# Regularized Structural Equation Modeling

### Description

Regularized Structural Equation Modeling

### Usage

1 2 3 4 5 6 7 8 | ```
regsem(model, lambda = 0, alpha = 0, type = "none", data = NULL,
optMethod = "default", gradFun = "ram", hessFun = "none",
parallel = "no", Start = "lavaan", subOpt = "nlminb", longMod = F,
pars_pen = NULL, diff_par = NULL, LB = -Inf, UB = Inf, block = TRUE,
full = FALSE, calc = "normal", max.iter = 500, tol = 1e-05,
solver = FALSE, solver.maxit = 5, alpha.inc = TRUE, step = 0.5,
momentum = FALSE, step.ratio = FALSE, nlminb.control = list(),
missing = "listwise")
``` |

### Arguments

`model` |
Lavaan output object. This is a model that was previously run with any of the lavaan main functions: cfa(), lavaan(), sem(), or growth(). It also can be from the efaUnrotate() function from the semTools package. Currently, the parts of the model which cannot be handled in regsem is the use of multiple group models, missing other than listwise, thresholds from categorical variable models, the use of additional estimators other than ML, most notably WLSMV for categorical variables. Note: the model does not have to actually run (use do.fit=FALSE), converge etc... regsem() uses the lavaan object as more of a parser and to get sample covariance matrix. |

`lambda` |
Penalty value. Note: higher values will result in additional
convergence issues. If using values > 0.1, it is recommended to use
mutli_optim() instead. See |

`alpha` |
Mixture for elastic net. Not currently working applied. |

`type` |
Penalty type. Options include "none", "lasso", "ridge", "enet" for the elastic net, "alasso" for the adaptive lasso, "scad, "mcp", and "diff_lasso". diff_lasso penalizes the discrepency between parameter estimates and some pre-specified values. The values to take the deviation from are specified in diff_par. |

`data` |
Optional dataframe. Only required for missing="fiml" which is not currently working. |

`optMethod` |
Solver to use. Recommended options include "nlminb" and "optimx". Note: for "optimx", the default method is to use nlminb. This can be changed in subOpt. |

`gradFun` |
Gradient function to use. Recommended to use "ram", which refers to the method specified in von Oertzen & Brick (2014). The "norm" procedure uses the forward difference method for calculating the hessian. This is slower and less accurate. |

`hessFun` |
Hessian function to use. Recommended to use "ram", which refers to the method specified in von Oertzen & Brick (2014). The "norm" procedure uses the forward difference method for calculating the hessian. This is slower and less accurate. |

`parallel` |
Logical. Whether to parallelize the processes? |

`Start` |
type of starting values to use. Only recommended to use "default". This sets factor loadings and variances to 0.5. Start = "lavaan" uses the parameter estimates from the lavaan model object. This is not recommended as it can increase the chances in getting stuck at the previous parameter estimates. |

`subOpt` |
Type of optimization to use in the optimx package. |

`longMod` |
If TRUE, the model is using longitudinal data? This changes the sample covariance used. |

`pars_pen` |
Parameter indicators to penalize. If left NULL, by default,
all parameters in the |

`diff_par` |
Parameter values to deviate from. Only used when type="diff_lasso". |

`LB` |
lower bound vector. Note: This is very important to specify when using regularization. It greatly increases the chances of converging. |

`UB` |
Upper bound vector |

`block` |
Whether to use block coordinate descent |

`full` |
Whether to do full gradient descent or block |

`calc` |
Type of calc function to use with means or not. Not recommended for use. |

`max.iter` |
Number of iterations for coordinate descent |

`tol` |
Tolerance for coordinate descent |

`solver` |
Whether to use solver for coord_desc |

`solver.maxit` |
Max iterations for solver in coord_desc |

`alpha.inc` |
Whether alpha should increase for coord_desc |

`step` |
Step size |

`momentum` |
Logical for coord_desc |

`step.ratio` |
Ratio of step size between A and S. Logical |

`nlminb.control` |
list of control values to pass to nlminb |

`missing` |
How to handle missing data. Current options are "listwise" and "fiml". "fiml" is not currently working well. |

### Value

out List of return values from optimization program

convergence Convergence status. 0 = converged, 1 or 99 means the model did not converge.

par.ret Final parameter estimates

Imp_Cov Final implied covariance matrix

grad Final gradient.

KKT1 Were final gradient values close enough to 0.

KKT2 Was the final Hessian positive definite.

df Final degrees of freedom. Note that df changes with lasso penalties.

npar Final number of free parameters. Note that this can change with lasso penalties.

SampCov Sample covariance matrix.

fit Final F_ml fit. Note this is the final parameter estimates evaluated with the F_ml fit function.

coefficients Final parameter estimates

nvar Number of variables.

N sample size.

nfac Number of factors

baseline.chisq Baseline chi-square.

baseline.df Baseline degrees of freedom.

### Examples

1 2 3 4 5 6 7 8 9 10 |