By Steve McIntyre
As CA readers are aware, Stephan Lewandowsky of the University of Western Australia recently published an article relying on fraudulent responses at stridently anti-skeptic blogs to yield fake results.
In addition, it turns out that Lewandowsky misrepresented explained variances from principal components as explained variances from factor analysis, a very minor peccadillo in comparison. In a recent post, I observed inconsistencies resulting from this misdescription, but was then unable to diagnose precisely what Lewandowsky had done. In today’s post, I’ll establish this point.
Rather than conceding the problems of his reliance on fake/fraudulent data and thanking his critics for enabling him to withdraw the paper, Lewandowsky has instead doubled down by not merely pressing forward with publication of results relying on fake data, but attempting to “manufacture doubt” about the validity of criticisms, including his most recent diatribe – to which I respond today.
In a post several days ago, I temporarily considered other issues in the Lewandowsky article beyond the reliance on fake responses, reporting on my then progress in trying to replicate results – not easy since his article omitted relevant methodological information. Separate from this, Roman Mureika and I (but especially Roman) have made further progress in trying to replicate the SEM steps – more on this later.
I reported a puzzle about explained variance results as reported in Lewandowsky’s article – results that could not be replicated using a standard factor analysis algorithm. Roman Mureika also tried to figure out the discrepancy without success. I pointed out that Lewandowsky’s factor analysis did not seem to have much effect on the downstream results where the real problems lay.
The reason why we were unable to replicate Lewandowsky’s explained variance from factor analysis was that his explained variance results were not from factor analysis, but from the different (though related) technique of principal components, a technique very familiar to CA readers.
The clue to reverse engineering this particular Lewandowsky misrepresentation came from a passim comment in Lewandowsky’s blog in which he stated:
Applied to the five “climate science” items, the first factor had an eigenvalue of 4.3, representing 86% of the variance. The second factor had an eigenvalue of only .30, representing a mere 6% of the variance. Factors are ordered by their eigenvalues, so all further factors represent even less variance.
Eigenvalues are a term that arise from singular value (“eigen”) decomposition SVD. As an experiment, I did a simple SVD of the correlation matrix – the first step in principal components, a technique used in principal components and was immediately able to replicate this and other Lewandowsky results, as detailed below. Lewandowsky’s explained variance did not come from the factors arising from factor analysis, but from the eigenvectors arising from principal components. No wonder that we couldn’t replicate his explained variances.
But instead of conceding these results, Lewandowsky fabricated an issue regarding the number of retained eigenvectors in this analysis, a point that I had not taken issue and which did not affect the criticism, as I’ll detail.
Please read the rest here: Conspiracy-Theorist Lewandowsky Tries to Manufacture Doubt
As a side show note, here’s a window into the mind of Professor Lewandowsky: