- matrix.type
Determines whether to build a covariance matrix,
"cov", or a precision matrix, "prec". See
correlation_builder{sim2Dpredictr} and
precision_builder{sim2Dpredictr} for more details.
- im.res
A vector defining the dimension of spatial data. The first
entry is the number of rows and the second entry is the number of columns.
- use.spam
If use.spam = TRUE then use tools from the R package
spam; otherwise, base R functions are employed. For large dimension
MVN with sparse correlation structure, spam is recommended;
otherwise, base R may be faster. Defaults to FALSE.
- corr.structure
One of "ar1", exponential,
gaussian, or "CS". Correlations between locations i and j
are rho\(^{d}\) for corr.structure = "ar1",
\(exp(-phi * d)\) for corr.structure = "exponential",
\(exp(-phi * d ^ 2)\) for corr.structure = "gaussian", and
rho when corr.structure = "CS". Note that d is the
Euclidean distance between locations i and j.
- rho
This is the maximum possible correlation between locations i
and j. For all i,j rho MUST be between -1 and 1.
- phi
A scalar value greater than 0 that determines the decay rate of
correlation. This argument is only utilized when corr.structure
%in% c("exponential", "gaussian").
- tau
A vector containing precision parameters. If of length 1, then
all precisions are assumed equal. Otherwise the length of tau should
equal the number of variables.
- alpha
A scalar value between 0 and 1 that defines the strength of
correlations. Note that when alpha = 0 the data are independent and
when alpha = 1, the joint distribution is the improper Intrinsic
Autoregression (IAR), which cannot be used to generate data. Note also that
while alpha does control dependence it is not interpretable as a
correlation.
- corr.min
Scalar value to specify the minimum non-zero correlation.
Any correlations below corr.min are set to 0. Especially for high
image resolution using this option can result in a sparser covariance
matrix, which may significantly speed up draws when using spam.
This option is preferred to using neighborhood and associated
arguments when the primary concern is to avoid very small correlations
and improve computation efficiency. Default is NULL, which places
no restrictions on the correlations.
- neighborhood
Defines the neighborhood within which marginal
correlations are non-zero. The default is "none", which allows
marginal correlations to extend indefinitely. neighborhood = "round"
defines a circular neighborhood about locations and
neighborhood = "rectangle" defines a rectangular neighborhood about
locations. Note that this argument differs from that in
precision_builder, in which neighborhood defines conditional non-zero
correlations.
- w, h
If neighborhood = "rectangle" then w and h are the number
of locations to the left/right and above/below a location i that define
its neighborhood. Any locations outside this neighborhood have have zero
correlation with location i.
- r
If neighborhood = "round", then if locations i,j are
separated by distance \(d \ge r\), the correlation between them is zero.
- print.R, print.S, print.Q
Logical. When TRUE, then print the
correlation, covariance, or precision matrix before taking the Cholesky
decomposition. If sigma = 1, then S = R.
- sigma
Specify the desired standard deviations; the default is 1, in
which case the Cholesky decomposition is of a correlation matrix. If
sigma != 1, then the Cholesky decomposition is of a covariance
Matrix.
If sigma is a vector then length(sigma) must be equal to the
total number of locations, i.e. \((n.row * n.col) by (n.row * n.col)\).
sigma can take any scalar value when specifying common standard
deviation.
- triangle
Determine whether to output an upper
(triangle = "upper") or lower (triangle = "lower") triangular
matrix.
- print.all
If print.all = TRUE, then prints each correlation
and allows you to check whether the correlations are as you intended. This
option is NOT recommended for large point lattices/images.
- round.d
If round.d = TRUE, then d is rounded to the nearest
whole number.
- return.cov, return.prec
Logical. When TRUE, also return the
covariance or precision matrix, respectively. This is recommended when
using spam to generate draws from the MVN.