Thursday, October 31, 2019 - 3:00pm

209 W Eighteenth Ave (EA), Room 170

Title

Are psychological variables random random variables?

## Speaker

Paul De Boeck, Department of Psychology, The Ohio State University

Abstract

The discipline of psychology works with constructs, such as intelligence, extraversion, etc. These constructs are given an operational definition for research purposes or for practice purposes. Alternatively, a measurement model is used based on observables called indicators. One of the founding fathers, Charles Spearman (1904), has formulated the principle of invariance as a criterion for measures of the same construct, in his case intelligence. Invariance means that the correlation (across persons) of measures of the same construct is perfect (=1.00). In his view, the reasons why this is not true in practice, are three sources of measurement uncertainty: (1) measurement error, (2) measure specificity, (3) measure cluster specificity. They are three layers of random person effects. Apart from these three, the expected correlation between measures would be 1.00. In Spearman’s case, the result would be g, also called general intelligence. The corresponding model is the well-known bi-factor model. An alternative invariance model, the correlated factor model, will also be briefly discussed. Unfortunately, neither of both invariance models fits well enough with the data. This is where random random variables (a neologism) can help. The same variable is perhaps a somewhat different variable in another study. Random random variables live in a two-level world: level 2 for between studies and level 1 for within studies. At level 2, the study specific true covariance matrix Σ is inverse Wishart distributed based on a covariance matrix Ω and a dispersion parameter m (Hu & Browne, 2015). At level 1, the sample covariance matrix S is based on a Wishart distribution with covariance matrix Σ and degrees of freedom n (sample size minus one). From these assumptions, it follows that (a) invariance models never fit in a perfect way, (b) measurement invariance across groups is difficult to establish, and (c) the replication crisis in psychology is an immanent phenomenon. These three points will be illustrated with simulation studies.

*Note: Seminars are free and open to the public. Reception to follow.*