mne.connectivity.phase_slope_index(data, indices=None, sfreq=6.283185307179586, mode='multitaper', fmin=None, fmax=inf, tmin=None, tmax=None, mt_bandwidth=None, mt_adaptive=False, mt_low_bias=True, cwt_freqs=None, cwt_n_cycles=7, block_size=1000, n_jobs=1, verbose=None)[source]

Compute the Phase Slope Index (PSI) connectivity measure.

The PSI is an effective connectivity measure, i.e., a measure which can give an indication of the direction of the information flow (causality). For two time series, and one computes the PSI between the first and the second time series as follows

indices = (np.array([0]), np.array([1])) psi = phase_slope_index(data, indices=indices, …)

A positive value means that time series 0 is ahead of time series 1 and a negative value means the opposite.

The PSI is computed from the coherency (see spectral_connectivity), details can be found in [1].

dataarray_like, shape=(n_epochs, n_signals, n_times)

Can also be a list/generator of array, shape =(n_signals, n_times); list/generator of SourceEstimate; or Epochs. The data from which to compute connectivity. Note that it is also possible to combine multiple signals by providing a list of tuples, e.g., data = [(arr_0, stc_0), (arr_1, stc_1), (arr_2, stc_2)], corresponds to 3 epochs, and arr_* could be an array with the same number of time points as stc_*.

indicestuple of array | None

Two arrays with indices of connections for which to compute connectivity. If None, all connections are computed.


The sampling frequency.


Spectrum estimation mode can be either: ‘multitaper’, ‘fourier’, or ‘cwt_morlet’.

fminfloat | tuple of float

The lower frequency of interest. Multiple bands are defined using a tuple, e.g., (8., 20.) for two bands with 8Hz and 20Hz lower freq. If None the frequency corresponding to an epoch length of 5 cycles is used.

fmaxfloat | tuple of float

The upper frequency of interest. Multiple bands are dedined using a tuple, e.g. (13., 30.) for two band with 13Hz and 30Hz upper freq.

tminfloat | None

Time to start connectivity estimation.

tmaxfloat | None

Time to end connectivity estimation.

mt_bandwidthfloat | None

The bandwidth of the multitaper windowing function in Hz. Only used in ‘multitaper’ mode.


Use adaptive weights to combine the tapered spectra into PSD. Only used in ‘multitaper’ mode.


Only use tapers with more than 90% spectral concentration within bandwidth. Only used in ‘multitaper’ mode.


Array of frequencies of interest. Only used in ‘cwt_morlet’ mode.

cwt_n_cyclesfloat | array of float

Number of cycles. Fixed number or one per frequency. Only used in ‘cwt_morlet’ mode.


How many connections to compute at once (higher numbers are faster but require more memory).


How many epochs to process in parallel.

verbosebool, str, int, or None

If not None, override default verbose level (see mne.verbose() and Logging documentation for more). If used, it should be passed as a keyword-argument only.


Computed connectivity measure(s). The shape of each array is either (n_signals, n_signals, n_bands) mode: ‘multitaper’ or ‘fourier’ (n_signals, n_signals, n_bands, n_times) mode: ‘cwt_morlet’ when “indices” is None, or (n_con, n_bands) mode: ‘multitaper’ or ‘fourier’ (n_con, n_bands, n_times) mode: ‘cwt_morlet’ when “indices” is specified and “n_con = len(indices[0])”.


Frequency points at which the connectivity was computed.


Time points for which the connectivity was computed.


Number of epochs used for computation.


The number of DPSS tapers used. Only defined in ‘multitaper’ mode. Otherwise None is returned.


[1] Nolte et al. “Robustly Estimating the Flow Direction of Information in

Complex Physical Systems”, Physical Review Letters, vol. 100, no. 23, pp. 1-4, Jun. 2008.

Examples using mne.connectivity.phase_slope_index