DP2LM: Deep neural network based penalized partially linear mediation model with high-dimensional mediators

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Mediation model

• Outcome-mediator model:
• Mediator-exposure model:
• Total model
• 
• Direct effect:
• Indirect effect:

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Estimation via deep neural networks

• Estimation of direct effect:

• Estimation of indirect effect:

  

  

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Inference via deep neural networks

• F-type test for direct effect:

• Wald test for indirect effect:

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Deep neural network hyperparameters and structures

• L: number of layers
• p: neurons per layer (uniform for all layers)
• s: dropout rate (data dependent)
• Loss function: mean squared loss
• Batch size: data dependent
• Epoch number: data dependent
• Activation function: ReLU
• Optimizer: Adam
• Regularizer: SCAD

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Function descriptions

• "estimation.R": estimation of direct effect via regularization and indirect effect by difference method using neural networks.
• "inference_direct.R": inference of direct effect using neural networks
• "inference_indirect.R" inference of indirect effect using neural networks

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Examples

• "data.R": a data generating example.