Help Desk: A Quant Methods Blog

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...
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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...
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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...
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How do you choose the best longitudinal data analytic method for testing your research questions?

We have worked with statistical models for longitudinal data for more than two decades and this remains a vexing question to us both. There are so many modeling options from which to choose that it is often overwhelming to know which statistical method to use when. This is further complicated by the ongoing refinement of existing models and the development...
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What is the difference between a growth model estimated as a multilevel model versus as a structural equation model?

This very common question reflects a great deal of unnecessary confusion about how to select a specific analytic approach for modeling longitudinal data. The general term “growth modeling” refers to a variety of statistical methods that allow for the estimation of inter-individual (or between-person) differences in intra-individual (or within-person) change. Often, the function describing within-person change is referred to as...
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How can I define nonlinear trajectories in a growth curve model?

Growth curve models, whether estimated as a multilevel model (MLM) or a structural equation model (SEM), have become widely used in many areas of behavioral, health, and education sciences. The most common type of growth model defines a linear trajectory in which the time scores defining the slopes increment evenly for equally spaced repeated measures (e.g., values representing time are...
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Can I estimate an SEM if the sample data are not normally distributed?

Continuous distributions are typically described by their mean (central tendency), variance (spread), skew (asymmetry), and kurtosis (thickness of tails). A normal distribution assumes a skew and kurtosis of zero, but truly normal distributions are rare in practice. Unfortunately, the fitting of standard SEMs to non-normal data can result in inflated model test statistics (leading models to be rejected more often...
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How do I know if my structural equation model fits the data well?

This is one of the most common questions we receive and, unfortunately, there are no quick answers. However, there are some initial guidelines that can be followed when assessing the fit of an SEM. For most SEMs, the goal of the analysis is to define a model that results in predicted values of the summary statistics (sometimes called “moment structures”...
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Best Methods for Handling Missing Data in Intensive Longitudinal Designs

In nearly every discipline within the behavioral, health, and educational sciences, longitudinal data have become requisite for establishing temporal precedence and distinguishing inter-individual differences in intra-individual change. Whereas traditional longitudinal designs often obtained repeated assessments at monthly or even yearly intervals, recent advances in mobile technology have allowed for the collection of multiple assessments throughout a single day. These so-called...
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Syntax for Computing Random Effect Estimates in SPSS

Many programs can be used to fit multilevel models. For instance, in our multilevel modeling summer workshop, we demonstrate three programs: SAS, SPSS, and Stata. Unlike SAS, Stata, and many other programs, however, SPSS does not currently offer the option to output estimates of the random effects. Obtaining estimates of the random effects can be useful for a variety of...
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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].

Livestream Workshops

Free Introduction to Structural Equation Modeling

May 10-12, 2023
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Applied Measurement Modeling

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Causal Inference

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Multilevel Models for Longitudinal Data

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Machine Learning: Theory and Applications

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Sample Size Planning for Power and Accuracy

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Analyzing Intensive Longitudinal Data

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Longitudinal Structural Equation Modeling

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Modern Missing Data Analysis

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Multilevel Models for Hierarchical Data

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Latent Curve Models

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Mixture Modeling and Latent Class Analysis: A Short Course

January 3-5, 2024
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Instructor: Dan Bauer