# **Quant Rants**

You can expect to find here a small compendium of proofs, mathematical arguments or just me reasoning through things I have read. I’ll try to keep it focused on Psychometrics, but the fact of the matter is that you’ll probably find some stuff from Geometry, Number Theory and all kinds of stuff every now and then.

I don’t think I’m aiming to be as ‘formal’ as I could be. Mostly because my arguments are basically me explaining things to myself… and maybe some other people will find it useful ðŸ™‚

Enjoy! And you can always email me if you think I made a mistake or something it not clear!

Why is Cronbach’s alpha a lower bound to reliability?

What is the volume of the shape described by all possible 3X3 correlation matrices?

Expressing R-squared in terms of correlations among the predictors and the dependent variable.Â

Why does centering in linear regression reduces multicollinearity?

What proportion of numbers are divisible by 2, 3, 5 or 7?

The parabolic relationship between skewness and kurtosis

Imagining multiple dimensions is hard

Multiple regression ran as a Canonical Correlation Analysis

If you run an ANOVA, where do you test the assumption of normality: the residuals or the dependent variable?

The Spearman correlation is under no obligation to tell you anything about the Pearson correlation

Sylvester’s criterion to help diagnose Heywood cases

Multivariate Poisson & Multivariate Exponential Distributions (not everything needs a copula ðŸ˜‰

How to simulate correlated log-normal random variables THE RIGHT WAY

Is there life beyond the 4th (central) moment?

(Small) Corrections to Nunnally & Bernstein (1994)

Simulating â€˜populationâ€™ standard errors in linear regression

Simulating multivariate outliers with known Mahalanobisâ€™ distance.

The relationship between the phi coefficient and the chi-square test of association.

The case of missing correlations and positive-definiteness

A few textbook exercises to keep the mind sharp!!!

From Christian Robert & George Casella Introducing Monte Carlo Methods with R:

From Richard Johnson & Dean WichenÂ Applied Multivariate Statistical Analysis: