Partial Cross-Correlation Analysis Resolves Ambiguity in the Encoding of Multiple Movement Features

Abstract

A classical question in neuroscience is which features of a stimulus or of an action are represented in brain activity. When several features are interdependent either at a given point in time or at distinct points in time, neural activity related to one feature appears to be correlated with other features. Thus techniques that simultaneously consider multiple features cannot account for delayed interdependencies between features. The result is an ambiguity with respect to the encoded features. Here, we resolve this ambiguity by applying a novel statistical method based on partial cross-correlations. The method yields estimates of linear correlations between neural activity and a given feature that are not affected by linear correlations with other features at multiple time delays. The method also provides a graphical output measured on a scale that allows for comparisons between different features, neurons, and experiments. We use real movement data and neural activity simulated according to a wide range of tuning models to illustrate the method. When applied to real neural activity, the procedure yields results that indicate which of the considered features the neural activity is related to and at what time delays.

Congruent Activity during Action and Action Observation in Motor Cortex

“…In this analysis, we followed the method described by Stark et al (2006) with the exception that we segmented our continuous data into relatively short epochs of equal lengths rather than organizing it by trials. Like the LFP data, binned time series representing instantaneous cursor and eye directions were concatenated across blocks of each condition and truncated to the length of the shortest condition.…”

“…We found that, especially in the cursor and target and target-only observation conditions, eye movements were highly correlated with the cursor movements, raising the possibility that the apparent correlation between neural activity and cursor movement we saw during observation was an indirect consequence of the correlation between neural activity and eye movements. To assess the degree to which the observed neural activity was independently related to eye or cursor movement, we followed the method described by Stark et al (2006). They rely on the method of partial correlations (Fisher, 1970) to assess the residual correlation between two variables when linear correlations with a third variable have been removed, and they expand the method to take into account multiple temporal leads and lags between two variables.…”

“…They rely on the method of partial correlations (Fisher, 1970) to assess the residual correlation between two variables when linear correlations with a third variable have been removed, and they expand the method to take into account multiple temporal leads and lags between two variables. Calculating partial correlations between neural activity and kinematic parameters at multiple leads and lags results in a PCCM (Stark et al, 2006). Figure 6, A and B, shows the mean PCCM for eye direction and cursor direction for each of the four experimental conditions averaged over all cells.…”

Factors affecting hare–lynx dynamics in the classic time series of the Hudson Bay Company, Canada

“…Thus, simple correlation is not suitable for evaluating effects of variables H t , L t , and S t on population dynamics. Partial cross correlation has been widely used for causal analysis by controlling co-varying variables (Stark et al 2006). Partial cross correlation is very useful for inferring direct or spurious causes of control variables.…”

Predicting Movement from Multiunit Activity

“…A third monkey (F) was trained to perform continuous curved movements with its preferred left hand by operating a two-joint low-friction planar manipulandum (Stark et al, 2006). A horizontal opaque screen, mounted at chest level, blocked view of manipulandum and hand, and a yellow cursor indicating hand end-point was projected on the screen (see Fig.…”