A friend was working on a paper and found himself in the situation of having to defend the null hypothesis that a particular effect is absent (or not measurable) when tested under more controlled conditions than those used in previous studies. He asked for some practical advice: “what would convince you as as a reviewer of a null result?"
No statistical test can “prove” a null results (intended as the point-null hypothesis that an effect of interest is zero).
This took me some time to make it work, so I’ll write the details here for the benefit of my future self and anyone else facing similar issues.
To run R in the Apocrita cluster (which runs CentOS 7) first load the modules
module load R module load gcc (gcc is required to compile the packages from source.)
Before starting you should make sure that you don’t have any previous installation of RStan in your system.
In experimental psychology and neuroscience the classical approach when comparing different models that make quantitative predictions about the behavior of participants is to aggregate the predictive ability of the model (e.g. as quantified by Akaike Information criterion) across participants, and then see which one provide on average the best performance. Although correct, this approach neglect the possibility that different participants might use different strategies that are best described by alternative, competing models.
Photo ©Roxie and Lee Carroll, www.akidsphoto.com.
In my previous lab I was known for promoting the use of multilevel, or mixed-effects model among my colleagues. (The slides on the /misc section of this website are part of this effort.) Multilevel models should be the standard approach in fields like experimental psychology and neuroscience, where the data is naturally grouped according to “observational units”, i.e. individual participants. I agree with Richard McElreath when he writes that “multilevel regression deserves to be the default form of regression” (see here, section 1.
Generating random variables with given variance-covariance matrix can be useful for many purposes. For example it is useful for generating random intercepts and slopes with given correlations when simulating a multilevel, or mixed-effects, model (e.g. see here). This can be achieved efficiently with the Choleski factorization. In linear algebra the factorization or decomposition of a matrix is the factorization of a matrix into a product of matrices. More specifically, the Choleski factorization is a decomposition of a positive-defined, symmetric1 matrix into a product of a triangular matrix and its conjugate transpose; in other words is a method to find the square root of a matrix.
In the study of human perception we often need to measure how sensitive is an observer to a stimulus variation, and how her/his sensitivity changes due to changes in the context or experimental manipulations. In many applications this can be done by estimating the slope of the psychometric function1, a parameter that relates to the precision with which the observer can make judgements about the stimulus. A psychometric function is generally characterized by 2-3 parameters: the slope, the threshold (or criterion), and an optional lapse parameter, which indicate the rate at which attention lapses (i.