What do differences between multi-voxel and univariate analysis mean? How subject-, voxel-, and trial-level variance impact fMRI analysis

Abstract

Multi-voxel pattern analysis (MVPA) has led to major changes in how fMRI data are analyzed and interpreted. Many studies now report both MVPA results and results from standard univariate voxel-wise analysis, often with the goal of drawing different conclusions from each. Because MVPA results can be sensitive to latent multidimensional representations and processes whereas univariate voxel-wise analysis cannot, one conclusion that is often drawn when MVPA and univariate results differ is that the activation patterns underlying MVPA results contain a multidimensional code. In the current study, we conducted simulations to formally test this assumption. Our findings reveal that MVPA tests are sensitive to the magnitude of voxel-level variability in the effect of a condition within subjects, even when the same linear relationship is coded in all voxels. We also find that MVPA is insensitive to subject-level variability in mean activation across an ROI, which is the primary variance component of interest in many standard univariate tests. Together, these results illustrate that differences between MVPA and univariate tests do not afford conclusions about the nature or dimensionality of the neural code. Instead, targeted tests of the informational content and/or dimensionality of activation patterns are critical for drawing strong conclusions about the representational codes that are indicated by significant MVPA results.

Keywords: Dimensionality; Distributed representations; MVPA; Voxel-level variability; fMRI analysis.

Figure 1

(A). A graphical depiction of how the neural response to different stimulus dimensions is measured via univariate voxel-wise analysis. The most common practice for testing whether the dimensions Size, Predacity, and Scariness are coded in the brain using voxel-wise analysis is to test whether the beta weights for the three dimensions are significantly different from zero in individual voxels or across an ROI. (B). A graphical depiction of one way in which MVPA may be used to examine whether a region of the brain codes for differences between the mammals. Activation patterns for test items are compared to those for a number of items using a similarity function. Here, the new pattern is classified as the mammal with highest similarity and the accuracy of this prediction is assessed. Accurate classification indicates that the activation patterns contain information about the differences between these mammals in some latent neural representational space. The question we address in the present paper is whether any conclusions can be reached about the content or dimensionality of this latent space using prediction accuracy or other basic similarity tests alone

Figure 2

An example of (A) unidimensional (B) multidimensional effects with respect to the scariness dimension. Mammals differ with respect to three dimensions: size, predacity, and scariness. Scary animals are depicted in red. In the case of a unidimensional effect, there is a direct mapping of scariness onto voxels within a region. Here Voxel 1 increases as a function of scariness, and scary and non-scary animals can be differentiated (i.e., the dotted-line marks a ‘scariness boundary’) based on the activation in this voxel. In the case of a multidimensional effect, no voxel activates for scariness per se; instead, voxels activate for either size or predacity, which are correlated with scariness. Decoding of mammals’ scariness (the latent dimension represented by the red line) is improved by taking into account both the voxels that code for size and the voxels that code for predacity. Scariness boundaries that take into account only a single dimension (i.e., the dotted lines that are orthogonal to the size and predacity dimensions) may be able to achieve some decoding of scariness, but will not achieve classification as accurate as scariness boundaries that take into account both dimensions (i.e., the dotted line orthogonal to the latent scariness dimension). Note that in the present example, a linear classifier could achieve high accuracy by assigning equal weight to both voxels, and thus in this context, it would also be possible to achieve high decoding accuracy by comparing the mean of the two voxels to an appropriate criterion.

Figure 3

A formal description of the 3-level mixed model for simulating fMRI data. At the trial level, the model simulates the activation on trial t, in voxel v, for subject s, as a linear combination of the voxel-wise regression coefficients α and trial-level error e_tvs, observed on trial t, in voxel v, for subject s. The voxel-wise regression coefficients included are an intercept term α_0vs, which corresponds to the mean or baseline activation in voxel v, for subject s, that is shared across trials, and α_pvs, which are the regression coefficients relating the p trial-level experimental X variables to activation in voxel v, for subject s. The trial-level errors, e_tvs represent the deviation on trial t, in voxel v, for subject s from the activation predicted by the αs, and are assumed to be normally distributed with mean of 0 and variance equal to σ². The voxel-wise regression coefficients in the trial-level model can be expanded into voxel-level models that take into account the repeated measurement of the baseline and X variables across voxels. The voxel-level models contain subject-wise β parameters that give the average baseline or effect of experimental variable p across all voxels for subject s (for, β_0s and β_ps, respectively), and voxel-level errors that give each voxel v’s deviation from the βs for subject s. These voxel-level error terms are assumed to be normally distributed with a mean of 0 and standard deviations equal to τ. In the present simulations, the voxel-level distributions for the baseline (e_0vs) and effect of experimental X variable (e_pvs) errors each have their own variance term (τ₀ and τ_p, respectively) and are uncorrelated. The subject-wise coefficients can likewise be expanded to subject-level models that take into account the repeated measurement of the baseline and X variables across subjects. The subject-level models have γ parameters, which correspond to the fixed effects of baseline and X variables across all subjects. Like the other levels, this subject-level has error terms, which correspond to the deviation from the fixed effect parameters observed for subject s. These error terms are also assumed to be normally distributed and uncorrelated in the present simulations, which is consistent with their estimation in standard univariate analysis. Substituting the parameters from the voxel- and subject-level models into the trial-level model gives the combined equation for activation A on trial t, in voxel v, for subject s, and illustrates how it is a function of the fixed effects parameters as well as the trial-,voxel-, and subject-level deviations from these fixed effects.

Figure 4

(A) A graphical depiction of the 3-level mixed model for simulating fMRI data (Figure 2). Each level of the mixed model (subject, voxel, and trial) contributes variability to the observed trial-wise activation patterns. This example depicts a case in which a dummy coded scariness variable (Not Scary (N) = 0; Scary (S) = 1) is included, and thus trials for scary stimuli receive an added fixed effect of S in addition to added subject-level and voxel-level random deviations from the fixed effect of S. (B) A graphical depiction of how spatial variability in mean/baseline activation persists over repeated trials and is not influenced by centering with respect to the mean activation across voxels (e.g., Baseline Variability Simulation). In this example, mean activation in individual voxels tends to decrease as a function of distance from the peak voxel in the region-of-interest (ROI), such that across trials the central voxels tend to have the highest signal, whereas the outside voxels have a lower signal. Such an effect may arise as a function of distance-to-capillary or any other anatomical differences that create reliable variability in signal across voxels. The pattern caused by voxel-level variability persists across trials and is not eliminated by centering with respect to the mean activation across voxels because the ROI mean does not include information about the voxel-wise deviations.

Figure 5

Parameter settings for different simulation models. The first column shows the parameters from Figure 3 and the second column has a short description of the parameter. The following 4 columns illustrate the settings for the 4 simulations.

Figure 6

Results from the Baseline, Condition, and Item Variability simulations. (A). Results from Baseline Variability Simulation. Points indicate the observed mean of the between-trial correlations for each level of voxel-level variance in baseline activation (τ₀) averaged over simulations. Error bars depict the 1st and 3rd quartiles of the distribution of the simulation means. The line depicts the analytical prediction for between-trial correlations generated using Equation A2. (B). Correlation results from Condition Variability Simulation. Points indicate observed mean correlations across simulations between trials within the scary (S) and not-scary (N) conditions, as well as between conditions (B). The lines depict analytical predictions for each correlation generated using Equations A2–A4. (C). Support vector machine classification results for Condition Variability Simulation (chance = 0.5). (D). Correlation results for Item Variability Simulation. Points indicate within-item correlation for 6 items that differ continuously with respect to a continuous scariness variable. (E). Support vector machine classification results for Item Variability Simulation. The support vector machine was trained to classify each of the 6 different items that varied continuously with respect to a single conditioning variable (chance = 0.167).

Figure 7

Results from Subject-level Variability Simulation. Column 1 depicts group-level t-tests for the mean effect of scariness. Column 2 depicts group-level t-tests for the difference in within-condition correlations between scary and not-scary stimuli. Column 3 indicates classification accuracy for linear SVMs trained to classify activation patterns of scary and not-scary stimuli. The dotted lines in the t-test figures reflect the minimum t needed for statistical significance. The black lines in the SVM analysis depict chance classification (50%). Rows correspond to different levels of voxel-level variability in the effect of memory (A = 0.01; B = 0.1; C = 0.2; D = 0.3).