Whenever a program is used for data analysis, it is important for the community at large to understand what algorithms were used in the analysis. And while NeuroElf is mostly written to make algorithms accessible (user friendliness aspect), it is equally relevant to ascertain that the methods implemented in any program have been accepted by the scientific community as “useful and reliable” (to achieve the intended goal) and are (as much as possible) free of errors, both when it comes to potential flaws in the algorithm as well as its specific implementation in the given program.

As an example, initially when using the alphasim button (NeuroElf GUI access to the alphasim.m function) the GUI would demand user input for the estimated smoothness of the data, and as a default value 6mm was presented to the user. This choice (of default value) was motivated by the fact that, at the lab where I work, the smoothing operation during the preprocessing stage would be configured with a 6mm Gaussian kernel. However, the correct number to use ought to be an estimate of the spatial smoothness of the residual, because that determines how likely it is that, by chance, a cluster of a given size will be encountered in a statistical map (at any given uncorrected threshold), and this issue has since been addressed!

The following list gives an overview on what methods of analysis and parameter estimation are implemented in NeuroElf (as far as they exceed basic operations, such as for example plain averaging across a dimension):

Mediation analysis as a whole can be described as the estimation (and test) of separate path coefficients, a and b, as well as their product, a*b, such that the “transmission” of an existing effect between an indepedent/explanatory variable, X, and an outcome variable, Y, is accomplished via one or several mediators, Mi. The analysis includes a test for significance of the a*b product term (as well as the individual path coefficients), and also allows to specify covariates. It is

• implemented in function mediationpset.m, where the pset indicates that the function returns path coefficients (p), standard errors (se), and t-statistics (t)
• options are: a*b product testing via bootstrapping or Sobel test, and robust regression
• supports multi-dimensionaging) data for X, M, and Y

An example would be, on the level of a between-subject effect, that a randomly assigned condition (X, e.g. strategy to apply to stimuli) has an effect on outcome (Y, e.g. appetite to a specific type of stimulus or difference in appetite to two kinds of stimuli) via a specific brain region (or network of regions) that work/s as a mediator/s (Mi, e.g. pre-frontal control regions). For a within-subjects design, a test could be whether, on any given trial, the response in pre-frontal cortex during an instructional cue (strategy stimulus) has an effect on outcome (self-reported craving for depicted food) via another brain region. In that case, either X (which brain regions has an influence on the “craving center” of the brain) or M (which brain region is influenced by the “control region” of the brain) could be “searched for”…

Multi-level kernel density analysis is trying to determine whether reported “peak coordinates” in previously published papers (given a selection criterion, such as publications concerned with a specific psychological construct, e.g. fear or working memory) occur in specific spatial locations (spatial specificity) significantly more often than warranted by chance, as a means to pool several publications to reduce the influence of a single publication on the “knowledge” of spatial distributions of activation patterns. It is

• implemented as a method for PLP objects, PLP::MKDA
• available via the Meta Analysis interface

Robust regression, in NeuroElf, is the estimation of regression parameters using an iteratively-reweighted-least-squares approach where outliers are “detected” using the bi-square weighting function. It is

• implemented for a single univariate regression (e.g. a time course, T, regressed on a design matrix, X) in function fitrobustbisquare.m
• implemented for a common design matrix (X) on mass-univariate data (e.g. fMRI imaging on the first or second level) in function fitrobustbisquare_img.m
  • is used in the GLM computation routine for first-level data (MDM::ComputeGLM) as well as from the NeuroElf GUI's contrast manager functionality when robust regression is selected
• implemented for individual design matrices (Xi, where the third dimension is the number of cases) on data (e.g. for a whole-brain robust mediation) in function fitrobustbisquare_multi.m
  • this is used by the NeuroElf GUI's mediation interface when robust regression is selected
• after the regression, to compute t-statistics from the output (beta values and sample weights), the function robustt.m can be used (correcting for the loss in degrees of freedom)
• a special case is for when, in a correlation, both “dependent” and “independent” variables may contain outliers, in which case robcorrcoef.m should be used, which uses both as the explanatory variable as quick check
• and to compare means between groups, the two simplified functions robustnsamplet.m and robustnsamplet_img.m are available as well