How good is good enough in path analysis of fMRI data?

This paper is concerned with the problem of evaluating goodness-of-fit of a path analytic model to an interregional correlation matrix derived from functional magnetic resonance imaging (fMRI) data. We argue that model evaluation based on testing the null hypothesis that the correlation matrix predicted by the model equals the population correlation matrix is problematic because P values are conditional on asymptotic distributional results (which may not be valid for fMRI data acquired in less than 10 min), as well as arbitrary specification of residual variances and effective degrees of freedom in each regional fMRI time series. We introduce an alternative approach based on an algorithm for automatic identification of the best fitting model that can be found to account for the data. The algorithm starts from the null model, in which all path coefficients are zero, and iteratively unconstrains the coefficient which has the largest Lagrangian multiplier at each step until a model is identified which has maximum goodness by a parsimonious fit index. Repeating this process after bootstrapping the data generates a confidence interval for goodness-of-fit of the best model. If the goodness of the theoretically preferred model is within this confidence interval we can empirically say that the theoretical model could be the best model. This relativistic and data-based strategy for model evaluation is illustrated by analysis of functional MR images acquired from 20 normal volunteers during periodic performance (for 5 min) of a task demanding semantic decision and subvocal rehearsal. A model including unidirectional connections from frontal to parietal cortex, designed to represent sequential engagement of rehearsal and monitoring components of the articulatory loop, is found to be irrefutable by hypothesis-testing and within confidence limits for the best model that could be fitted to the data.