Correlations With Continuous Variable

This analysis calculates crosscorrelations between a continuously recorded variable and a neuronal firing rate, or crosscorrelations between a continuously recorded variable and another continuous variable.

Parameters

Parameter	Description
Reference	Specifies a reference continuous variable.
XMin	Time axis minimum in seconds.
XMax	Time axis maximum in seconds.
Bin Type	An option to specify how the bin value is determined. If this option is Auto, NeuroExplorer will use the bin equal to the A/D sampling interval of the reference variable.
Bin	Bin size in seconds. Used if Bin Type is set to User defined.
Select Data	If Select Data is From Time Range, only the data from the specified (by Select Data From and Select Data To parameters) time range will be used in analysis. See also Data Selection Options.
Select Data From	Start of the time range in seconds.
Select Data To	End of the time range in seconds.
Interval filter	Specifies the interval filter(s) that will be used to preselect data before analysis. See also Data Selection Options.
Smooth	Option to smooth the histogram after the calculation. See Post-Processing Options for details.
Smooth Filter Width	The width of the smooth filter. See Post-Processing Options for details.
Add to Results / Bin left	An option to add an additional vector (containing a left edge of each bin) to the matrix of numerical results.
Add to Results / Bin middle	An option to add an additional vector (containing a middle point of each bin) to the matrix of numerical results.
Add to Results / Bin right	An option to add an additional vector (containing a right edge of each bin) to the matrix of numerical results.
Send to Matlab	An option to send the matrix of numerical results to Matlab. See also Matlab Options.
Matrix Name	Specifies the name of the results matrix in Matlab workspace.
Matlab command	Specifies a Matlab command that is executed after the numerical results are sent to Matlab.
Send to Excel	An option to send numerical results or summary of numerical results to Excel. See also Excel Options.
Sheet Name	The name of the worksheet in Excel where to copy the numerical results.
TopLeft	Specifies the Excel cell where the results are copied. Should be in the form CR where C is Excel column name, R is the row number. For example, A1 is the top-left cell in the worksheet.

Summary of Numerical Results

The following information is available in the Summary of Numerical Results

Column	Description
Variable	Variable name.
Reference	Reference variable name.
YMin	Y axis minimum.
YMax	Y axis maximum.
Mean Hist.	Mean of all the correlation values for this variable.
St. Dev. Hist	Standard deviation of all the correlation values for this variable.
St. Err. Mean Hist	Standard error of mean of all the correlation values for this variable

Algorithm

This analysis calculates standard correlograms for two (continuously recorded) vectors. For spike trains and events, NeuroExplorer first calculates the rate histograms with the specified bin size, and then calculates the correlations between the reference variable and the rate histogram.

If x[i], i=1,...N is the vector of all the values of the reference variable with sampling rate SR and y[i], i=1,...,N is the vector of all the values of another continuous variable or values of spike train rate histogram, then

correlation[lag_n_seconds] = Pearson correlation between vectors

{ x[1], x[2], ..., x[N-lag_in_samples] }

and

{ y[1+lag_in_samples], y[2+lag_in_samples], ..., y[N] }

where lag_in_samples = lag_in_seconds*SR.

Let’s consider the following example. We have continuous variable Cont1. We create continuous variable Cont2 by running shift operation on Cont1 with shift=0.02s.

For each value of time t, we have Cont1[t] = Cont2[t+0.02]. This means that if reference is Cont1 and lag_in_seconds = 0.02s, we will calculate Pearson correlation of identical vectors. That is, our correlation result will have the highest value close to 1.0 at 0.02 seconds.