mathematics

OpenMx

OpenMx is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand OpenMx rather than just read about it. In short: OpenMx is an open source program for extended structural equation modeling. It runs as a package under R.

Key takeaways

OpenMx belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect OpenMx to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of OpenMx from memory before moving on to harder problems.

Reference excerpt

OpenMx is an open source program for extended structural equation modeling. It runs as a package under R. Cross platform, it runs under Linux, Mac OS and Windows.

Overview OpenMx consists of an R library of functions and optimizers supporting the rapid and flexible implementation and estimation of SEM models. Models can be estimated based on either raw data (with FIML modelling) or on correlation or covariance matrices. Models can handle mixtures of continuous and ordinal data. The current version is OpenMx 2, and is available on CRAN. Path analysis, Confirmatory factor analysis, Latent growth modeling, Mediation analysis are all implemented. Multiple group models are implemented readily. When a model is run, it returns a model, and models can be updated (adding and removing paths, adding constraints and equalities; giving parameters the same label equates them). An innovation is that labels can consist of address of other parameters, allowing easy implementation of constraints on parameters by address. RAM models return standardized and raw estimates, as well as a range of fit indices (AIC, RMSEA, TLI, CFI etc.). Confidence intervals are estimated robustly. The program has parallel processing built-in via links to parallel environments in R, and in general takes advantage of the R programming environment. Users can expand the package with functions. These have been used, for instance, to implement Modification indices. Models can be written in either a "pathic" or "matrix" form. For those who think in terms of path models, paths are specified using mxPath() to describe paths. For models that are better suited to description in terms of matrix algebra, this is done using similar functional extensions in the R environment, for instance mxMatrix and mxAlgebra. The code below shows how to implement a simple Confirmatory factor analysis in OpenMx, using either path or matrix formats. The model is diagrammed here:

Example path model specification Below is the code to implement, run, and print a summary for estimating a one-factor path model with five indicators.

Example matrix specification Below is the code to implement, run, and print a summary for estimating a one-factor path model with five indicators.

References

External links Home Page

Illustrations

Worked examples

Example 1 — a first encounter with OpenMx

Start with the simplest possible case. Write down what OpenMx claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to OpenMx before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about OpenMx ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of OpenMx

In research: OpenMx appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses OpenMx in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: OpenMx is common in secondary-school and first-year university syllabi. It links to neighbouring topics Free statistical software, R (programming language), Structural equation models, so understanding it makes those chapters shorter.
In everyday life: Look for OpenMx outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study OpenMx in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what OpenMx means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain OpenMx out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is OpenMx in simple terms?

OpenMx is an open source program for extended structural equation modeling. It runs as a package under R.

Why does OpenMx matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study OpenMx?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on OpenMx.