Help Desk

My advisor told me to use principal components analysis to examine the structure of my items and compute scale scores, but I was taught not to use it because it is not a “true” factor analysis. Help!

Help, indeed. This issue has been a source of both confusion and contention for more than 75 years, and papers have been published on this topic as recently as just a few years ago. A thorough discussion of principal components analysis (PCA) and the closely related methods of exploratory factor analysis (EFA) would require pages of text and dozens of...

I fit a multilevel model and got the warning message “G Matrix is Non-Positive Definite.” What does this mean and what should I do about it?

Anyone who uses multilevel models will eventually encounter the dreaded “G matrix is non-positive definite” message (or “Tau Matrix” or “Psi Matrix”, depending on the labeling used by your software). This anxiety-inducing warning is often a signal that something is wrong in your model that needs fixing. With an NPD G matrix, the obtained estimates usually reflect an “improper” solution...

I’m reporting within- and between-group effects in from a multilevel model, and my reviewer says I need to address “sampling error” in the group means. What does this mean, and what can I do to address this?

This is a long-neglected topic, and one that is receiving increasing attention in the methodological literature. The problem that the reviewer is referring to is that the usual ways we obtain within- and between-group effects for lower-level predictors within the multilevel model (MLM) oftentimes generate biased estimates. The same issue arises with any form of clustering, such as when trying...

My advisor told me I should group-mean center my predictors in my multilevel model because it might “make my effects significant” but this doesn’t seem right to me. What exactly is involved in centering predictors within the multilevel model?

This is an excellent question and the topic of centering is often a source of confusion when using multilevel models (MLMs) in practice. This confusion is in part due to the need to address a complexity that arises within the MLM but is not relevant within the traditional multiple regression model: when modeling the effect of a lower-level predictor on...

A reviewer recently asked me to comment on the issue of equivalent models in my structural equation model. What is the difference between alternative models and equivalent models within an SEM?

Differentiating between alternative models and equivalent models has long been a point of confusion in many research applications. Although the challenge of equivalent models can arise within almost any analytic setting, this is particularly salient within the structural equation model (or SEM). It is helpful first distinguish between alternative and equivalent models. To begin, one of the greatest strengths of...

I have a fair amount of missing data that I don’t want to delete prior to my analysis. What are the best options available for me to retain these partially missing cases?

Missing data are a common problem faced by nearly all data analysts, particularly with the increasing emphasis on the collection of repeated assessments over time. Data values can be missing for a variety of reasons. A common situation is when a subject provides data at one time point but fails to provide data at a later time point; this is...

The Cronbach’s Alphas for all the scales in my path analysis are in the .7s, so why is a reviewer criticizing me for not paying sufficient attention to reliability?

The issue of reliability can be a complex and often misunderstood issue. Entire text books have been written about reliability, validity, and scale construction, so we only briefly touch on the key issues here (see Bandalos, 2018, for an excellent recent example). To begin, in most areas across the behavioral, educational, and health sciences, theoretical constructs are hypothesized to exist...

How can I estimate statistical power for a structural equation model?

This is a question that often arises when using structural equation models in practice, sometimes once a study is completed but more often in the planning phase of a future study. To think about power, we must first consider ways in which we can make errors in hypothesis testing (Cohen, 1992). Briefly, the Type I error rate is the probability...

What are modification indices and should I use them when fitting SEMs to my own data?

This is a great question and is one that prompts much disagreement among quantitative methodologists. Nearly all confirmatory factor analysis or structural equation models impose some kind of restrictions on the number parameters to be estimated. Usually, some parameters are set to zero (and thus not estimated at all), but sometimes restrictions come in the form of equality constraints or...

Do you have any materials that demonstrate how to estimate structural equation models using lavaan in R?

This is a question we often hear, particularly from students and junior researchers who don’t have access to expensive commercial software for fitting structural equation models. It is possible to estimate a wide array of SEMs, ranging from simple path models to fully latent SEMs to growth curve models and beyond, using the lavaan package within R. For those who...

CenterStat's Help Desk is a blog in which Dan and Patrick respond to commonly asked questions about a variety of topics behavioral, educational, and health research including experimental design, measurement, data analysis, and interpretation of findings. The responses are intentionally brief and concise, and additional resources are provided such as recommended readings, provision of exemplar data and computer code, or links to other potential learning materials. Readers are welcome to submit their own questions for future Help Desk responses at [email protected].