combine_effects.stan File Reference

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Functions
vector	combine_effects (array[] real intercept, vector beta, int nobs, int neffs, matrix fdesign, tuple(vector, array[] int, array[] int) sparse, vector beta_sd, matrix rdesign, int add_intercept, int sparse_design)

Function Documentation

combine_effects()

vector combine_effects	(	array[]real	intercept,
		vector	beta,
		int	nobs,
		int	neffs,
		matrix	fdesign,
		tuple(vector, array[] int, array[] int)	sparse,
		vector	beta_sd,
		matrix	rdesign,
		int	add_intercept,
		int	sparse_design )

Combine nested regression effects using design matrices

This function combines nested regression effects based on a design matrix and applies effect pooling using a second design matrix. It allows for scaling of effects with specified standard deviations, enabling the pooling of these effects. The function can also incorporate an intercept into the linear predictions.

Parameters

intercept	Array containing the regression intercept (length one).
beta	Vector of regression effects, typically unit-scaled for possible rescaling with beta_sd.
nobs	Integer the number of observations (i.e. design matrix columns).
neffs	Integer the number of effects (i.e. the number of rows in the design matrix).
fdesign	Dense matrix mapping observations (rows) to fixed effects (columns).
beta_sd	Vector of standard deviations for scaling and pooling effects.
rdesign	Dense matrix relating effect sizes to standard deviations. The first column indicates no scaling for independent effects.
sparse	Sparse matrix components for fixed effects design matrix. The output from csr_extract(fdesign).
add_intercept	Binary flag to indicate if the intercept should be added to the beta vector.
sparse_design	Binary flag to indicate whether to use sparse or dense matrices.

Returns

A vector of linear predictions without error.

Note

The function scales the beta vector using the product of beta_sd and rdesign, then combines these scaled effects with the fdesign matrix. If add_intercept is true, the intercept is included in the linear predictions. The function handles cases with no effects by returning a vector of the intercept repeated for each observation.

# Example usage in R:
intercept <- 1
beta <- c(0.1, 0.2, 0.4)
design <- matrix(c(1, 1, 1, 0,
                   0, 1, 0, 0,
                   0, 1, 1, 1), nrow = 3, byrow = TRUE)
beta_sd <- c(0.1)
sd_design <- matrix(c(1, 1, 0,
                      0, 0, 1), nrow = 2, byrow = TRUE)
 
# Check effects are combined as expected:
combine_effects(
  intercept, beta, 4, 3, design, list({}, {}, {}), beta_sd, sd_design, 1, 0
)
# Output: 1.04 1.12 1.00 1.04

Definition at line 62 of file combine_effects.stan.