Bootstrap-based methods for testing factor-by-curve interactions in generalized additive models: assessing prefrontal cortex neural activity related to decision-making

Abstract

In many situations the effect of a continuous covariate on response varies across groups defined by levels of a categorical variable. This paper addresses generalized additive models incorporating the so-called factor-by-curve interaction. A local scoring algorithm based on local linear kernel smoothers was used to estimate the model. Two different types of bootstrap-based procedures are proposed for testing interaction terms, namely, the likelihood ratio test, and a procedure based on an estimate of the interaction terms. Given the high computational cost involved, binning techniques were used to speed up computation in the estimation and testing processes. A simulation study was conducted to assess the validity of these bootstrap-based tests. This methodology was applied to studying prefrontal cortex neural activity associated with decision-making in monkeys. The proposed statistical procedure proved very useful in revealing the neural activity correlates of decision-making strategies adopted by monkeys in accordance with different behavioural tasks.