how can I make goodness of fit test for my calculated AICc for a neuron's spike train

Hellow everyone

I have a spike information of a neuron based on X and Y coordinates by time (because this data is collected from Place Cells of an aminal). Based on this data I propose a conditional intensity function (CIF) and run the following codes to calculate required information.

Here is my code ;

load('datasetofneuron.mat'); % I am loading the data from file

t=0:1e-3:T; % building the t variable (T is total duration, 1e-3 is the step size

Z=[X,Y,X.*Y]; % my proposed CIF function

et=zeros(size(t)); % my event train (et) filling with zeros

et(round(neuron.spikeTimes*1e3))=1; % replacing 1 for

et=et(1:size(Z,1));

mdl=fitglm(Z,et','distr','Poisson'); % fitting the generalized linearized model by poisson distribution

L = mdl1.LogLikelihood; % finding the loglikelihood

AICc1 = mdl1.ModelCriterion.AICc;

beta_values=mdl.Coefficients.Estimate; % finding the estimated beta coefficients

beta_values_count= mdl1.NumCoefficients; % how many beta values will I have

Ldt=exp(beta_values(1)+XX*beta_values(2)+YY*beta_values(3)+XX.*YY*beta_values(4)); % Lambda*dt

% after then, I need to make a goodness-of-fit test (KS and autocorrelation)

after this line, I need to make a goodness-of-fit (KS and autocorrelation tests). Could you please help me how can I code in Matlab?

Thank you

Answer 1

[Abhishek]

Hi Mustafa,

I understand that you want to apply certain goodness-of-fit tests, namely Kolmogorov-Smirnov (KS) test and autocorrelation test for your dataset.

For KS test, you could perform Two-sample Kolmogorov-Smirnov test. First simulate a new set of data points based on the model by drawing random numbers from a Poisson distribution with the same mean as the data. Then compare the simulated data to a Poisson distribution with the same mean as the new set using the 'kstest2' function.

Assume that your original dataset is 'x1'. You can simulate a net set if data points based on the model using: -

x2 = poissrnd(Ldt)

Then apply the function 'kstest2' as follows: -

[h,p,ks2stat] = kstest2(x1,x2,'Alpha',0.01)

where 'h' is hypothesis test result, 'p' is Asymptotic p-value and 'ks2stat' is the test statistic. 'Alpha' can be varied between (0,1) based on significance level of desirability.

You can know more about KS tests from these documentation pages: -

1. One-sample Kolmogorov-Smirnov test - MATLAB kstest (mathworks.com)
2. Two-sample Kolmogorov-Smirnov test - MATLAB kstest2 (mathworks.com)

For autocorrelation test, you can use 'xcorr' function of MATLAB to compute the autocorrelation function (ACF) of the residuals, where residual = data - fit. Further you can use 'stem' function to plot the ACF.

residuals = et' - Ldt; %Calculate the residual
[acf, lags] = xcorr(residuals,'coeff') %Calculate the autocorrelation

For more information regarding the ACF function, refer to the documentation: Cross-correlation - MATLAB xcorr (mathworks.com).