Multi-Group comparison in Partial Least Squares Path Models

This post is about multi-group partial least squares path modeling (PLS-PM). There is already a useful list of references on this blog post. As the author noticed, ensuring measurement invariance is often thought of as a prerequisite before dwelling into multi-group comparison, at least in the psychometric literature that I am familiar with. From a measurement perspective, this is easily understandable since we need to ensure that we are indeed measuring in a similar way the exact same construct in specific subpopulation.

lost+found 2015

Here are some draft notes, written in 2015, unfilled but not lost forever. With slight edits to accomodate a proper archive blog post. R and psychometrics (February 2015) I have been using R for most of my statistical projects since 10 years or so. In the beginning it really was an awesome software for psychometric modeling because there were some nice packages for multidimensional and optimal scaling, IRT modeling, and factor analysis, which were otherwise not available, at least on OS X.

lost+found 2014

Here are some draft notes, written in 2014, unfilled but not lost forever. With slight edits to accomodate a proper archive blog post. Stata for structural equation modeling (October 2014) As Mplus syntax often appears a bit cryptic to carry out basic operations in Confirmatory Factor Analysis (CFA), I decided to write out some of the notes I took when using Mplus for recent psychometric studies. In what follows, I will use data described and analysed in Acock’s Stata textbook, Discovering Structural Equation Modeling Using Stata.

Structural equation modeling with Stata

Stata 12 came with a module to perform Structural Equation Modeling. Like Amos, there is a SEM diagram builder and fancy dialog boxes but as always commands are directly returned on the command-line so it is not difficult to learn how to write your SEM model directly at Stata prompt or in a do file. Recently, a book on Discovering Structural Equation Modeling Using Stata was published by Stata Press (Alan C.

Hierarchical Omega in factor analysis

While browsing questions related to psychometrics posted late in 2012 on Cross Validated, I noticed two questions dealing with hierarchical ωh. These questions come from the use of William Revelle’s psych package, which offers a very nice toolkit for serious psychometrics, especially work related to factor analysis. Just take a look at some of his Psychology 454 syllabus to get an idea of what’s available in psych. The ωh measure was popularized by Zinbarg, Revelle and coll few years ago.

Cognitive diagnosis models

As its name suggests, a cognitive diagnosis model aims at “diagnosing” which skills examinees have or do not have. It has become very popular in recent years because it overcomes standard limitations of summated scale scores derived from classical test or item response theory. There is a detailed overview of CDM by DiBello and coll. in the Handbook of Statistics, vol. 26: DiBello, L.V., Roussos, L.A., and Stout, W.F. (2007).

Notes on the ISOQOL 2012 conference

Here some are notes I took during the 19th annual conference of the International Society for Quality of Life Research which was held in Budapest, Hungary. On the use of mixed methods to assess content validity of patient reported outcomes Mixed methods consist in an iterative, cyclical, and hypothesis-driven decision approach that alternate between qualitative and quantitative methods. With application in prospective, observational data, or in-trial evaluation. Now becoming a recommended step by FDA for developing PRO measures before psychometric validation of a new instrument.

Testlet response theory

Here is a brief overview of Testlet Response Theory and its Applications, by Wainer, Bradlow, and Wang (Cambridge University Press, 2007). This book provides a very nice introduction to true score (which focus on test scores) and item response (which focus on item scores) theory, and discusses the advantages of using testlets as the basis of measurement. I like such clear overview of main concepts which form the basis of one’s field of study.

Factor analysis with categorical data

I often read questions on the use of Factor Analysis (FA) with categorical data, typically binary (yes/no) indicators or ordinal responses (e.g., Likert-type items). Here is a brief list of references that justify its use in this context, and provide comparison with other measurement models (mostly from the Item Response Theory literature). Usually, my first thought when someone ask whether we can use exploratory or confirmatory FA on dichotomous or polytomous items is a paper by Jan de Leeuw: Takane and de Leeuw, On the relationship between item response theory and factor analysis of discretized variables, Psychometrika (1987) 52(3):393.


I thougth it would be funny to relate how I came from a query about ‘biplot displays in lisp’ to statistical computing in R, using Google. So, basically I was looking for existing implementation of biplots for Common Lisp. To be honest, I was suspecting that something would be available for xlispstat, and that was the very first hit: xls-biplot was written by Frederic Udina eight years ago. His paper published in the Journal of Statistical Software explains available transformations (functional transformation, weighting, centering) of the raw data and the way coordinates (standard, principal, canonical) can be computed to express variables relationships in a reduced factorial space.