News and Updates
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 other kinds of structured relations among parameters. The model chi-square test reflects the extent to which these imposed restrictions impede the ability of the model to reproduce the means, variances, and covariances that were observed in the sample. Smaller chi-square values reflect that the estimated model is able to adequately reproduce the observed sample statistics whereas larger values reflect that some aspect of the hypothesized model is inconsistent with characteristics of the observed sample.Read More
This is a question we often hear, particularly from students and junior researchers who don’t have access to sometimes 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 may be interested, we have developed detailed demonstrations of how to estimate a broad class of SEMs using lavaan and these are now freely available for download.Read More
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 of wholly new models as each year passes. To help orient researchers to these many options, we recently presented a professional development workshop at the 2019 meeting of the Society for Research on Child Development titled Longitudinal Data Analysis: Knowing What to Do and Learning How to Do It and are pleased to make the materials for this workshop publicly available. We hope these materials help researchers identify which longitudinal data analysis techniques are best suited to test various kinds of hypotheses, and to decide among the many different training opportunities that exist for learning how to use these techniques with greater confidence.Read More
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 a “growth curve” or “trajectory” and can produce different patterns from person to person: trajectories might be flat (not changing over time) or they might be systematically increasing or decreasing in some linear or non-linear form over time. These trajectories might be the primary focus of analysis or they might represent just part of a more complex longitudinal model. Regardless of purpose, there are two general approaches most often used to fit growth models to sample data.Read More
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 set to 0, 1, 2, 3, etc.). These values can be modified to allow for unequally spaced time assessments or to place the zero value at the beginning, middle, or end of the series, but the slope of the line always implies an equal change in the outcome per-unit change in time.
However, many constructs we study do not change linearly over time. Instead of equal change per-unit time, there is often differential change with respect to time. So there might be greater change earlier in time that then systematically slows (e.g., reading ability in young children), or the rate of change might increase positively but accelerate with the passage of time (e.g., substance use in adolescence), or the construct might slowly increase, peak, and then slowly decrease (e.g., heavy drinking in young adults). Regardless of particular form, it is critical that an appropriate nonlinear function be incorporated into the growth model to protect against making biased inferences about the nature of change over time. Fortunately, there are many options available to capture nonlinear change over time in growth models.Read More