qrcm (version 3.1)

predict.iqrL: Prediction After Quantile Regression Coefficients Modeling with Longitudinal Data

Description

Predictions from an object of class “iqrL”.

Usage

# S3 method for iqrL
predict(object, level, type = c("coef", "CDF", "QF", "sim"), newdata, p, se = FALSE, ...)

Value

• if type = "coef" a list with one item for each covariate. Each element of the list is a data frame with columns (u, beta, se, low, up), if level = 1, and (v, gamma, se, low, up), if level = 2. If se = FALSE, the last three columns are not computed.

• if type = "CDF", a two-columns data frame (CDF,PDF).

• if type = "QF" and se = FALSE, a data frame with one row for each observation, and one column for each value of p. If se = TRUE, a list of two data frames, fit (predictions) and se.fit (standard errors).

• if type = "sim", a vector of simulated data.

Arguments

object

an object of class “iqrL”, the result of a call to iqrL.

level

a numeric scalar. Use level = 1 to predict \(y_{it} - \alpha_i\), and level = 2 to predict \(\alpha_i\) (see iqrL for the notation).

type

a character string specifying the type of prediction. See ‘Details’.

newdata

an optional data frame in which to look for variables with which to predict (ignored if type = "coef"). For type = "CDF", newdata must include a response variable named ‘y_alpha’, if level = 1, and ‘alpha’ if level = 2. If newdata is omitted, the observed data will be used, and y_alpha and alpha will be taken from object$fit.

p

a numeric vector indicating the order(s) of the quantile to predict. Only used if type = "coef" or type = "QF".

se

logical. If TRUE (the default), standard errors of the prediction will be computed. Only used if type = "coef" or type = "QF".

...

for future methods.

Author

Paolo Frumento

Details

• if type = "coef" (the default), quantile regression coefficients are returned: if level = 1, \(\beta(p)\); and if level = 2, \(\gamma(p)\). If p is missing, a default p = (0.01, ..., 0.99) is used.

• if type = "CDF", the value of the fitted CDF (cumulative distribution function) and PDF (probability density function) are computed. If level = 1, these refer to the distribution of \(Y_{it} - \alpha_i = x_{it}\beta(U_{it})\), and the CDF is an estimate of \(U_{it}\). If level = 2, they refer to the distribution of \(\alpha_i = z_i\gamma(V_i)\), and the CDF is an estimate of \(V_i\).

• if type = "QF", the fitted values \(x\beta(p)\) (if level = 1), or \(z\gamma(p)\) (if level = 2).

• if type = "sim", data are simulated from the fitted model. If level = 1, simulated values are from the distribution of \(Y_{it} - \alpha_i\), while if level = 2, they are from the distribution of \(\alpha_i\).

See Also

iqrL, for model fitting; summary.iqrL and plot.iqrL, for summarizing and plotting iqrL objects.

Examples

  # using simulated data
  
  n <- 1000 # n. of observations
  n.id <- 100 # n. of clusters
  id <- rep(1:n.id, each = n/n.id) # cluster id

  x1 <- runif(n) # a level-1 covariate
  z1 <- rbinom(n.id,1,0.5) # a level-2 covariate

  V <- runif(n.id) # V_i
  U <- runif(n) # U_it

  alpha <- qlogis(V)*(0.5 + z1) # alpha
  y_alpha <- 1 + 2*qexp(U) + 3*x1 # y - alpha
  y <- y_alpha + alpha[id] # observed outcome
  mydata <- data.frame(id = id, y = y, x1 = x1, z1 = z1[id])

  # true model: Y_it = beta0(U_it) + beta1(U_it)*x1 + gamma0(V_i) + gamma1(V_i)*z1
  # beta0(u) = 1 + 2*pexp(u)
  # beta1(u) = 3
  # gamma0(v) = 0.5*qlogis(v)
  # gamma1(v) = qlogis(V)
  
  model <- iqrL(fx = y ~ x1, fu = ~ I(qexp(u)), fz = ~ z1, fv = ~ -1 + I(qlogis(v)), 
    id = id, data = mydata) 
  
  # predict beta(0.25), beta(0.5), beta(0.75)
  predict(model, level = 1, type = "coef", p = c(0.25,0.5,0.75))
 
  # predict gamma(0.1), gamma(0.9)
  predict(model, level = 2, type = "coef", p = c(0.1,0.9))

  # predict the CDF (u) and the PDF of (y - alpha), at new values of x1
  predict(model, level = 1, type = "CDF", 
    newdata = data.frame(x1 = c(.1,.2,.3), y_alpha = c(1,2,3)))
 
  # predict the CDF (v) and the PDF of alpha, at new values of z1
  predict(model, level = 2, type = "CDF", 
    newdata = data.frame(z1 = c(0,1), alpha = c(-1,1)))
 
  # computes the quantile function of (y - alpha) at new x1, for u = (0.25,0.5,0.75)
  predict(model, level = 1, type = "QF", p = c(0.25,0.5,0.75), 
    newdata = data.frame(x1 = c(.1,.2,.3)))

  # computes the quantile function of alpha at new z1, for v = (0.25,0.5,0.75)
  predict(model, level = 2, type = "QF", p = c(0.25,0.5,0.75), 
    newdata = data.frame(z1 = c(.1,.2,.3)))


  # simulate data from the fitted model
  y_alpha_sim <- predict(model, level = 1, type = "sim")
  alpha_sim <- predict(model, level = 2, type = "sim")
  y_sim = y_alpha_sim + alpha_sim[id]