pdInd: Construct pdInd object

In gmonette/spida2: Collection of tools developed for the Summer Programme in Data Analysis 2000-2012

Construct pdInd object

Description

This function is a constructor for the pdInd class used to represent a positive-definite random effects variance matrix with some specified patterns of zero covariances.

Usage

pdInd(
  value = numeric(0),
  form = NULL,
  nam = NULL,
  data = sys.parent(),
  cov = NULL
)

Arguments

value	an optional initialization value
form	an optional one-sided linear formula specifying the row/column names for the matrix represented by object.
nam	and optional vector of character strings specifying the row/column names for the matrix represented by object.
data	and optional data frame i which to evaluate the variables names in value and form. ...
cov	optional position in lower triangle of covariances that are estimated and, thus, possibly non-zero. The default is that the covariances in the first column are estimated and possibly non-zero.
object	an object inheriting from the class pdInd, representing a positive definite matrix with zero covariances except in the first row and column.

Details

Mixed models in which many predictors have random slopes often fail to converge in part because of the large number of parameters in the full covariance (G) matrix for random effects. One way of fitting a more parsimonious model that includes random slopes is to use pdDiag with zeros off the diagonal. However, this also forces zero covariances between random slopes and and the random intercept, resulting in a model that is not equivariant with respect to location transformations of the predictors with random slopes. The alternative remedy of omitting random slopes for some predictors can lead to biased estimates and incorrect standard errors of regression coefficients.

The default covariance pattern for pdInd produces a G matrix with zero covariances except in the first row and column. If the first random effect is the intercept, the resulting model assumes independence between random slopes without imposing minimality of variance over the possibly arbitrary origin. This imposition is the reason that having all covariances equal to zero results in a model that fails to be equivariant under location transformations.

The optional cov parameter can be used to allow selected non-zero covariance between random slopes. and biased eIt is often desirable to fit a parsimonious model with more than one variable with a random slope.

gmonette/spida2 documentation built on Aug. 20, 2023, 7:21 p.m.