In our last four posts in this series, we showed you how to calculate power for a t test using Monte Carlo simulations, how to integrate your simulations into Stata’s power command, and how to do this for linear and logistic regression models and multilevel models. In today’s post, I’m going to show you how to estimate power for structural equation models (SEM) using simulations.

Our goal is to write a program that will calculate power for a given SEM at different sample sizes. We’ll follow the same general procedure as the previous two posts, but the way we’ll go about simulating data is a bit different. Rather than individually simulating each variable for our specified model, we’ll be simulating all our variables simultaneously from a given covariance matrix. Means for each of the variables can also be used to simulate the data if your SEM has a mean structure, such as in group analysis or growth curve analysis. Read more…

When fitting almost any model, we may be interested in investigating whether parameters differ across groups such as time periods, age groups, gender, or school attended. In other words, we may wish to perform tests of moderation when the moderator variable is categorical. For regression models, this can be as simple as including group indicators in the model and interacting them with other predictors.

We naturally have hypotheses regarding differences in parameters across groups when fitting structural equation models as well. When these models involve latent variables and the corresponding observed measurements, we can test whether those measurements are invariant across groups. Evaluation of measurement invariance typically involves a series of tests for equality of measurement coefficients (factor loadings), equality of intercepts, and equality of error variances across groups.

In this post, I demonstrate how to use the sem command’s group() and ginvariant() options as well as the postestimation command estat ginvariant to easily perform tests of measurement invariance. Read more…

New to Stata 14 is a suite of commands to fit item response theory (IRT) models. IRT models are used to analyze the relationship between the latent trait of interest and the items intended to measure the trait. Stata’s irt commands provide easy access to some of the commonly used IRT models for binary and polytomous responses, and irtgraph commands can be used to plot item characteristic functions and information functions.

To learn more about Stata’s IRT features, I refer you to the [IRT] manual; here I want to go beyond the manual and show you a couple of examples of what you can do with a little bit of Stata code. Read more…

gsem is a very flexible command that allows us to fit very sophisticated models. However, it is also useful in situations that involve simple models.

For example, when we want to compare parameters among two or more models, we usually use suest, which combines the estimation results under one parameter vector and creates a simultaneous covariance matrix of the robust type. This covariance estimate is described in the Methods and formulas of [R] suest as the robust variance from a “stacked model”. Actually, gsem can estimate these kinds of “stacked models”, even if the estimation samples are not the same and eventually overlap. By using the option vce(robust), we can replicate the results from suest if the models are available for gsem. In addition, gsem allows us to combine results from some estimation commands that are not supported by suest, like models including random effects. Read more…

The new command gsem allows us to fit a wide variety of models; among the many possibilities, we can account for endogeneity on different models. As an example, I will fit an ordinal model with endogenous covariates. Read more…

I just got back from the 2012 Stata Conference in San Diego where I gave a talk on Psychometric Analysis Using Stata and from the 2012 American Psychological Association Meeting in Orlando. Stata’s structural equation modeling (SEM) builder was popular at both meetings and I wanted to show you how easy it is to use. If you are not familiar with the basics of SEM, please refer to the references at the end of the post. My goal is simply to show you how to use the SEM builder assuming that you already know something about SEM. If you would like to view a video demonstration of the SEM builder, please click the play button below: Read more…

xtmixed was built from the ground up for dealing with multilevel random effects — that is its raison d’être. sem was built for multivariate outcomes, for handling latent variables, and for estimating structural equations (also called simultaneous systems or models with endogeneity). Can sem also handle multilevel random effects (REs)? Do we care?

This would be a short entry if either answer were “no”, so let’s get after the first question. Read more…

We are pleased to announce a new version of Stata: Stata 12. You can order it today, it starts shipping on July 25, and you can find out about it at www.stata.com/stata12/.

Here are the highlights of what’s new: Read more…