First check that it is not structural: uncentred interaction terms, polynomials, dummies from one categorical variable, or a total score sitting alongside its own subscales. If it is real, you have three routes: combine the redundant predictors into a single composite, drop one on theoretical grounds and report the model with and without it, or keep them and interpret the block jointly rather than the individual coefficients, stating explicitly that you have done so.

Does multicollinearity invalidate my regression results?

It does not invalidate the model. R², overall fit and predictive accuracy are unaffected, and the coefficients remain unbiased. What inflates is the standard errors: at a VIF of 10, the standard error is 3.16 times what it would be without collinearity. The result is a significant model with non-significant predictors inside it, and coefficients that flip sign when variables are added or removed. What you lose is the interpretation of each predictor on its own, not the model.

With the VIF range in your assumptions paragraph or your table note, the cut-off cited as a convention, and a written decision for when the number climbs, that part of the manuscript stops causing trouble. If your worry is not where to put the number but what to do with two predictors that overlap and cannot be dropped, that is what my statistical consulting is for.