SEMdeep (version 0.1.0)

predict.SEM: 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 SEM
predict(object, newdata, verbose = FALSE, ...)

Value

A list of 2 objects:

1. "PE", vector of the prediction error equal to the Mean Squared Error (MSE) for each out-of-bag prediction. The first value of PE is the AMSE, where we average over all (sink and mediators) graph nodes.

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

Arguments

object

An object, as that created by the function SEMrun() with the argument fit set to fit = 0 or fit = 1.

newdata

A matrix with new data, with rows corresponding to subjects, and columns to variables. If object$fit is a model with the group variable (fit = 1), the first column of newdata must be the new group binary vector (0=control, 1=case).

verbose

A logical value. If FALSE (default), the processed graph will not be plotted to screen.

...

Currently ignored.

Author

Mario Grassi

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 organised in topological layers, j=1,...,L. In each iteration, the response variables y are the nodes in the j layer and the predictors x are the nodes belonging to the previous j-1 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.

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
ig<- alsData$graph
data<- alsData$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))

# SEM fitting
sem0<- SEMrun(ig, data[train,], SE="none", limit=1000)

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

res0<- predict(sem0, newdata=data[-train,]) 
print(res0$PE)

# SEM fitting
sem1<- SEMrun(ig, data[train,], group[train], SE="none", limit=1000)

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

res1<- predict(sem1, newdata=cbind(group,data)[-train,]) 
print(res1$PE)

# \donttest{
#...with a binary outcome (1=case, 0=control)

ig1<- mapGraph(ig, type="outcome"); gplot(ig1)
outcome<- ifelse(group == 0, -1, 1); table(outcome)
data1<- cbind(outcome, data); data1[1:5,1:5]

sem10 <- SEMrun(ig1, data1[train,], SE="none", limit=1000)
res10<- predict(sem10, newdata=data1[-train,], verbose=TRUE) 

yobs<- group[-train]
yhat<- res10$Yhat[,"outcome"]
benchmark(yobs, yhat)

#...with predictors, source nodes; outcomes, sink nodes
ig2<- mapGraph(ig, type= "source"); gplot(ig2)

sem02 <- SEMrun(ig2, data[train,], SE="none", limit=1000)
res02<- predict(sem02, newdata=data[-train,], verbose=TRUE) 
# }