approx_mult_prod is sensitive to variable order

[Jack M Wolf]

The output of approx_mult_prod() changes based on the order of response means/covariances.
The returned lists from both of the approx_mult_prod() statements in the reprex below should be equal but they are not.

library(grass)
ex_data <- bin_data[c("g", "x", "y1", "y2", "y3")]
head(ex_data)
#>   g          x y1 y2 y3
#> 1 0 -0.9161478  1  0  1
#> 2 0  1.2496985  0  1  0
#> 3 1 -1.2708514  0  0  0
#> 4 2  0.0832760  0  1  0
#> 5 0  0.4686342  0  1  1
#> 6 2  0.4620154  0  1  0

means <- colMeans(ex_data)
covs <- cov(ex_data)
n <- nrow(ex_data)

predictors <- list(
  new_predictor_snp(maf = mean(ex_data$g) / 2),
  new_predictor_normal(mean = mean(ex_data$x), sd = sd(ex_data$x))
)
responses <- lapply(means[3:length(means)], new_predictor_binary)

approx_mult_prod(means, covs, n, response = "binary",
  predictors = predictors, responses = responses, verbose = TRUE)
#> Approximating with responses ordered as:  y1 * y2 * y3 
#> Approximating with responses ordered as:  y1 * y3 * y2 
#> Approximating with responses ordered as:  y2 * y3 * y1
#> $means
#>           g           x      y1y2y3 
#>  0.56800000 -0.02927950  0.05444547 
#> 
#> $covs
#>                  g           x      y1y2y3
#> g       0.40978579 -0.04510754 -0.02670105
#> x      -0.04510754  0.99460726  0.04906614
#> y1y2y3 -0.02670105  0.04906614  0.05153269


# Reorder response means/covariances
means <- means[c(1, 2, 5, 4, 3)]
covs  <- covs[c(1, 2, 5, 4, 3), c(1, 2, 5, 4, 3)]

responses <- lapply(means[3:length(means)], new_predictor_binary)

approx_mult_prod(means, covs, n, response = "binary",
                 predictors = predictors, responses = responses, verbose = TRUE)
#> Approximating with responses ordered as:  y3 * y2 * y1 
#> Approximating with responses ordered as:  y3 * y1 * y2 
#> Approximating with responses ordered as:  y2 * y1 * y3
#> $means
#>           g           x      y3y2y1 
#>  0.56800000 -0.02927950  0.08101557 
#> 
#> $covs
#>                  g           x      y3y2y1
#> g       0.40978579 -0.04510754 -0.03324090
#> x      -0.04510754  0.99460726  0.05203570
#> y3y2y1 -0.03324090  0.05203570  0.07452658

^{Created on 2020-08-05 by the reprex package (v0.3.0)}