Analysing visual receptive fields through generalised additive models with interactions

  1. Rodríguez Álvarez, María Xosé
  2. Cadarso Suárez, Carmen María
  3. Gonzalez Garcia, Francisco
Revista:
Sort: Statistics and Operations Research Transactions

ISSN: 1696-2281

Ano de publicación: 2012

Volume: 36

Número: 1

Páxinas: 3-44

Tipo: Artigo

Outras publicacións en: Sort: Statistics and Operations Research Transactions

Resumo

Visual receptive fields (RFs) are small areas of the visual field where a stimulus induces a re- sponses of a particular neuron from the visual system. RFs can be mapped using reverse cross- correlation technique, which produces raw matrices containing both spatial and temporal informa- tion about the RF. Though this technique is frequently used in electrophysiological experiments, it does not allow formal comparisons between RFs obtained under different experimental condi- tions. In this paper we propose the use of Generalised Additive Models (GAM) including com- plex interactions, to obtain smoothed spatio-temporal versions of RFs. Moreover, the proposed methodology also allow for the statistical comparisons of the RFs obtained across various experi- mental conditions. Data analysed here derive from studies of neurons� activity in the visual cortex of behaving monkeys. Our results suggest that the GAM-based technique proposed in this paper can be a flexible and powerful tool for assessing receptive field properties.

Referencias bibliográficas

  • Crainiceanu, C. and Ruppert, D. (2004). Likelihood ratio tests for goodness-of-fit of a nonlinear regression model. Journal of Multivariate Analysis, 91, 35–52.
  • Fahrmeir, L. and Kneib, T. (2011). Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data. Oxforf University Press.
  • Greven, S., Crainiceanu, C. M. and Kuchenhoff, H. (2008). Restricted likelihood ratio testing ¨ for zero variance components in linear mixed models. Journal of Computational and Graphical Statistics, 17, 870–891.
  • Greven, S. and Kneib, T. (2010). On the Behavior of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models. Biometrika, 97, 773–789.
  • Lee, D.-J. (2010). Smothing mixed model for spatial and spatio-temporal data. PhD thesis, Department of Statistics, Universidad Carlos III de Madrid, Spain.
  • Lee, D.-J. and Durban, M. (2011). P-spline ANOVA-type interaction models for s ´ patio-temporal smoothing. Statistical Modelling, 11, 49–69.
  • Liang, H., Wu, H. and Zou, G. (2008). A note on conditional AIC for linear mixed-effects models. Biometrika, 95, 773–778.
  • Marra, G. and Radice, R. (2010). Penalised regression splines: theory and application to medical research. Statistical Methods in Medical Research, 19, 107–125.
  • Scheipl, F., Greven, S. and Kuchenhoff, H. (2008). Size and power of tests for a zero rando ¨ m effect variance or polynomial regression in additive and linear mixed models. Computational Statistics & Data Analysis, 52, 3283–3299.
  • Wood, S. N. (2006). Generalized Additive Models. An Introduction with R. Chapman & Hall/CRC.