Skip to contents

Standardisation

Source: R/helpers.R
dot-forescale.Rd

Transforms variables to mean 0 and variance 1.

Usage

.forescale(x, y = NULL, family = NULL, pars = NULL)

Arguments

x

\(n_0 \times p\) predictor matrix, where \(n_0\) is the number of observations used for model training and \(p\) is the number of variables

y

response vector (only required if family="gaussian") or NULL

family

character string "gaussian", "binomial", "poisson", or "cox"; or NULL (if pars is provided)

pars

list as defined in section Value, or NULL (if family is provided)

Value

Returns a list with multiple slots:

  • standardised \(n_0 \times p\) or \(n_1 \times p\) predictor matrix \(x\)

  • standardised \(n_0\)-dimensional or \(n_1\)-dimensional response vector \(y\) (only if \(y\) is provided and family = "gaussian" or pars$family = "gaussian"; otherwise output equals input)

  • character string family indicates the model ("gaussian", "binomial", "poisson", or "cox"), determined by argument family or pars$family

  • list pars 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")

Details

This function is called by corila() for the training data and by predict.corila() for the testing data.

See also

Use function .backscale() to bring coefficients and predictions back to original scale.

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
# }