Multivariate Normal Log-likelihood and Score Functions for Reduced Rank Covariances

Computes the log-likelihood (contributions) of interval-censored observations from multivariate normal distributions with reduced rank structure and evaluates corresponding score functions.

Usage

lpRR(lower, upper, mean = 0, B, D = rep(1, nrow(B)), 
     Z, weights = 1 / ncol(Z), log.p = TRUE)
slpRR(lower, upper, mean = 0, B, D = rep(1, nrow(B)), 
      Z, weights = 1 / ncol(Z), log.p = TRUE)

Arguments

lower: vector of lower limits (one element for each dimension, \(J\) elements).
upper: vector of upper limits (one element for each dimension, \(J\) elements).
mean: vector of means (one element for each dimension, length is recycled to length of lower and upper).
B: matrix of dimension \(J \times K\).
D: vector of \(J\) diagonal elements.
Z: matrix of standard normal random variables, with \(K\) nrows.
weights: optional weights.
log.p: logical. By default, log-probabilities are returned.

Details

Evaluates the multivariate normal log-likelihood defined by mean, B and D when the covariance is \(\Sigma = B B^\top + D\) over boxes defined by lower and upper. Details are given in mvtnorm::Genz_Bretz_2009, Chapter 2.3.1.

slpRR computes the corresponding score functions with respect to lower, upper, mean, B and D.

More details can be found in the lmvnorm_src package vignette.

Value

The log-likelihood (log.p = TRUE) or corresponding probability. slpRR return the scores.

References

Examples

  J <- 6
  K <- 3
  B <- matrix(rnorm(J * K), nrow = J)
  D <- runif(J)
  S <- tcrossprod(B) + diag(D)
  a <- -(2 + runif(J))
  b <- 2 + runif(J)
  M <- 1e4
  Z <- matrix(rnorm(K * M), nrow = K)
  ## log-likelihood
  lpRR(lower = a, upper = b, B = B, D = D, Z = Z)
#> [1] -0.9192491
  ## score wrt all arguments
  slpRR(lower = a, upper = b, B = B, D = D, Z = Z)
#> $lower
#> [1] -0.03988543 -0.12240585 -0.17089697 -0.02782872 -0.01103652 -0.03572410
#> 
#> $upper
#> [1] 0.047466928 0.136029202 0.171690296 0.034421322 0.011890107 0.009547452
#> 
#> $mean
#> [1] -0.0075814980 -0.0136233552 -0.0007933255 -0.0065925984 -0.0008535898
#> [6]  0.0261766484
#> 
#> $B
#>              [,1]        [,2]         [,3]
#> [1,]  0.003603196  0.13314225  0.070729942
#> [2,] -0.233602044  0.09589090 -0.024994580
#> [3,]  0.117938557  0.08653291 -0.244982777
#> [4,] -0.038944886 -0.03972351 -0.042174926
#> [5,]  0.033221322  0.01782221 -0.016100244
#> [6,] -0.051816628 -0.01113051 -0.004687892
#> 
#> $D
#> [1] -0.06482371 -0.10429223 -0.09454297 -0.05619978 -0.03794360 -0.05200137
#>