GLMs

Generalized Linear Models (GLMs)

This folder contains MATLAB functions for estimating Generalized Linear Models (GLMs) and evaluating their significance in neural recordings. It includes two main functions: SetGLMsParams for defining options such as which variables to use, how to bin them and over which subset of the data these GLMs should be estimated. GLMsAnalysis then takes these options as an input, together with a structure containing the variables to use as predictors (called Nav here) and an array of responses for which you want to fit GLMs (e.g Spk.spikeTrain). See the Load function section to see how the Nav and Spk structures should be constructed.

SetGLMsParams

The SetGLMsParams function is used to define options required for estimating GLMs using the GLMAnalysis function. It takes as an input a structure containing explanatory variables (Nav) and neural response data (Srep). The output is a structure glmsparams containing parameters for running the GLM analysis.

Parameters included in glmsparams:

• subset: Define conditions and their values for data subsetting.
• cellidx: Logical array to select a subset of cells for analysis.
• sampleRate: Sampling rate of the data.
• scalingFactor: Scaling factor applied to response data.
• variablenames: Names of predictor variables (up to 2).
• smthNbins, binedges: Smoothing window and bin edges for each predictor.
• occ_th: Occupancy threshold for predictor inclusion.
• nspk_th: Minimal spikes required for cell inclusion.
• kfold: Number of folds for cross-validation.
• intercept: Flag for including a constant term in the GLM model.
• alpha: Regularization type in glmnet (lasso, ridge, elastic net).
• maxit, thresh: Convergence parameters for glmnet.
• pval_th: P-value threshold for predictor significance.

GLMAnalysis

The GLMAnalysis function estimates tuning curves using a Poisson GLM model. it performs k-fold cross-validation, evaluating model significance. Model comparison is performed by comparing likelihood values of held-out data under the model. This function only works up to two explanatory variables. It takes behavioral data (Nav), neural response data (Srep), and glmsparams as inputs and outputs a structure GLMs containing various results about the optimal GLM models.

Results included in GLMs:

• glmsparams: Input parameters for the GLM analysis.
• bestmodel: Best model indicator for each cell.
• LLH, LLH_cst: Log likelihood values for different models and constant mean model.
• tuning: Array of structures for each variable containing the following fields:
  • bincenters: Bin centers for the variable.
  • map, mapcv: Tuning curves for selected cells.
  • map_SE: Standard error estimates for tuning curves.
  • pval: P-values for variable significance. Results returned in tuning corresponds to the best model as estimated by a likelihood ratio test on held-out data.

Usage

1. Load behavioral data and spike data:

   datapath = 'path/to/your/data'

   loadparams = SetLoadParams(datapath);

   Nav = LoaddataNav(loadparams);

   Spk = LoaddataSpk(loadparams, Nav.sampleTimes);

   Srep = Spk.spikeTrain;

2. Define parameters using SetGLMsParams:

   glmsparams = SetGLMsParams(Nav, Srep);

3. Modify paramters in glmsparams if needed. For instance:

   glmsparams.subset.Condition = [1 3 5];

   glmsparams.subset.Condition_op = 'ismember';

   glmsparams.subset.Spd = 2.5;

   glmsparams.subset.Spd = '>=';

   glmsparams.variablename = {'Xpos', 'Spd'};

   glmsparams.binedges = {0:2:100, [0:5:50 inf];

4. Estimate GLMs using GLMsAnalysis

   GLMs = GLMsAnalysis(Nav, Srep, glmsparams);

For more detailed information and usage examples of each function, please refer to the function documentation, Tutorial2.2 and Tutorial_handson.

Developed by J. Fournier in August 2023 for the Summer school "Advanced computational analysis for behavioral and neurophysiological recordings."