predict.SEM: SEM-based out-of-sample prediction using layer-wise ordering

In SEMdeep: Structural Equation Modeling with Deep Neural Network and Machine Learning

SEM-based out-of-sample prediction using layer-wise ordering

Description

Given the values of (observed) x-variables in a SEM, this function may be used to predict the values of (observed) y-variables. The predictive procedure consists of two steps: (1) construction of the topological layer (TL) ordering of the input graph; (2) prediction of the node y values in a layer, where the nodes included in the previous layers act as predictors x.

Usage

## S3 method for class 'SEM'
predict(object, newdata, newoutcome = NULL, verbose = FALSE, ...)

Arguments

object	An object, as that created by the function SEMrun() with the argument group set to the default group = NULL.
newdata	A matrix with new data, with rows corresponding to subjects, and columns to variables.
newoutcome	A new character vector (as.factor) of labels for a categorical output (target)(default = NULL).
verbose	A logical value. If FALSE (default), the processed graph will not be plotted to screen.
...	Currently ignored.

Details

The function first creates a layer-based structure of the input graph. Then, a SEM-based predictive approach (Rooij et al., 2022) is used to produce predictions while accounting for the graph structure based on the topological layer (j=1,…,L) of the input graph. In each iteration, the response (output) variables, y are the nodes in the j=1,...,(L-1) layer and the predictor (input) variables, x are the nodes belonging to the successive, (j+1),...,L layers. Predictions (for y given x) are based on the (joint y and x) model-implied variance-covariance (Sigma) matrix and mean vector (Mu) of the fitted SEM, and the standard expression for the conditional mean of a multivariate normal distribution. Thus, the layer structure described in the SEM is taken into consideration, which differs from ordinary least squares (OLS) regression.

Value

A list of 3 objects:

1. "PE", vector of the amse = average MSE over all (sink and mediators) graph nodes; r2 = 1 - amse; and srmr= Standardized Root Means Square Residual between the out-of-bag correlation matrix and the model correlation matrix.

2. "mse", vector of the Mean Squared Error (MSE) for each out-of-bag prediction of the sink and mediators graph nodes.

3. "Yhat", the matrix of continuous predicted values of graph nodes (excluding source nodes) based on out-of-bag samples.

Author(s)

Mario Grassi [e-mail]

References

de Rooij M, Karch JD, Fokkema M, Bakk Z, Pratiwi BC, and Kelderman H (2023). SEM-Based Out-of-Sample Predictions, Structural Equation Modeling: A Multidisciplinary Journal, 30:1, 132-148 <https://doi.org/10.1080/10705511.2022.2061494>

Grassi M, Palluzzi F, Tarantino B (2022). SEMgraph: An R Package for Causal Network Analysis of High-Throughput Data with Structural Equation Models. Bioinformatics, 38 (20), 4829–4830 <https://doi.org/10.1093/bioinformatics/btac567>

Examples

# load ALS data
data<- alsData$exprs
data<- transformData(data)$data
group<- alsData$group

#...with train-test (0.5-0.5) samples
set.seed(123)
train<- sample(1:nrow(data), 0.5*nrow(data))

# predictors, source+mediator; outcomes, mediator+sink

ig <- alsData$graph; gplot(ig)
sem0 <- SEMrun(ig, data[train,], algo="ricf", n_rep=0)
pred0 <- predict(sem0, newdata=data[-train,], verbose=TRUE) 

# predictors, source+mediator+group; outcomes, source+mediator+sink

ig1 <- mapGraph(ig, type = "group"); gplot(ig1)
data1 <- cbind(group, data); head(data1[,5])
sem1 <- SEMrun(ig1, data1[train,], algo="ricf", n_rep=0)
pred1 <- predict(sem1, newdata= data1[-train,], verbose=TRUE) 

# predictors, source nodes; outcomes, sink nodes

ig2 <- mapGraph(ig, type = "source"); gplot(ig2)
sem2 <- SEMrun(ig2, data[train,], algo="ricf", n_rep=0)
pred2 <- predict(sem2, newdata=data[-train,], verbose=TRUE)

SEMdeep documentation built on April 12, 2025, 2:24 a.m.