1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
|
# OpenMx <img src="https://openmx.ssri.psu.edu/sites/default/files/guineapig.png" align="right" width="120" />
<!-- badges: start -->
[](https://app.travis-ci.com/github/OpenMx/OpenMx)
[](https://app.codecov.io/gh/OpenMx/OpenMx?branch=master)
[](https://cran.r-project.org/package=OpenMx)
[](https://cranlogs.r-pkg.org/badges/OpenMx)
[](https://cranlogs.r-pkg.org/badges/grand-total/OpenMx)
[](https://doi.org/10.1007/s11336-014-9435-8)
<!-- badges: end -->
> OpenMx is a [Structural Equation Modeling](https://en.wikipedia.org/wiki/Structural_equation_modeling)
package that encourages users to treat model specifications as something to be generated
and manipulated programmatically.
# TOC
- [Overview](#overview)
- [Installation](#installation)
* [Development versions](#development-versions)
- [Documentation](#documentation)
- [Quick usage examples](#quick-usage-examples)
* [Simple regression in path specification](#simple-regression-in-path-specification)
* [Simple regression using matrix algebra](#simple-regression-using-matrix-algebra)
- [Related work](#related-work)
- [Community and getting help](#community-and-getting-help)
* [Training](#training)
# Overview
OpenMx is the next generation of the Mx structural equation modeling tool. It is an R package activelly maintained and supported with the work of developers around the globe. It is designed to allow the user the most freedom possible while specifying structural equation models, therefore providing minimal defaults. This helps the user know that each specification/optimization decision comes with their own assumptions and influences model interpretation.
# Installation
The package is on CRAN and should be installed with:
```r
install.packages("OpenMx")
```
## Development versions
Developers commit to the `master` branch. Intrepid users are encouraged to install the `master` branch. In order to install locally clone this repo and run:
```r
make cran-install # for the CRAN version
make install # for the version with the proprietary NPSOL optimizer
```
The `stable` branch can be considered our current alpha release.
The `stable` branch is updated automatically when all `models/passing`
and `models/nightly` tests pass along with `make cran-check`.
On macOS, this can be installed as a binary via travis:
```r
install.packages("https://vipbg.vcu.edu/vipbg/OpenMx2/software/bin/macosx/travis/OpenMx_latest.tgz")
```
# Documentation
OpenMx can fit everything from confirmatory factor analyses,
through multiple group, mixture distribution, categorical threshold,
modern test theory, differential equations, state space, and many others. Models may be specified as RAM or LISREL paths, or directly in matrix algebra. Fit functions include ML (summary and full information) and WLS.
The package manual can be accessed online in the [link](https://vipbg.vcu.edu/vipbg/OpenMx2/docs//OpenMx/latest/), and as a pdf from the [link](https://vipbg.vcu.edu/vipbg/OpenMx2/docs//OpenMx/latest/OpenMxUserGuide.pdf). The manual includes example models and scripts for the most common cases.
# Quick usage examples
Path specifications are matematically complete and is often considered an easier approach to teaching and analysis. The path below represents a simple regression:
## Simple regression in path specification
One can specify the above model using the following code:
```r
require(OpenMx)
data(myRegDataRaw) # load data
names(myRegDataRaw) # get names
SimpleDataRaw <- myRegDataRaw[,c("x","y")] # take only what is needed
dataRaw <- mxData( observed=SimpleDataRaw, type="raw" )
# variance paths
varPaths <- mxPath( from=c("x","y"), arrows=2,
free=TRUE, values = c(1,1), labels=c("varx","residual") )
# regression weights
regPaths <- mxPath( from="x", to="y", arrows=1,
free=TRUE, values=1, labels="beta1" )
# means and intercepts
means <- mxPath( from="one", to=c("x","y"), arrows=1,
free=TRUE, values=c(1,1), labels=c("meanx","beta0") )
uniRegModel <- mxModel(model="Simple Regression Path Specification", type="RAM",
dataRaw, manifestVars=c("x","y"), varPaths, regPaths, means)
uniRegFit <- mxRun(uniRegModel) # run it
summary(uniRegFit)
```
And the following output should appear in your R environment:
```
Summary of Simple Regression Path Specification
free parameters:
name matrix row col Estimate Std.Error A
1 beta1 A y x 0.48311962 0.07757687
2 varx S x x 1.10531952 0.15631652
3 residual S y y 0.66520320 0.09407411
4 meanx M 1 x 0.05415975 0.10513428
5 beta0 M 1 y 2.54776414 0.08166814
Model Statistics:
| Parameters | Degrees of Freedom | Fit (-2lnL units)
Model: 5 195 536.8226
Saturated: 5 195 NA
Independence: 4 196 NA
Number of observations/statistics: 100/200
Information Criteria:
| df Penalty | Parameters Penalty | Sample-Size Adjusted
AIC: 146.8226 546.8226 547.4609
BIC: -361.1856 559.8484 544.0572
CFI: NA
TLI: 1 (also known as NNFI)
RMSEA: 0 [95% CI (NA, NA)]
Prob(RMSEA <= 0.05): NA
To get additional fit indices, see help(mxRefModels)
timestamp: 2022-05-01 09:53:24
```
## Simple regression using matrix algebra
Since OpenMx is considered the specialist tool, you are probably more interested in the flexibility provided by the fact that you can build your own formulas. So going back to the simple regression, now in the formula (equivalent to the path specified in previous section):
It can be implemented with the following code:
```r
require(OpenMx)
data(myRegDataRaw) # load data
SimpleDataRaw <- myRegDataRaw[,c("x","y")] # take only what is needed
# create a data object
dataRaw <- mxData( observed=SimpleDataRaw, type="raw" )
# A matrix
matrA <- mxMatrix( type="Full", nrow=2, ncol=2,
free=c(F,F,T,F), values=c(0,0,1,0),
labels=c(NA,NA,"beta1",NA), byrow=TRUE, name="A" )
# S matrix
matrS <- mxMatrix( type="Symm", nrow=2, ncol=2,
free=c(T,F,F,T), values=c(1,0,0,1),
labels=c("varx",NA,NA,"residual"), byrow=TRUE, name="S" )
# Filter matrix
matrF <- mxMatrix( type="Iden", nrow=2, ncol=2, name="F" )
# M matrix
matrM <- mxMatrix( type="Full", nrow=1, ncol=2,
free=c(T,T), values=c(0,0),
labels=c("meanx","beta0"), name="M")
# Which expectation? RAM in this case
expRAM <- mxExpectationRAM("A","S","F","M", dimnames=c("x","y"))
# Run a maximum likelihood
funML <- mxFitFunctionML()
# Name it, pass the objects on to a final model object
uniRegModel <- mxModel("Simple Regression Matrix Specification",
dataRaw, matrA, matrS, matrF, matrM, expRAM, funML)
# Run it!
uniRegFit <- mxRun(uniRegModel)
summary(uniRegFit)
```
Now the output looks like:
```
Running Simple Regression Matrix Specification with 5 parameters
Summary of Simple Regression Matrix Specification
free parameters:
name matrix row col Estimate Std.Error A
1 beta1 A 2 1 0.48311963 0.07757699
2 varx S 1 1 1.10531937 0.15631498
3 residual S 2 2 0.66520312 0.09407369
4 meanx M 1 x 0.05416001 0.10513400
5 beta0 M 1 y 2.54776424 0.08166812
Model Statistics:
| Parameters | Degrees of Freedom | Fit (-2
Model: 5 195
Saturated: 5 195
Independence: 4 196
Number of observations/statistics: 100/200
Information Criteria:
| df Penalty | Parameters Penalty | Sample-Size Adju
AIC: 146.8226 546.8226 547.
BIC: -361.1856 559.8484 544.
CFI: NA
TLI: 1 (also known as NNFI)
RMSEA: 0 [95% CI (NA, NA)]
Prob(RMSEA <= 0.05): NA
To get additional fit indices, see help(mxRefModels)
timestamp: 2022-05-01 10:04:52
Wall clock time: 0.3507566 secs
optimizer: SLSQP
OpenMx version number: 2.19.6.6
Need help? See help(mxSummary)
```
# Related work
[umx()](https://github.com/tbates/umx) is a sister R package that bridges the gap between [lavaan](https://github.com/yrosseel/lavaan) and OpenMx. If you are coming from lavaan it is perhaps useful to check umx() too.
# Community and getting help
1. The support communication is centered around the OpenMx [forum](https://openmx.ssri.psu.edu/forums)
2. Also, but less often, at the StackOverflow OpenMx [tag](https://stackoverflow.com/questions/tagged/openmx).
## Training
We gather annually in beautiful [Boulder, CO](https://www.colorado.edu/ibg/workshop) for the international workshop for traning in behavioral genetics applications of OpenMx.
|
