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A lavaan-like syntax for structural equation models with OpenMx
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mxsem provides alavaan-like (Rosseel, 2012) syntax to implementstructural equation models (SEM) withOpenMx (Boker et al., 2011).The objective is to simplify fitting basic SEM withOpenMx, whilealso unlocking some very useful advanced features. For instance,mxsem allows for parameter transformations and definition variables.However,mxsem is intentionally incomplete in order to focus onsimplicity. The main function (mxsem()) is similar tolavaan’ssem()-function in that it tries to set up parts of the modelautomatically (e.g., adding variances automatically or scaling thelatent variables automatically).
Warning: The syntax and settings ofmxsem may differ fromlavaan in some cases. See
vignette("Syntax", package = "mxsem")for more details on the syntax and the default arguments.
mxsem is not the first package providing alavaan-like syntaxforOpenMx. You will find similar functions in the followingpackages:
- metaSEM (Cheung, 2015)provides a
lavaan2RAMfunction that can be combined with thecreate.mxModelfunction. This combination offers more features thanmxsem. For instance, constraints of the forma < baresupported. Inmxsem such constraints require algebras (e.g.,!diff; a := b - exp(diff)). - umx (Bates et al., 2019) providesthe
umxRAMandumxLav2RAMfunctions that can parse singlelavaan-style statements (e.g.,eta =~ y1 + y2 + y3) or an entirelavaan models toOpenMx models. - tidySEM (van Lissa, 2023)provides the
as_ramfunction to translatelavaan syntax toOpenMx and also implements a unified syntax to specify both,lavaan andOpenMx models. Additionally, it works well with thetidyverse. - ezMx (Bates, et al. 2014)simplifies fitting SEM withOpenMx and also provides a translationoflavaan models toOpenMx with the
lavaan.to.OpenMxfunction.
Becausemxsem implements the syntax parser from scratch, it canextend thelavaan syntax to account for specificOpenMxfeatures. This enablesimplicit transformations withcurly braces.
CiteOpenMx (Boker et al., 2011) for the modeling andlavaan forthe syntax (Rosseel, 2012). To citemxsem, checkcitation("mxsem").
mxsem is available from CRAN:
install.packages("mxsem")The newest version of the package can be installed from GitHub using thefollowing commands in R:
if(!require(devtools)) install.packages("devtools")devtools::install_github("jhorzek/mxsem",ref="main")
Becausemxsem uses Rcpp, you will need a compiler for C++ (e.g., byinstalling Rtools on Windows, Xcode on Mac and build-essential onlinux).
The following example is directly adapted fromlavaan:
library(mxsem)model<-' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a1*y2 + b*y3 + c1*y4 dem65 =~ y5 + a2*y6 + b*y7 + c2*y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8'mxsem(model=model,data=OpenMx::Bollen)|> mxTryHard()|> summary()
Show summary
#> Summary of untitled2 #> #> free parameters:#> name matrix row col Estimate Std.Error A lbound ubound#> 1 ind60→x2 A x2 ind60 2.012660e+00 0.38891027 #> 2 ind60→x3 A x3 ind60 1.650326e+00 0.36081541 #> 3 ind60→dem60 A dem60 ind60 4.091644e+00 0.82825703 #> 4 ind60→dem65 A dem65 ind60 4.476238e+01 33.03590013 #> 5 a1 A y2 dem60 1.296343e+00 0.22069102 #> 6 b A y3 dem60 1.187559e+00 0.13597913 #> 7 c1 A y4 dem60 1.413415e+00 0.18183251 #> 8 dem60→dem65 A dem65 dem60 -9.854813e+00 5.74179618 #> 9 a2 A y6 dem65 1.121844e+00 0.16042018 #> 10 c2 A y8 dem65 1.224479e+00 0.14984899 #> 11 y1↔y1 S y1 y1 2.686888e+00 0.59075793 1e-06 #> 12 y2↔y2 S y2 y2 8.576610e+00 1.48229765 1e-06 #> 13 y3↔y3 S y3 y3 5.847195e+00 1.09096957 1e-06 #> 14 y2↔y4 S y2 y4 1.987018e+00 0.78013870 #> 15 y4↔y4 S y4 y4 3.387325e+00 0.74388310 1e-06 #> 16 y2↔y6 S y2 y6 2.385179e+00 0.76306049 #> 17 y6↔y6 S y6 y6 5.129115e+00 0.91213692 1e-06 #> 18 x1↔x1 S x1 x1 3.013521e-01 0.06239685 1e-06 #> 19 x2↔x2 S x2 x2 1.325533e+00 0.27206604 1e-06 #> 20 x3↔x3 S x3 x3 1.326978e+00 0.25275042 1e-06 #> 21 y1↔y5 S y1 y5 7.307489e-01 0.40428182 #> 22 y5↔y5 S y5 y5 2.262309e+00 0.47568663 1e-06 #> 23 y3↔y7 S y3 y7 1.315088e+00 0.74793582 #> 24 y7↔y7 S y7 y7 3.819416e+00 0.79913029 1e-06 #> 25 y4↔y8 S y4 y8 3.442654e-01 0.46177893 #> 26 y6↔y8 S y6 y8 1.438664e+00 0.60291913 #> 27 y8↔y8 S y8 y8 3.402689e+00 0.72529659 1e-06 #> 28 ind60↔ind60 S ind60 ind60 2.286328e-01 0.08085603 1e-06 #> 29 dem60↔dem60 S dem60 dem60 1.000001e-06 NA ! 0! #> 30 dem65↔dem65 S dem65 dem65 1.334856e-01 0.24827033 1e-06 #> 31 one→y1 M 1 y1 5.464667e+00 0.29473841 #> 32 one→y2 M 1 y2 4.256443e+00 0.44738225 #> 33 one→y3 M 1 y3 6.563110e+00 0.38723974 #> 34 one→y4 M 1 y4 4.452533e+00 0.38359678 #> 35 one→y6 M 1 y6 2.978074e+00 0.38247416 #> 36 one→x1 M 1 x1 5.054383e+00 0.08406584 #> 37 one→x2 M 1 x2 4.792195e+00 0.17327643 #> 38 one→x3 M 1 x3 3.557690e+00 0.16123756 #> 39 one→y5 M 1 y5 5.136252e+00 0.30340241 #> 40 one→y7 M 1 y7 6.196264e+00 0.37176597 #> 41 one→y8 M 1 y8 4.043390e+00 0.37170879 #> #> Model Statistics: #> | Parameters | Degrees of Freedom | Fit (-2lnL units)#> Model: 41 784 3274.152#> Saturated: 77 748 NA#> Independence: 22 803 NA#> Number of observations/statistics: 75/825#> #> Information Criteria: #> | df Penalty | Parameters Penalty | Sample-Size Adjusted#> AIC: 1706.152 3356.152 3460.515#> BIC: -110.759 3451.169 3321.947#> To get additional fit indices, see help(mxRefModels)#> timestamp: 2024-07-21 20:44:38 #> Wall clock time: 0.1139431 secs #> optimizer: SLSQP #> OpenMx version number: 2.21.11 #> Need help? See help(mxSummary)Lower and upper bounds can be added to any of the parameters in themodel. The following demonstrates bounds on a loading:
library(mxsem)model<-' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a1*y2 + b*y3 + c1*y4 dem65 =~ y5 + a2*y6 + b*y7 + c2*y8 # lower bound on a1 a1 > 0 # upper bound on a2 a2 < 10.123'mxsem(model=model,data=OpenMx::Bollen,# use latent variances to scale the modelscale_loadings=FALSE,scale_latent_variances=TRUE)|> mxTryHard()|> summary()
Show summary
#> Summary of untitled4 #> #> free parameters:#> name matrix row col Estimate Std.Error A lbound ubound#> 1 ind60→x1 A x1 ind60 -0.66602168 0.06402911 #> 2 ind60→x2 A x2 ind60 -1.45290840 0.12615652 #> 3 ind60→x3 A x3 ind60 -1.21127230 0.12698816 #> 4 dem60→y1 A y1 dem60 2.21018030 0.24806182 #> 5 a1 A y2 dem60 2.98303646 0.39464650 0 #> 6 b A y3 dem60 2.52119429 0.27195610 #> 7 c1 A y4 dem60 2.86625955 0.31512659 #> 8 dem65→y5 A y5 dem65 2.08192035 0.25256395 #> 9 a2 A y6 dem65 2.61417796 0.33067157 10.123#> 10 c2 A y8 dem65 2.72104603 0.30578894 #> 11 x1↔x1 S x1 x1 0.08176774 0.01979715 1e-06 #> 12 x2↔x2 S x2 x2 0.11868552 0.07038039 1e-06 #> 13 x3↔x3 S x3 x3 0.46717050 0.08933577 1e-06 #> 14 y1↔y1 S y1 y1 1.92282818 0.40072499 1e-06 #> 15 y2↔y2 S y2 y2 6.51159526 1.20284012 1e-06 #> 16 y3↔y3 S y3 y3 5.31392061 0.95937939 1e-06 #> 17 y4↔y4 S y4 y4 2.88902582 0.63409911 1e-06 #> 18 y5↔y5 S y5 y5 2.38176160 0.45553891 1e-06 #> 19 y6↔y6 S y6 y6 4.36051128 0.82332444 1e-06 #> 20 y7↔y7 S y7 y7 3.58248880 0.68191696 1e-06 #> 21 y8↔y8 S y8 y8 2.95767562 0.62791664 1e-06 #> 22 ind60↔dem60 S ind60 dem60 -0.43953545 0.10490002 #> 23 ind60↔dem65 S ind60 dem65 -0.54935145 0.09041729 #> 24 dem60↔dem65 S dem60 dem65 0.97753003 0.02697925 #> 25 one→x1 M 1 x1 5.05438406 0.08369988 #> 26 one→x2 M 1 x2 4.79219545 0.17243259 #> 27 one→x3 M 1 x3 3.55769028 0.16060761 #> 28 one→y1 M 1 y1 5.46466541 0.30131941 #> 29 one→y2 M 1 y2 4.25644008 0.45333817 #> 30 one→y3 M 1 y3 6.56310968 0.39450506 #> 31 one→y4 M 1 y4 4.45253268 0.38484200 #> 32 one→y5 M 1 y5 5.13625169 0.29928682 #> 33 one→y6 M 1 y6 2.97807303 0.38639154 #> 34 one→y7 M 1 y7 6.19626363 0.36407370 #> 35 one→y8 M 1 y8 4.04338969 0.37174814 #> #> Model Statistics: #> | Parameters | Degrees of Freedom | Fit (-2lnL units)#> Model: 35 790 3130.995#> Saturated: 77 748 NA#> Independence: 22 803 NA#> Number of observations/statistics: 75/825#> #> Information Criteria: #> | df Penalty | Parameters Penalty | Sample-Size Adjusted#> AIC: 1550.9954 3200.995 3265.611#> BIC: -279.8202 3282.107 3171.797#> To get additional fit indices, see help(mxRefModels)#> timestamp: 2024-07-21 20:44:40 #> Wall clock time: 0.2327423 secs #> optimizer: SLSQP #> OpenMx version number: 2.21.11 #> Need help? See help(mxSummary)mxsem adds lower bounds to any of the variances by default. Toremove these lower bounds, setlbound_variances = FALSE when callingmxsem().
Definition variables are, for instance, used in latent growth curvemodels when the time intervals between observations are different forthe subjects in the data set. Here is an example, where the variablest_1-t_5 indicate the person-specific times of observation:
library(mxsem)set.seed(3489)dataset<- simulate_latent_growth_curve(N=100)head(dataset)#> y1 y2 y3 y4 y5 t_1 t_2 t_3#> [1,] 1.2817946 5.159870 7.178191 8.950046 11.4822306 0 1.5792322 2.304777#> [2,] 1.1796379 3.588279 5.927219 8.381157 10.4640667 0 1.6701976 3.530621#> [3,] 0.2196010 0.763441 2.499564 3.672995 4.4505868 0 0.6452145 2.512730#> [4,] 0.5688185 1.440709 1.523483 1.416965 1.9674847 0 1.7171826 3.245522#> [5,] 3.4928919 2.620657 1.753159 1.080701 -0.4436508 0 1.4055839 2.024568#> [6,] 0.3520293 5.126854 7.390669 10.721785 12.6363472 0 1.5249299 2.400432#> t_4 t_5#> [1,] 3.120797 4.217403#> [2,] 5.004695 6.408367#> [3,] 3.761189 4.729461#> [4,] 4.331997 6.145424#> [5,] 3.570780 5.517224#> [6,] 3.654230 4.222212
InOpenMx, parameters can be set to the values found in the columnsof the data set with thedata. prefix. This is used in the followingto fix the loadings of a latent slope variable on the observations tothe times recorded int_1-t_5:
library(mxsem)model<-" # specify latent intercept I =~ 1*y1 + 1*y2 + 1*y3 + 1*y4 + 1*y5 # specify latent slope S =~ data.t_1 * y1 + data.t_2 * y2 + data.t_3 * y3 + data.t_4 * y4 + data.t_5 * y5 # specify means of latent intercept and slope I ~ int*1 S ~ slp*1 # set intercepts of manifest variables to zero y1 ~ 0*1; y2 ~ 0*1; y3 ~ 0*1; y4 ~ 0*1; y5 ~ 0*1;"mxsem(model=model,data=dataset)|> mxTryHard()|> summary()
Show summary
#> Summary of untitled6 #> #> free parameters:#> name matrix row col Estimate Std.Error A lbound ubound#> 1 y1↔y1 S y1 y1 0.02578029 0.014488230 0! #> 2 y2↔y2 S y2 y2 0.04010524 0.008389744 0! #> 3 y3↔y3 S y3 y3 0.04008175 0.006984929 0! #> 4 y4↔y4 S y4 y4 0.01752572 0.006930952 ! 0! #> 5 y5↔y5 S y5 y5 0.05936968 0.016067405 1e-06 #> 6 I↔I S I I 1.02593614 0.148068976 1e-06 #> 7 I↔S S I S -0.14724710 0.110019557 #> 8 S↔S S S S 1.13050977 0.160502645 1e-06 #> 9 int M 1 I 0.93112329 0.102209132 #> 10 slp M 1 S 0.48442608 0.106476404 #> #> Model Statistics: #> | Parameters | Degrees of Freedom | Fit (-2lnL units)#> Model: 10 10 841.2609#> Saturated: 20 0 NA#> Independence: 10 10 NA#> Number of observations/statistics: 100/20#> #> Information Criteria: #> | df Penalty | Parameters Penalty | Sample-Size Adjusted#> AIC: 821.2609 861.2609 863.7328#> BIC: 795.2092 887.3126 855.7301#> To get additional fit indices, see help(mxRefModels)#> timestamp: 2024-07-21 20:44:41 #> Wall clock time: 0.4582329 secs #> optimizer: SLSQP #> OpenMx version number: 2.21.11 #> Need help? See help(mxSummary)Sometimes, one may want to express one parameter as a function of otherparameters. In moderated non-linear factor analysis, for example, modelparameters are often expressed in terms of a covariate k. For instance,the effect
library(mxsem)set.seed(9820)dataset<- simulate_moderated_nonlinear_factor_analysis(N=100)head(dataset)#> x1 x2 x3 y1 y2 y3 k#> [1,] -1.2166034 -1.2374549 -1.3731943 -1.01018683 -0.8296293 -1.2300555484 0#> [2,] 1.1911346 0.9971499 1.0226322 0.86048030 0.4509088 0.6052786392 1#> [3,] -0.7777169 -0.4725291 -0.8507347 -1.09582848 -0.5035753 -0.8048378456 0#> [4,] 1.0027847 1.2351709 0.6951317 0.94040287 0.6684979 0.6596891858 0#> [5,] 0.4387896 0.3919877 0.3260557 -0.58188691 -0.3614349 -0.4901022121 0#> [6,] -1.4951549 -0.8834637 -1.1715535 0.01173845 -0.4697865 -0.0006475256 0
mxsem currently supports two ways of specifying suchtransformations. First, they can be specified explicitly. To this end,the parameters!a0 and!a1. Additionally, the transformation must be defined witha := a0 + a1*data.k.
model<-" # loadings xi =~ x1 + x2 + x3 eta =~ y1 + y2 + y3 # regression eta ~ a*xi # we need two new parameters: a0 and a1. These are created as follows: !a0 !a1 # Now, we redefine a to be a0 + k*a1, where k is found in the data a := a0 + data.k*a1"fit_mx<- mxsem(model=model,data=dataset)|> mxTryHard()summary(fit_mx)# get just the value for parameter a:mxEval(expression=a,model=fit_mx)
Show summary
#> Summary of untitled20 #> #> free parameters:#> name matrix row col Estimate Std.Error A lbound ubound#> 1 xi→x2 A x2 xi 0.79157856 0.026246030 #> 2 xi→x3 A x3 xi 0.89166084 0.027991530 #> 3 eta→y2 A y2 eta 0.81610417 0.028977422 #> 4 eta→y3 A y3 eta 0.90741898 0.027924339 #> 5 x1↔x1 S x1 x1 0.04060218 0.011022272 0! #> 6 x2↔x2 S x2 x2 0.04519854 0.008621602 0! #> 7 x3↔x3 S x3 x3 0.04647176 0.010143713 0! #> 8 y1↔y1 S y1 y1 0.03388953 0.008495337 0! #> 9 y2↔y2 S y2 y2 0.04210954 0.007766716 ! 0! #> 10 y3↔y3 S y3 y3 0.03107018 0.007268297 ! 0! #> 11 xi↔xi S xi xi 1.07304573 0.157790632 1e-06 #> 12 eta↔eta S eta eta 0.26127595 0.041232498 1e-06 #> 13 one→x1 M 1 x1 -0.14881004 0.105059830 #> 14 one→x2 M 1 x2 -0.10969640 0.084340983 #> 15 one→x3 M 1 x3 -0.15448448 0.094428639 #> 16 one→y1 M 1 y1 -0.05304588 0.089763143 #> 17 one→y2 M 1 y2 -0.13040824 0.074580498 #> 18 one→y3 M 1 y3 -0.05666192 0.081649015 #> 19 a0 new_parameters 1 1 0.78168122 0.069380240 #> 20 a1 new_parameters 1 2 -0.19334116 0.107739139 #> #> Model Statistics: #> | Parameters | Degrees of Freedom | Fit (-2lnL units)#> Model: 20 7 475.3822#> Saturated: 27 0 NA#> Independence: 12 15 NA#> Number of observations/statistics: 100/27#> #> Information Criteria: #> | df Penalty | Parameters Penalty | Sample-Size Adjusted#> AIC: 461.3822 515.3822 526.0151#> BIC: 443.1460 567.4856 504.3206#> To get additional fit indices, see help(mxRefModels)#> timestamp: 2024-07-21 20:44:42 #> Wall clock time: 0.07763433 secs #> optimizer: SLSQP #> OpenMx version number: 2.21.11 #> Need help? See help(mxSummary)#> [,1]#> [1,] 0.7816812Alternatively, the transformations can be defined implicitly by placingthe algebra in curly braces and directly inserting it in the syntax inplace of the parameter label. This is inspired by the approach inmetaSEM (Cheung, 2015).
model<-" # loadings xi =~ x1 + x2 + x3 eta =~ y1 + y2 + y3 # regression eta ~ {a0 + a1*data.k} * xi"mxsem(model=model,data=dataset)|> mxTryHard()|> summary()
Show summary
#> Summary of untitled48 #> #> free parameters:#> name matrix row col Estimate Std.Error A lbound ubound#> 1 xi→x2 A x2 xi 0.79157856 0.026246030 #> 2 xi→x3 A x3 xi 0.89166084 0.027991530 #> 3 eta→y2 A y2 eta 0.81610417 0.028977422 #> 4 eta→y3 A y3 eta 0.90741898 0.027924339 #> 5 x1↔x1 S x1 x1 0.04060218 0.011022272 0! #> 6 x2↔x2 S x2 x2 0.04519854 0.008621602 0! #> 7 x3↔x3 S x3 x3 0.04647176 0.010143713 0! #> 8 y1↔y1 S y1 y1 0.03388953 0.008495337 0! #> 9 y2↔y2 S y2 y2 0.04210954 0.007766716 ! 0! #> 10 y3↔y3 S y3 y3 0.03107018 0.007268297 ! 0! #> 11 xi↔xi S xi xi 1.07304573 0.157790632 1e-06 #> 12 eta↔eta S eta eta 0.26127595 0.041232498 1e-06 #> 13 one→x1 M 1 x1 -0.14881004 0.105059830 #> 14 one→x2 M 1 x2 -0.10969640 0.084340983 #> 15 one→x3 M 1 x3 -0.15448448 0.094428639 #> 16 one→y1 M 1 y1 -0.05304588 0.089763143 #> 17 one→y2 M 1 y2 -0.13040824 0.074580498 #> 18 one→y3 M 1 y3 -0.05666192 0.081649015 #> 19 a0 new_parameters 1 1 0.78168122 0.069380240 #> 20 a1 new_parameters 1 2 -0.19334116 0.107739139 #> #> Model Statistics: #> | Parameters | Degrees of Freedom | Fit (-2lnL units)#> Model: 20 7 475.3822#> Saturated: 27 0 NA#> Independence: 12 15 NA#> Number of observations/statistics: 100/27#> #> Information Criteria: #> | df Penalty | Parameters Penalty | Sample-Size Adjusted#> AIC: 461.3822 515.3822 526.0151#> BIC: 443.1460 567.4856 504.3206#> To get additional fit indices, see help(mxRefModels)#> timestamp: 2024-07-21 20:44:42 #> Wall clock time: 0.0693748 secs #> optimizer: SLSQP #> OpenMx version number: 2.21.11 #> Need help? See help(mxSummary)You can also provide custom names for the algebra results:
model<-" # loadings xi =~ x1 + x2 + x3 eta =~ y1 + y2 + y3 # regression eta ~ {a := a0 + a1*data.k} * xi"fit_mx<- mxsem(model=model,data=dataset)|> mxTryHard()summary(fit_mx)# get just the value for parameter a:mxEval(expression=a,model=fit_mx)
Show summary
#> Summary of untitled76 #> #> free parameters:#> name matrix row col Estimate Std.Error A lbound ubound#> 1 xi→x2 A x2 xi 0.79157856 0.026246030 #> 2 xi→x3 A x3 xi 0.89166084 0.027991530 #> 3 eta→y2 A y2 eta 0.81610417 0.028977422 #> 4 eta→y3 A y3 eta 0.90741898 0.027924339 #> 5 x1↔x1 S x1 x1 0.04060218 0.011022272 0! #> 6 x2↔x2 S x2 x2 0.04519854 0.008621602 0! #> 7 x3↔x3 S x3 x3 0.04647176 0.010143713 0! #> 8 y1↔y1 S y1 y1 0.03388953 0.008495337 0! #> 9 y2↔y2 S y2 y2 0.04210954 0.007766716 ! 0! #> 10 y3↔y3 S y3 y3 0.03107018 0.007268297 ! 0! #> 11 xi↔xi S xi xi 1.07304573 0.157790632 1e-06 #> 12 eta↔eta S eta eta 0.26127595 0.041232498 1e-06 #> 13 one→x1 M 1 x1 -0.14881004 0.105059830 #> 14 one→x2 M 1 x2 -0.10969640 0.084340983 #> 15 one→x3 M 1 x3 -0.15448448 0.094428639 #> 16 one→y1 M 1 y1 -0.05304588 0.089763143 #> 17 one→y2 M 1 y2 -0.13040824 0.074580498 #> 18 one→y3 M 1 y3 -0.05666192 0.081649015 #> 19 a0 new_parameters 1 1 0.78168122 0.069380240 #> 20 a1 new_parameters 1 2 -0.19334116 0.107739139 #> #> Model Statistics: #> | Parameters | Degrees of Freedom | Fit (-2lnL units)#> Model: 20 7 475.3822#> Saturated: 27 0 NA#> Independence: 12 15 NA#> Number of observations/statistics: 100/27#> #> Information Criteria: #> | df Penalty | Parameters Penalty | Sample-Size Adjusted#> AIC: 461.3822 515.3822 526.0151#> BIC: 443.1460 567.4856 504.3206#> To get additional fit indices, see help(mxRefModels)#> timestamp: 2024-07-21 20:44:43 #> Wall clock time: 0.0685575 secs #> optimizer: SLSQP #> OpenMx version number: 2.21.11 #> Need help? See help(mxSummary)#> [,1]#> [1,] 0.7816812mxsem returns anmxModel object that can be adapted further by usersfamiliar withOpenMx.
Sometimes things may go wrong. One way to figure out wheremxsemmessed up is to look at the parameter table generated internally. Thisparameter table is not returned by default. Seevignette("create_parameter_table", package = "mxsem") for moredetails.
Another point of failure are the default labels used bymxsem toindicate directed and undirected effects. These are based on unicodecharacters. If you see parameter labels similar to"eta\u2192y1" inyour output, this indicates that your editor cannot display unicodecharacters. In this case, you can customize the labels as follows:
library(mxsem)model<-' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a1*y2 + b*y3 + c1*y4 dem65 =~ y5 + a2*y6 + b*y7 + c2*y8'mxsem(model=model,data=OpenMx::Bollen,directed="_TO_",undirected="_WITH_")|> mxTryHard()|> summary()
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#> Summary of untitled90 #> #> free parameters:#> name matrix row col Estimate Std.Error A lbound ubound#> 1 ind60_TO_x2 A x2 ind60 2.18115702 0.13928666 #> 2 ind60_TO_x3 A x3 ind60 1.81852890 0.15228797 #> 3 a1 A y2 dem60 1.40364256 0.18390038 #> 4 b A y3 dem60 1.17009172 0.10871747 #> 5 c1 A y4 dem60 1.34853386 0.14637663 #> 6 a2 A y6 dem65 1.20074512 0.14855357 #> 7 c2 A y8 dem65 1.25031848 0.13637438 #> 8 x1_WITH_x1 S x1 x1 0.08169539 0.01979123 1e-06 #> 9 x2_WITH_x2 S x2 x2 0.11895803 0.07035954 1e-06 #> 10 x3_WITH_x3 S x3 x3 0.46715652 0.08931226 1e-06 #> 11 y1_WITH_y1 S y1 y1 1.96249145 0.40675153 ! 1e-06 #> 12 y2_WITH_y2 S y2 y2 6.49922273 1.20251628 1e-06 #> 13 y3_WITH_y3 S y3 y3 5.32559112 0.95894588 1e-06 #> 14 y4_WITH_y4 S y4 y4 2.87950917 0.63665763 1e-06 #> 15 y5_WITH_y5 S y5 y5 2.37088343 0.45487035 1e-06 #> 16 y6_WITH_y6 S y6 y6 4.37313277 0.82251242 1e-06 #> 17 y7_WITH_y7 S y7 y7 3.56699590 0.68171379 1e-06 #> 18 y8_WITH_y8 S y8 y8 2.96557681 0.62443800 ! 1e-06 #> 19 ind60_WITH_ind60 S ind60 ind60 0.44829143 0.08675629 1e-06 #> 20 ind60_WITH_dem60 S ind60 dem60 0.63807497 0.19920187 #> 21 dem60_WITH_dem60 S dem60 dem60 4.50351167 1.00616960 1e-06 #> 22 ind60_WITH_dem65 S ind60 dem65 0.81413650 0.21697272 #> 23 dem60_WITH_dem65 S dem60 dem65 4.52636825 0.93243049 #> 24 dem65_WITH_dem65 S dem65 dem65 4.75141153 1.04835747 1e-06 #> 25 one_TO_x1 M 1 x1 5.05438446 0.08405796 #> 26 one_TO_x2 M 1 x2 4.79219580 0.17325941 #> 27 one_TO_x3 M 1 x3 3.55769067 0.16122376 #> 28 one_TO_y1 M 1 y1 5.46466750 0.29359270 #> 29 one_TO_y2 M 1 y2 4.25644400 0.45268169 #> 30 one_TO_y3 M 1 y3 6.56311167 0.39140003 #> 31 one_TO_y4 M 1 y4 4.45253335 0.38413637 #> 32 one_TO_y5 M 1 y5 5.13625263 0.30813153 #> 33 one_TO_y6 M 1 y6 2.97807393 0.38680848 #> 34 one_TO_y7 M 1 y7 6.19626358 0.36642683 #> 35 one_TO_y8 M 1 y8 4.04339058 0.37222072 #> #> Model Statistics: #> | Parameters | Degrees of Freedom | Fit (-2lnL units)#> Model: 35 790 3131.168#> Saturated: 77 748 NA#> Independence: 22 803 NA#> Number of observations/statistics: 75/825#> #> Information Criteria: #> | df Penalty | Parameters Penalty | Sample-Size Adjusted#> AIC: 1551.1683 3201.168 3265.784#> BIC: -279.6473 3282.280 3171.970#> To get additional fit indices, see help(mxRefModels)#> timestamp: 2024-07-21 20:44:44 #> Wall clock time: 0.1770966 secs #> optimizer: SLSQP #> OpenMx version number: 2.21.11 #> Need help? See help(mxSummary)- Bates, T. C., Maes, H., & Neale, M. C. (2019). umx: Twin andPath-Based Structural Equation Modeling in R. Twin Research and HumanGenetics, 22(1), 27–41.https://doi.org/10.1017/thg.2019.2
- Bates, T. C., Prindle, J. J. (2014). ezMx.https://github.com/OpenMx/ezMx
- Boker, S. M., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T.,Spies, J., Estabrook, R., Kenny, S., Bates, T., Mehta, P., & Fox, J.(2011). OpenMx: An Open Source Extended Structural Equation ModelingFramework. Psychometrika, 76(2), 306–317.https://doi.org/10.1007/s11336-010-9200-6
- Cheung, M. W.-L. (2015). metaSEM: An R package for meta-analysis usingstructural equation modeling. Frontiers in Psychology, 5.https://doi.org/10.3389/fpsyg.2014.01521
- Rosseel, Y. (2012). lavaan: An R package for structural equationmodeling. Journal of Statistical Software, 48(2), 1–36.https://doi.org/10.18637/jss.v048.i02
- van Lissa, C. J. (2023). tidySEM: Tidy Structural Equation Modeling. Rpackage version 0.2.4,https://cjvanlissa.github.io/tidySEM/.
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A lavaan-like syntax for structural equation models with OpenMx
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