logrr: Log ratio of spatial densities

Description Usage Arguments Details Value Author(s) References Examples

View source: R/logrr.R

Description

logrr computes the log ratio of spatial density functions for cases and controls. The numerator in this ratio is related to the "cases" and the denominator to the "controls". If nsim > 0, then pointwise tolerance intervals are used to assess potential clustering of cases and controls relative to each other.

Usage

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logrr(x, sigma = NULL, sigmacon = NULL, case = 2, nsim = 0,
  level = 0.9, alternative = "two.sided", ..., bwargs = list(),
  weights = NULL, edge = TRUE, varcov = NULL, at = "pixels",
  leaveoneout = TRUE, adjust = 1, diggle = FALSE, kernel = "gaussian",
  scalekernel = is.character(kernel), positive = FALSE, verbose = TRUE)

Arguments

x

Point pattern (object of class "ppp").

sigma

Standard deviation of isotropic smoothing kernel for cases. Either a numerical value, or a function that computes an appropriate value of sigma.

sigmacon

Standard deviation of isotropic smoothing kernel for controls. Default is the same as sigma.

case

The position of the name of the "case" group in levels(x$marks). The default is 2. x$marks is assumed to be a factor. Automatic conversion is attempted if it is not.

nsim

The number of simulated data sets from which to construct the tolerance intervals under the random labeling hypothesis. Default is 0 (i.e., no intervals).

level

The tolerance level used for the pointwise tolerance intervals.

alternative

The direction of the significance test to identify potential clusters using a Monte Carlo test based on the pointwise tolerance intervals. Default is "two.sided" (logrr != 0). The values "less" (logrr < 0) and "greater" (logrr > 0) are also valid.

...

Additional arguments passed to pixellate.ppp and as.mask to determine the pixel resolution, or passed to sigma if it is a function.

bwargs

A list of arguments for the bandwidth function supplied to sigma and sigmacon, if applicable.

weights

Optional weights to be attached to the points. A numeric vector, numeric matrix, an expression, or a pixel image.

edge

Logical value indicating whether to apply edge correction.

varcov

Variance-covariance matrix of anisotropic smoothing kernel. Incompatible with sigma.

at

String specifying whether to compute the intensity values at a grid of pixel locations (at="pixels") or only at the points of x (at="points").

leaveoneout

Logical value indicating whether to compute a leave-one-out estimator. Applicable only when at="points".

adjust

Optional. Adjustment factor for the smoothing parameter.

diggle

Logical. If TRUE, use the Jones-Diggle improved edge correction, which is more accurate but slower to compute than the default correction.

kernel

The smoothing kernel. A character string specifying the smoothing kernel (current options are "gaussian", "epanechnikov", "quartic" or "disc"), or a pixel image (object of class "im") containing values of the kernel, or a function(x,y) which yields values of the kernel.

scalekernel

Logical value. If scalekernel=TRUE, then the kernel will be rescaled to the bandwidth determined by sigma and varcov: this is the default behaviour when kernel is a character string. If scalekernel=FALSE, then sigma and varcov will be ignored: this is the default behaviour when kernel is a function or a pixel image.

positive

Logical value indicating whether to force all density values to be positive numbers. Default is FALSE.

verbose

Logical value indicating whether to issue warnings about numerical problems and conditions.

Details

The plot function makes it easy to visualize the log ratio of spatial densities (if nsim = 0) or the regions where the log ratio deviates farther from than what is expected under the random labeling hypothesis (i.e., the locations of potential clustering). The shaded regions indicate the locations of potential clustering.

The two.sided alternative test assesses whether the observed ratio of log densities deviates more than what is expected under the random labeling hypothesis. When the test is significant, this suggests that the cases and controls are clustered, relative to the other. The greater alternative assesses whehter the cases are more clustered than the controls. The less alternative assesses whether the controls are more clustered than the cases. If the estimated density of the case or control group becomes too small, this function may produce warnings due to numerical underflow. Increasing the bandwidth (sigma) may help.

Value

The function produces an object of type logrrenv. Its components are similar to those returned by the density.ppp function from the spatstat package, with the intensity values replaced by the log ratio of spatial densities of f and g. Includes an array simr of dimension c(nx, ny, nsim + 1), where nx and ny are the number of x and y grid points used to estimate the spatial density. simr[,,1] is the log ratio of spatial densities for the observed data, and the remaining nsim elements in the third dimension of the array are the log ratios of spatial densities from a new ppp simulated under the random labeling hypothesis.

Author(s)

Joshua French (and a small chunk by the authors of the density.ppp) function for consistency with the default behavior of that function)

References

Waller, L.A. and Gotway, C.A. (2005). Applied Spatial Statistics for Public Health Data. Hoboken, NJ: Wiley.

Kelsall, Julia E., and Peter J. Diggle. "Kernel estimation of relative risk." Bernoulli (1995): 3-16.

Kelsall, Julia E., and Peter J. Diggle. "Non-parametric estimation of spatial variation in relative risk." Statistics in Medicine 14.21-22 (1995): 2335-2342.

Examples

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data(grave)
r = logrr(grave)
plot(r)
r2 = logrr(grave, sigma = spatstat::bw.scott)
plot(r2)
rsim = logrr(grave, nsim = 9)
plot(rsim)

smacpod documentation built on May 14, 2018, 5:07 p.m.

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