| Title: | Estimate structural equation models using computation graphs |
|---|---|
| Description: | Use lavaan code to create structural equation models, use torch to estimate them. This package provides the interface between lavaan and torch. |
| Authors: | Erik-Jan van Kesteren |
| Maintainer: | Erik-Jan van Kesteren <[email protected]> |
| License: | GPL-3 |
| Version: | 2.1.0 |
| Built: | 2024-09-14 02:37:07 UTC |
| Source: | https://github.com/vankesteren/tensorsem |
This function prepares a dataframe for a tensorsem model. It first converts the variables to a design matrix, then centers it, and lastly converts it to a torch_tensor
df_to_tensor(df, dtype = NULL, device = NULL)df_to_tensor(df, dtype = NULL, device = NULL)
df |
data frame |
dtype |
data type of the resulting tensor |
device |
device to store the resulting tensor on |
Torch tensor of scaled and processed data
torch::torch_tensor(), stats::model.matrix()
Create a torch options list from a lavaan Model class.
lav_mod_to_torch_opts(lav_mod)lav_mod_to_torch_opts(lav_mod)
lav_mod |
lavaan Model class object |
list of tensorsem options
Multivariate normal negative log-likelihood loss function for tensorsem nn module.
mvn_negloglik(dat, Sigma)mvn_negloglik(dat, Sigma)
dat |
The centered dataset as a tensor |
Sigma |
The model() implied covariance matrix |
torch_tensor: scalar negative log likelihood
See examples in tensorsem for how to save the output.
partable_from_torch(pars, syntax)partable_from_torch(pars, syntax)
pars |
data frame of parameter estimates (est) and their standard errors (se) |
syntax |
syntax of the original model |
SEM fitting function
sem_fitfun(S, Sigma)sem_fitfun(S, Sigma)
S |
The observed covariance matrix |
Sigma |
The model implied covariance matrix |
torch_tensor: scalar loss function
Create a torch options list from lavaan syntax.
syntax_to_torch_opts(syntax)syntax_to_torch_opts(syntax)
syntax |
lavaan syntax |
list of tensorsem options
Compute jacobian of output wrt input tensor
torch_jacobian(output, input)torch_jacobian(output, input)
output |
Tensor vector of size Po |
input |
Tensor vector of size Pi |
jacobian: Tensor of size Pi, Po
Function for creating a structural equation model
torch_sem(syntax, dtype = torch_float32(), device = torch_device("cpu"))torch_sem(syntax, dtype = torch_float32(), device = torch_device("cpu"))
syntax |
lavaan syntax for the SEM model |
dtype |
(optional) torch dtype for the model (default torch_float32()) |
device |
(optional) device type to put the model on. see |
This function instantiates a torch object for computing the model-implied covariance matrix
based on a structural equation model. Through torch, gradients of this forward model can then
be computed using backpropagation, and the parameters can be optimized using gradient-based
optimization routines from the torch package.
Because of this, it is easy to add additional penalties to the standard objective function, or to write a new objective function altogether.
A torch_sem object, which is an nn_module (torch object)
free_paramsVector of free parameters
$initialize()The initialize method. Don't use this, just use torch_sem()
syntax lavaan syntax for the SEM model
dtype (optional) torch dtype for the model (default torch_float32())
device (optional) device type to put the model on. see torch::torch_device()
A torch_sem object, which is an nn_module (torch object)
$forward()Compute the model-implied covariance matrix.
Don't use this; nn_modules are callable, so access this method by calling
the object itself as a function, e.g., my_torch_sem().
In the forward pass, we apply constraints to the parameter vector, and we
create matrix views from it to compute the model-implied covariance matrix.
A torch_tensor of the model-implied covariance matrix
$inverse_Hessian(loss)Compute and return the asymptotic covariance matrix of the parameters with respect to the loss function
loss torch_tensor of freshly computed loss function (needed by torch
for backwards pass)
A torch_tensor, representing the ACOV of the free parameters
$standard_errors(loss)Compute and return observed information standard errors of the parameters, assuming the loss function is the likelihood and the current estimates are ML estimates.
loss torch_tensor of freshly computed loss function (needed by torch
for backwards pass)
A numeric vector of standard errors of the free parameters
$partable(loss)Create a lavaan-like parameter table from the current parameter estimates in the torch_sem object.
loss (optional) torch_tensor of freshly computed loss function (needed by torch
for backwards pass)
lavaan partable object
$fit(dat, lrate, maxit, verbose, tol)Fit a torch_sem model using the default maximum likelihood objective. This function uses the Adam optimizer to estimate the parameters of a torch_sem
dat dataset (centered!) as a torch_tensor
lrate learning rate of the Adam optimizer.
maxit maximum number of epochs to train the model
verbose whether to print progress to the console
tol parameter change tolerance for stopping training
Self, i.e., the torch_sem object with updated parameters
$loglik(dat)Multivariate normal log-likelihood of the data.
dat dataset (centered!) as a torch_tensor
Log-likelihood value (torch scalar)
Half-vectorization of square matrices
torch_vech(x)torch_vech(x)
x |
square (symmetric) matrix tensor |
column vector of stacked lower-diagonal elements
Constructs index vector for transforming a vech vector into a vec vector to create an n*n symmetric matrix from the vech vector. tensor$index_select(0, idx)$view(3,3)
vech_dup_idx(n)vech_dup_idx(n)
n |
size of the resulting square matrix |
array containing the indices