Inverse standardisation

Transforms response variable back to original scale or transforms coefficients for predictor variables and response variable on original scales.

Usage

.backscale(pars, y = NULL, coef = NULL)

Arguments

pars

list with slots mu.x and sd.x (\(p\)-dimensional vectors of means and standard deviations of the predictor variables), mu.y and sd.y (mean and standard deviation of response variable for Gaussian family, 0 and 1 for other families), and family (character string "gaussian", "binomial", "poisson", or "cox")

y

\(n_1\)-dimensional response vector or response matrix with \(n_1\) rows and multiple columns (for multiple values of the regularisation parameter), or NULL (default)

coef

\((1 + p)\)-dimensional vector containing the estimated intercept and the estimated slopes, or NULL (default)

Value

Returns a list with slots y or coef.

Details

This function is called by predict.cv.corila() for the predicted values and by coef.cv.corila() for the estimated coefficients.

See also

Use function .forescale() to standardise variables.

Examples

# \donttest{
# simulate data
family <- "gaussian"
n0 <- 100; n1 <- 50; p <- 3
n <- n0 + n1
fold <- rep(c(0, 1), times = c(n0, n1))
sd <- stats::rpois(n = p, lambda = 5)
x <- data.frame(x = sapply(X = sd,
                           FUN = function(x) stats::rnorm(n = n, sd = x)))
beta <- stats::rnorm(n = p)
eta <- as.matrix(x) %*% beta
if (identical(family, "gaussian")) {
  y <- stats::rnorm(n = n, mean = eta)
} else if (identical(family, "binomial")) {
  y <- stats::rbinom(n = n, size = 1, prob = 1 / (1 + exp(-eta)))
} else if (identical(family, "poisson")) {
  y <- stats::rpois(n = n, lambda = exp(eta))
} else if (identical(family, "cox")) {
  time <- stats::rexp(n = n, rate = exp(eta))
  status <- stats::rbinom(n = n, prob = 0.5, size = 1)
  y <- survival::Surv(time = time, event = status)
}

# regression without standardisation
if (identical(family, "cox")) {
  lm1 <- survival::coxph(y[fold == 0]~., data=x[fold == 0, ])
} else {
  lm1 <- stats::glm(y[fold == 0]~., data=x[fold == 0, ], family=family)
}
coef1 <- stats::coef(lm1)
yhat1 <- predict(lm1, newdata = x[fold == 1, ])

# regression with standardisation
scale <- corila:::.forescale(x = as.matrix(x)[fold == 0, ],
                   y = y[fold == 0],
                   family = family)
if (identical(family, "cox")) {
  lm2 <- survival::coxph(scale$y~., data = data.frame(scale$x))
} else {
  lm2 <- stats::glm(scale$y~., data = data.frame(scale$x), family = family)
}
coef_temp <- stats::coef(lm2)
newx_temp <- corila:::.forescale(x = as.matrix(x)[fold == 1, ],
                                 pars = scale$pars)$x
yhat_temp <- predict(object = lm2, newdata = data.frame(newx_temp))
result <- corila:::.backscale(pars = scale$pars,
                              y = yhat_temp,
                              coef = coef_temp)
coef2 <- result$coef
yhat2 <- result$y

# equality
all.equal(coef1, coef2, check.attributes = FALSE)
#> [1] TRUE
all.equal(yhat1, yhat2, check.attributes = FALSE)
#> [1] TRUE
# }